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Accession Number

000000075

Author

Zeldovich BYa. Perelomov AM. Popov VS .

Title

Relaxation of a quantum oscillator.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.55, no.2, 1968, pp.589-606. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Relaxation of a quantum harmonic oscillator to the thermodynamic equilibrium state is considered on basis of a kinetic equation. The method of generating functions is employed for solving the equation. A number of exact solutions for various initial conditions is considered. For large quantum numbers it can be transformed to the Fokker-Planck equation. The Green function for the latter is determined. It is shown how the results obtained can be applied to the problem of statistics of photocounts. The given kinetic equation is extended to the case when an external classical force f(t) which arbitrarily depends on time acts on the oscillator. Methods for describing the evolution of the oscillator (characteristic functions, distributions of quasiprobabilities on the alpha plane) are briefly considered. The methods are valid in the presence of a force f(t). The equations of motion of the corresponding quantities are derived. The partial solutions for the density matrix rho are presented in a table. The so-called 'harmonic oscillator paradox' is discussed. (30 References).

Abstract Number

A69000081

Subject Headings

Quantum theory

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B]; Solutions of wave equations: bound state in quantum theory [A0365G].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

196900.

Accession Number

000001459

Author

Kotova LP. Perelomov AM. Popov VS .

Title

Quasiclassical approximation in ionization problems.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.54, no.4, April 1968, pp.1151-61. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The paper is dedicated to the development of the complex trajectory technique (description of the tunnel effect in the quasiclassical case with the help of trajectories corresponding to imaginary 'times'). The following problems are considered: ionization of a bound level in collisions with a charged particle; ionization of atoms by a constant electric field in the presence of a magnetic field; evaluation of adiabatic corrections to the probability for tunnelling through a potential barrier of arbitrary shape. (14 References).

Abstract Number

A69001580

Non-Thesaurus Subject Headings

ionisation of solids

Classification Codes

Diffusion in solids [A6630].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

196900.

Accession Number

000045029

Author

Belavin AA. Zel'dovich BYa. Perelomov AM. Popov VS .

Title

Relaxation of quantum systems with equidistant spectra.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.56, no.1, 1969, pp.264-74. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The structure of a kinetic equation which describes the relaxation of quantum systems with equidistant spectra is discussed. Examples of such systems are harmonic oscillators (with linear or nonlinear damping), a spin in a magnetic field, an ensemble of two-level atoms interacting with a radiation field (Dicke problem). It is demonstrated that equations of this type retain positive determinacy of the density matrix. A solution of the kinetic equation is obtained for the Dicke problem and an exact quantum expression is found for the shape of the radiation line. Interference line narrowing due to the equidistant nature of the spectrum is discussed. (18 References).

Abstract Number

A69029193

Subject Headings

Quantum theory
Relaxation

Classification Codes

Quantum theory; quantum mechanics [A0365].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

196900.

Accession Number

000045746

Author

Popov VS. Perelomov AM .

Title

Parametric excitation of a quantum oscillator.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.56, no.4, 1969, pp.1375-90. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

An exact solution is obtained for the problem of a quantum oscillator with a time dependent frequency omega (t) varying in an arbitrary manner. The quantum transition probabilities w/sub mn/ between the discrete spectrum states which are stationary for t to +or- infinity are calculated. The variation of the adiabatic invariant I=E/ omega under the action of a variable frequency omega (t) is calculated for an arbitrary initial state. (32 References).

Abstract Number

A69029957

Subject Headings

Quantum optics

Non-Thesaurus Subject Headings

quantum theory applications

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B]; Solutions of wave equations: bound state in quantum theory [A0365G]; Atomic lifetimes, absolute and relative intensities, transition probabilities [A3270F]; Photon interactions with atoms [A3280].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

196900.

Accession Number

000087817

Author

Zel'dovich BYa. Perelomov AM. Popov VS .

Title

Relaxation of quantum oscillator in the presence of an external force.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.57, no.1, 1969, pp.196-206. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A solution of the kinetic equation for a quantum oscillator with damping on which an external classical force f(t) is acting has been obtained. A number of exact solutions for various initial conditions are considered and the spectrum of the radiation emitted by the oscillator is determined. (11 References).

Abstract Number

A70000321; B70004106

Subject Headings

Lasers

Classification Codes

Lasing processes [A4255]; Laser systems and laser beam applications [A4260]; Lasers and masers [B4300].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000108504

Author

Popov VS. Perelomov AM .

Title

Parametric excitation of a quantum oscillator. II.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.57, no.5, Nov. 1969, pp.1684-90. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

For Pt.I see ibid. 56, 1375, 1969. An exact solution of the Schroedinger equation is obtained for a quantum oscillator with a varying frequency omega (t) which is acted upon by an external force f(t). The time dependence of omega (t) and f(t) may be arbitrary. The population distribution at the end of the processes is calculated for the case when at t to - infinity the oscillator was in the ground state mod 0, omega /sub -/). The quasi-energy spectrum for an oscillator with periodically varying parameters is determined. (15 References).

Abstract Number

A70016171; B70010223

Subject Headings

Laser theory
Lasers

Classification Codes

General theory of lasing action [A4255B]; Lasers [B4320].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000164658

Author

Gribov VN. Kobsarev IYu. Mur VD. Okun LB. Popov VS .

Institution

Acad. Scis., Moscow, USSR.

Title

On properties of amplitudes not satisfying the Pomeranchuk theorem conditions.

Source

Physics Letters B, vol.32b, no.2, 8 June 1970, pp.129-32. Netherlands.

Country of Publication

Netherlands.

Abstract

Properties of the scattering amplitudes as functions of the momentum transfer (t) and of the impact parameter ( rho ) are investigated in the case when the total cross sections for particle (p) and antiparticle (a) are symptotically (s to infinity ) constant and are not equal to each other. It is shown that if the equality Imf/sup p/(s,t)=Imf/sup a/(s,t) is violated, the weaker integral equality integral ImF/sup p/(s,t)s/sup -2/ds approximately= integral ImF/sup a/(s,t)s/sup -2/ds, t<0 must hold. The equality provides for the absence of singularities at t=0 in the amplitude. It follows from this equality that t-(and s-) dependence of ImF/sup p/ and ImF/sup a/ must be different.

Abstract Number

A70052478

Non-Thesaurus Subject Headings

hadron scattering

Classification Codes

Complex angular momentum plane; Regge poles and cuts (Reggeons) [A1240M]; Specific reactions and phenomenology [A1300].

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000165034

Author

Popov VS .

Institution

USSR Acad. Sci., USSR.

Title

Electron energy levels at Z>137.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.11, no.5, 5 March 1970, pp.254-6. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.11, no.5, 5 March 1970, pp.162-5. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

As is well known, the solution of the Dirac equation in the field of a point charge Ze is mathematically correct only if Z<137. The energy of the lower level of the discrete spectrum (n=1, j=1/2) is epsilon /sub 0/= square root (1-a/sup 2/) (a=Ze/sup 2/=Z/137, h(cross)=c=m=1). (1) epsilon /sub 0/ reaches zero when alpha =1, and the continuation of formula (1) to the region alpha >1 leads to imaginary values of epsilon /sub 0/. When alpha >1 it is therefore necessary to take into account the finite dimensions of the nucleus. A critical charge is reached which determines the 'electrodynamic boundary' of the periodic system of elements and is also the pair production threshold.

Abstract Number

A70052865

Subject Headings

Atomic structure

Classification Codes

Specific calculations and results for atoms and molecules [A3120].

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000190846

Author

Popov VS .

Title

'Fall down to the center' at Z>137 and critical nuclear charge.

Source

Yadernaya Fizika, vol.12, no.2, 1970, pp.429-47. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Solution is considered of the Dirac equation for electron in the Coulomb field with Z>137, when for the point nuclear charge an 'incidence to the center' occurs. Account of a finite size of the nucleus resulting in regularization of the Coulomb potential at r to 0 allows one to deal with charges Z>137 up to a 'critical' value Z/sub cr/, such that the ground state energy reaches the boundary of the lower continuum, E=-mc/sup 2/. An equation for Z/sub cr/ is obtained and dependence of Z/sub cr/ on the nuclear radius R and on the charge distribution inside the nucleus is studied. Mean radius of the ground state is calculated and it is shown that at Z to Z/sub cr/ the electron state remains localized, though Sigma =E/mc/sup 2/ to -1 and lambda = square root (1- epsilon /sup 2/) to 0. Relativistic Coulomb problem is also discussed for particles with spins 0 and 1. (23 References).

Abstract Number

A70070329

Subject Headings

Nucleus

Classification Codes

Nuclear structure [A2100].

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000193948

Author

Popov VS .

Title

Positron production in a coulomb field with Z>137.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.59, no.3, 1970, pp.965-84. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Spontaneous production of positrons in a strong coulomb field with Z>Z/sub cr/ is considered, where Z/sub cr/ is the critical value of the nuclear charge (for Z=Z/sub cr/ the energy of /sup 1/S/sub 1/2/ ground state reaches the limit of the lower continuum epsilon =-mc/sup 2/; the value of Z/sub cr/ always exceeds 137 and depends on the cut-off radius R and, to a less degree, on the nature of the electric charge distribution over the nuclear volume). It is shown that at the threshold (i.e. for (Z-Z/sub cr/)<

Abstract Number

A70073852

Subject Headings

Beta-decay theory
Positrons

Classification Codes

beta decay; electron and muon capture [A2340].

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197000.

Accession Number

000222351

Author

Gribov VN. Kobsarev IYu. Mur VD. Okun LB. Popov VS .

Title

On properties of the amplitudes not satisfying the conditions of the Pomeranchuk theorem.

Source

Yadernaya Fizika, vol.12, no.6, pp.1271-85. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Properties of the scattering amplitudes as functions of the momentum transfer t and of the impact parameter rho are considered in case when the total cross sections for a particle and the antiparticle are asymptotically (s to infinity ) constant and not equal. A detailed consideration is performed for a so called scale-invariant case when the partial amplitudes ( up to a common factor) depend only on one variable x= rho /1n s. (24 References).

Abstract Number

A71011315

Non-Thesaurus Subject Headings

hadron scattering

Classification Codes

Complex angular momentum plane; Regge poles and cuts (Reggeons) [A1240M]; Specific reactions and phenomenology [A1300].

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000266107

Author

Popov VS .

Title

On the properties of a discrete spectrum for values of Z close to 137.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.60, no.4, 1971, pp.1228-44. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The nature of the discrete spectrum for an electron in the Coulomb field of a bare nucleus of charge close to 137 is investigated. In this region of Z values the level spectrum significantly depends on cut-off of the Coulomb potential at small distances. An equation is derived for the level energies epsilon /sub n/. In the logarithmic approximation (i.e. on the condition that L=In (h(cross)/mcR)>>1, where m is the electron mass and R the nuclear radius) the equation can be solved explicitly and the simple expressions can be obtained for epsilon /sub n/. (15 References).

Abstract Number

A71039501

Non-Thesaurus Subject Headings

atomic spectra

Key Phrase Identifiers

discrete spectrum; bare nucleus; Z values; coulomb potential; atomic spectrum.

Classification Codes

Atomic spectra grouped by wavelength ranges [A3220].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000287154

Author

Popov VS .

Institution

Acad. Sci., USSR.

Title

Production of e/sup +/e/sup -/ pairs in an alternating external field.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.13, no.5, 5 March 1971, pp.261-3. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.13, no.5, 5 March 1971, pp.185-7. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

Interaction of an electromagnetic field with a vacuum of charged particles leads to the appearance of nonlinear additions to the Lagrangian L of the electromagnetic field. In particular, there appears an imaginary part Im L, which determines the probability w of pair production by the external field. In the case of fields E and H constant in time (but alternating in space) it is possible to solve this problem exactly. The author using Dirac's theory in a quasiclassical approach obtains probabilities for pair production in time-varying fields E(t).

Abstract Number

A71054636

Subject Headings

Electron pair production

Key Phrase Identifiers

electron pairs; production; alternating external field; vacuum of charged particles; Dirac's theory; tunnelling; quasiclassical approach; time varying fields; electromagnetic field interaction; electron velocity; pulse fields.

Classification Codes

Specific reactions and phenomenology [A1300]; Electrons and positrons [A1460C].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000308648

Author

Popov VS .

Title

On the problem of the critical charge of nucleus.

Source

Yadernaya Fizika, vol.14, no.2, 1971, pp.458-68. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The critical charge Z/sub cr/ is by definition the value of the charge of nucleus (or of the system of nuclei) at which the energy of the ground state of the discrete spectrum decreases down to the boundary of the lower continuum E=-mc/sup 2/. To calculate Z/sub cr/, the method of the effective potential is developed and the variational principle is formulated. With their help one can obtain Z/sub cr/ for the system of two colliding nuclei. (13 References).

Abstract Number

A71067794

Subject Headings

Nuclear size

Key Phrase Identifiers

critical charge; nucleus; effective potential; variational principle.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000324461

Author

Popov VS .

Title

Pair production in a varying external field (quasiclassical approximation).

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.61, no.4, 1971, pp.1334-51. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A quasiclassical method is developed for calculating the probability for pair production in a varying electromagnetic field. The conditions of applicability of the method are: E<

Abstract Number

A71078231

Subject Headings

Electron pair production

Key Phrase Identifiers

pair production; varying electromagnetic field; quasiclassical approximation; probability calculation.

Classification Codes

Specific reactions and phenomenology [A1300]; Electrons and positrons [A1460C].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000327282

Author

Migdal AB. Perelomov AM. Popov VS .

Title

Analytical properties of wave functions at low energy.

Source

Yadernaya Fizika, vol.14, no.4, 1971, pp.874-85. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Analytical properties of the continuum wave functions chi /sub k/(r) are investigated for the case when there is a level with energy near zero (the level may be real, virtual, or quasistationary). It is shown that at small distances, r<

Abstract Number

A71081282

Subject Headings

Wave equations

Key Phrase Identifiers

analytical properties of wave functions; low energy; resonance width; scattering amplitude.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Quantum theory; quantum mechanics [A0365].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000327926

Author

Popov VS. Rozhdestvenskaya TI .

Title

Critical charge in collisions of nuclei.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.14, no.4, 20 Aug. 1971, pp.267-70. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.14, no.4, 20 Aug. 1971, pp.177-80. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

In order to verify the theory of supercritical atoms a calculation is made for the collision of the two bare uranium nuclei and the probability of positron emission as a function of internuclear distance.

Abstract Number

A71082167

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

bare U nuclei; critical charge; collisions; supercritical atoms; probability; positron emission; internuclear distance.

Classification Codes

Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197100.

Accession Number

000339242

Author

Perelomov AM. Popov VS .

Title

Perturbation of a continuous spectrum by a near-lying level.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.61, no.5, 1971, pp.1743-55. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The nature of the perturbation of continuous spectrum functions chi /sub k/(r) and the analytic properties of the S matrix in the region k to 0 in the presence of a level close to zero are considered. Formulas are obtained which express parameters of the low energy expansion of the S matrix in terms of the wave function chi /sub 0/(r) at the moment of formation of the level. Exact solutions of the problem are obtained for a number of potentials. (16 References).

Abstract Number

A72005146

Subject Headings

Quantum theory
S-matrix theory

Key Phrase Identifiers

S matrix; near lying level; perturbation; continuous spectrum functions; analytic properties; low energy expansion.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Quantum theory; quantum mechanics [A0365]; S-matrix theory [A1120]; Nuclear level density and structure [A2110M].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197200.

Accession Number

000402002

Author

Popov VS .

Title

Method for a calculation of the nuclear critical charge.

Source

Yadernaya Fizika, vol.15, no.5, May 1972, pp.1069-81. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

A simple formula is given for the nuclear critical charge. The formula is asymptotically exact at the condition R<

Abstract Number

A72046105

Subject Headings

Nuclear size

Key Phrase Identifiers

formula; nuclear critical charge; calculation method.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F].

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197200.

Accession Number

000413504

Author

Marinov MS. Popov VS .

Title

Pair production in electromagnetic field (case of arbitrary spin).

Source

Yadernaya Fizika, vol.15, no.6, 1972, pp.1271-85. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The quasiclassical method of 'imaginary time' is generalized for the case of a particle with spin. The production probability of pairs in strong electromagnetic field for particles with an arbitrary spin and magnetic moment is calculated. (26 References).

Abstract Number

A72052543

Subject Headings

Elementary particle interactions

Key Phrase Identifiers

imaginary time method; pair production; electromagnetic field; arbitrary spin.

Classification Codes

Specific theories and interaction models; particle systematics [A1200]; Specific reactions and phenomenology [A1300].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197200. Revised: 19921204.

Accession Number

000428942

Author

Migdal AB. Perelomov AM. Popov VS .

Title

Notes on analytic properties of wave functions at very low energy.

Source

Yadernaya Fizika, vol.16, no.1, 1972, pp.222-4. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Proposes some additions and refinements to results obtained in studies of the behaviour of continuous spectral wave functions in the case where there is an almost-zero energy level in the system, and in the so-called 'narrow-pit' example. In regard to wave function factorization, a refinement is introduced for barrier permeability. Also an interpretation of the 'narrow pit' leads to expansion of the region of applicability of factorization. (4 References).

Abstract Number

A72062999

Subject Headings

Wave equations

Key Phrase Identifiers

very low energy; wave function factorization; barrier permeability; spectral wave functions; almost zero energy level; narrow pit example.

Classification Codes

Quantum theory; quantum mechanics [A0365].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197200.

Accession Number

000437795

Author

Zel'dovich YaB. Popov VS .

Title

Electronic structure of superheavy atoms.

Source

Uspekhi Fizicheskikh Nauk, USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Uspekhi (USA), vol.14, no.6, May-June 1972, pp.673-94. CODEN: SOPUAP. ISSN: 0038-5670.

Abstract

The authors describe the status of the problem of the electron structure of superheavy atoms with nuclear charge Z>Z/sub c/; here Z/sub c/ approximately=170 is the critical value of the nuclear charge, at which the energy of the ground state of the 1S/sub 1/2/ electron reaches the limit of the lower continuum of the solutions of the Dirac equation ( epsilon =-m/sub e/c/sup 2/). They discuss the dependence of Z/sub c/ on the nuclear radius R and on the character of the distribution of the electric charge inside the nucleus, and also the form of the wave functions at Z close to Z/sub c/. Owing to the Coulomb barrier, the state of the electron remains localized at Z>Z/sub c/, in spite of the fact that its energy approaches the continuum. An analysis of the polarization of the vacuum in a strong Coulomb field shows that a bare nucleus with supercritical charge Z>Z/sub c/ produces spontaneously two positrons and, in addition a charge density with a total of two units of negative charge in the vacuum. (86 References).

Abstract Number

A72067385

Subject Headings

Atomic structure
Reviews

Key Phrase Identifiers

polarization of vacuum in strong Coulomb field; electronic structure; superheavy atoms; Dirac equation; nuclear radius; Coulomb barrier.

Classification Codes

Specific calculations and results for atoms and molecules [A3120].

Treatment

Theoretical or mathematical.

CODEN

UFNAAG

Language

English.

ISSN

0042-1294.

Publication Type

Journal Paper.

Update Code

197200.

Accession Number

000460158

Author

Popov VS. Marinov MS .

Title

e/sup +/e/sup -/-pair production in variable electric field.

Source

Yadernaya Fizika, vol.16, no.4, 1972, pp.809-22. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The calculation of probability w of production of fermion pairs in vacuum under the influence of variable electric field E(t) comes to a solution of the problem on parametric excitation of quantum oscillator. The cases, when external field E(t) preserves constant direction in space or is situated in a definite plane, are treated in detail. By the 'imaginary time' method a closed formula has been obtained for probability w in the case of the field with elliptical polarization. (26 References).

Abstract Number

A72082632

Subject Headings

Electron pair production
Fermions
Quantum electrodynamics

Key Phrase Identifiers

variable electric field; fermion pairs; parametric excitation; quantum oscillator; elliptical polarization; electron pair production.

Classification Codes

Quantum field theory [A1110]; Specific reactions and phenomenology [A1300]; Weak and electromagnetic interactions of leptons [A1310]; Neutrino interactions [A1315]; Photon and charged-lepton interactions with hadrons [A1360]; Other topics in specific reactions and phenomenology of elementary particles [A1390]; Electrons and positrons [A1460C].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197200.

Accession Number

000483806

Author

Popov VS .

Title

Critical charge in the two-center problem.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.16, no.6, 20 Sept. 1972, pp.355-8. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.16, no.6, 20 Sept. 1972, pp.251-4. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract Number

A73014114

Subject Headings

Nuclear charge

Key Phrase Identifiers

critical charge; two centre problem.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000501135

Author

Popov VS .

Institution

Inst. Theoretical & Experimental Phys., USSR.

Title

Pair production in a variable and homogeneous electric field as an oscillator problem.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.62, no.4, April 1972, pp.1248-62. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.35, no.4, Oct. 1972, pp.659-66. CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The calculation of the probability w of pair production in a strong electric field E(t) which is homogeneous in space reduces to the problem of the parametric excitation of a quantum oscillator (or, what is equivalent, to the calculation of the reflection coefficient for a plane wave incident on a one-dimensional potential barrier). Because of this relation, the calculation of the pair-production probability does not require the determination of the exact solutions of the relativistic wave equations and the Green's function. In the particular case when E(t)=E(cosh omega t)/sup -2/ the probability w coincides with the coefficient of reflection from the Eckart potential. The relation between the exact formulas for w and the quasiclassical approximation (the 'imaginary time' method) is investigated in detail, and the limits of applicability of the quasiclassical approximation are indicated. (25 References).

Abstract Number

A73023074

Subject Headings

Electron pair production

Key Phrase Identifiers

oscillator problem; probability; pair production; strong electric field; parametric excitation; quantum oscillator; reflection coefficient; plane wave; coefficient of reflection; Eckart potential; exact formulas; quasiclassical approximation; variable homogeneous electric field; one dimensional potential barrier.

Classification Codes

Weak and electromagnetic interactions of leptons [A1310]; Neutrino interactions [A1315]; Photon and charged-lepton interactions with hadrons [A1360]; Other topics in specific reactions and phenomenology of elementary particles [A1390].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000510722

Author

Popov VS .

Title

Critical charge for colliding nuclei.

Source

Yadernaya Fizika, vol.17, no.3, 1973, pp.621-33. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Using the approximation (Z/sub i/+Z/sub 2/-Z/sub c/)<

Abstract Number

A73029415

Subject Headings

Nuclear charge
Nucleon-nucleon interactions
Relativistic scattering theory

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

critical charge; colliding nuclei; ground state energy; quasimolecule; spontaneous production; positrons.

Classification Codes

Relativistic scattering theory [A1180]; Nuclear shape, charge, radius, form factors and structure functions [A2110F]; Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000522642

Author

Gershtein SS. Popov VS .

Institution

Inst. High-Energy Phys., Serpukhov, USSR.

Title

Spontaneous production of positrons in collisions of heavy nuclei.

Source

Lettere Al Nuovo Cimento, vol.6, ser.2, no.14, 7 April 1973, pp.593-6. Italy.

Country of Publication

Italy.

Abstract

The authors show that spontaneous production of positrons takes place even when only one of the nuclei is bare (and the second one has an ordinary electron shell structure). This fact provides an opportunity to carry out the experiment with a heavy target. (14 References).

Abstract Number

A73038168

Subject Headings

Positrons

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

spontaneous production of positrons; collisions of heavy nuclei; heavy target; bare nuclei.

Classification Codes

Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical. Experimental.

CODEN

LNUCAE

Language

English.

ISSN

0024-1318.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000547139

Author

Marinov MS. Popov VS .

Title

Effect of screening on the critical charge of a nucleus.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.17, no.9, 5 May 1973, pp.511-4. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.17, no.9, 5 May 1973, pp.368-71. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

In view of the difficulty of calculating Z/sub c/ in the two-center problem the authors consider, in order to determine the scale of the screening correction, a model problem with a spherical superheavy nucleus. (6 References).

Abstract Number

A73054374

Subject Headings

Nuclear charge
Superheavy nuclei

Key Phrase Identifiers

critical charge; nucleus; scale; screening correction; spherical superheavy nucleus; screening effects; two centre problem.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000575341

Author

Popov VS. Mur VD .

Title

Quasistationary levels in lower continuum.

Source

Yadernaya Fizika, vol.18, no.3, 1973, pp.684-98. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Quasistationary levels in the lower continuum of solutions of the Dirac equation are considered. Depth of the potential V(r) is assumed to be sufficient ( mod V mod >2mc/sup 2/) for the bound states to cross the boundary of the lower continuum epsilon =-mc/sup 2/ at V=V/sub c/. In so doing the bound state becomes a quasistationary state whose width gamma determines probability of spontaneous positron production in the static field. Behaviour of gamma at the threshold V to V/sub c/ and at V>>V/sub c/ is investigated. It is shown that gamma is limited even at mod epsilon mod >>mc/sup 2/, i.e. for a level sunken deeply into the lower continuum. For the Coulomb field gamma /mc/sup 2/ approximately exp(-2 pi Z alpha )<<1. This result shows that the description of the K shell of a supercritical atom with the nuclear charge Z>Z/sub c/, (see abstr. A67385 of 1972), is valid not only at epsilon to -mc/sup 2/, but also for deep levels. The angular momentum (j) dependence of gamma and analytical properties of the S matrix near V=V/sub c/ are studied in detail. In particular, the case of the p/sub 1/2/ level, having some peculiar properties, is considered, as well as the s levels of a scalar particle. (20 References).

Abstract Number

A73074323

Subject Headings

Atomic structure
Dirac equation

Key Phrase Identifiers

quasistationary levels; lower continuum; Dirac equation; spontaneous positron production.

Classification Codes

Bound and unstable states; Bethe-Salpeter equations [A1110S]; Specific calculations and results for atoms and molecules [A3120].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000575622

Author

Popov VS .

Institution

Inst. Theoretical & Experimental Phys., Acad. Sci., USSR.

Title

Spontaneous positron production by the Coulomb field of a heavy nucleus.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.18, no.1, 5 July 1973, pp.53-8. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.18, no.1, 5 July 1973, pp.29-31. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The spontaneous production of positrons in a Coulomb field with Z>Z/sub c/ (where Z/sub c/ approximately=170 is the critical charge of the nucleus) is of interest as an example of e/sup +/e/sup -/ pair production via an unusual static mechanism. The most realistic way of searching for this phenomenon is in collisions of heavy nuclei with Z/sub 1/+Z/sub 2/>Z/sub c/, for example uranium or californium nuclei. It is not necessary that both colliding nuclei be 'bare' (i.e., have no electron shells). When a beam of bare nuclei Z/sub 1/ is incident on an ordinary heavy target Z/sub 2/, vacant places are produced in the K shell of the combined atom if Z/sub 1/>Z/sub 2/. The cross section sigma for the production of e/sup +/ has in this case practically the same value as for bare nuclei. (11 References).

Abstract Number

A73074604

Subject Headings

Electron pair production
Positrons

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

spontaneous positron production; coulomb field; heavy nucleus.

Classification Codes

Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197300.

Accession Number

000598692

Author

Popov VS .

Institution

Inst. Theoretical & Experimental Phys., USSR.

Title

The 'imaginary-time' method in problems concerning the ionisation of atoms and pair production.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.63, no.5, Nov. 1972, pp.1586-98. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.36, no.5, May 1973, pp.840-6. CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The 'imaginary-time' method was originally proposed in order to solve the problem of the ionisation of non-relativistic bound systems of atoms and ions in the field of an intense light wave. The method is a generalisation of the quasiclassical WKB approximation to the case of time-dependent fields. It describes the tunnelling transition of an electron from a bound state to the continuum by using the classical equations of motion, but with an imaginary time. Such an approach has also been found useful in connection with investigations of ionisation in Coulomb collisions. It has also been established that the method is successful in calculating the probability for pair production from vacuum due to an external field, although the relation between these two problems has remained nuclear. It is shown that the ionisation of atoms and the production of e/sup +/e/sup -/ pairs from vacuum correspond to two limiting cases of the general relativistic problem of the ionisation of a level with arbitrary energy E due to the influence of an internal electric field. Advantages associated with such a generalisation are discussed. In particular, by going to the non-relativistic limit a closed expression can be obtained for the atomic ionisation probability omega in an arbitrary electric field-a new result. The findings are of interest in laser technology. (18 References).

Abstract Number

A74012494

Subject Headings

Electron pair production

Non-Thesaurus Subject Headings

ionisation of atoms

Key Phrase Identifiers

pair production; quasiclassical WKB approximation; tunnelling transition; classical equations of motion; Coulomb collisions; general relativistic problem; imaginary time method; atomic ionisation; time dependent fields; electric field effect; intense light field effect; e/sup +/e/sup -/ pairs; from vacuum.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F]; Other topics in atomic spectra and interactions with photons [A3290].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000607225

Author

Popov VS .

Title

Spontaneous production of positrons at collisions of heavy nuclei (production cross section and the energy spectrum of e/sup +/).

Source

Yadernaya Fizika, vol.19, no.1, 1974, pp.155-68. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The analytical solution of the two-centre Coulomb problem for the Dirac equation is obtained in the approximation (Z/sub 1/+Z/sub 2/-Z/sub c/)/Z/sub c/<<1. Using the solution, the total cross section sigma of positron production in the quasistatic field of the colliding nuclei, the cross section d sigma /d Omega corresponding to the scattering of the nucleus under a fixed angle theta , and the energy spectrum of the produced positrons are calculated. Dependence of these quantities on the incident nucleus energy E is considered. This enables one to suggest the optimal energy region for the experiment. The similar problem of e/sup +/e/sup -/-pair production from vacuum in a variable electric field E(t) is discussed briefly. (29 References).

Abstract Number

A74015912

Subject Headings

Dirac equation
Electron pair production
Positrons

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

spontaneous production of positrons; cross section; energy spectrum; Dirac equation; heavy nuclei collisions; two centre Coulomb problem.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F]; Electrons and positrons [A1460C]; Heavy ion induced reactions and scattering [A2570].

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000609643

Author

Popov VS .

Institution

Inst. Theoretical & Experimental Phys., USSR.

Title

Resonant pair production in a strong electric field.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.18, no.7, 5 Oct. 1973, pp.435-9. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.18, no.7, 5 Oct. 1973, pp.255-8. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

Pair production anomalies connected with the periodicity of the field are investigated. An analogy is found between the problems of fermion pair production from vacuum and resonant excitation of atomic levels in a strong optical wave field. The analogy no longer holds if excitation of multilevel atomic systems is considered. (6 References).

Abstract Number

A74019209

Subject Headings

Electron pair production

Non-Thesaurus Subject Headings

atomic excitation

Key Phrase Identifiers

strong electric field; fermion pair production; resonant excitation; atomic levels; strong optical wave field; multilevel atomic systems; resonant pair production; field periodicity.

Classification Codes

Weak and electromagnetic interactions of leptons [A1310]; Neutrino interactions [A1315]; Photon and charged-lepton interactions with hadrons [A1360]; Other topics in specific reactions and phenomenology of elementary particles [A1390].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000653275

Author

Popov VS .

Title

Method of imaginary time for periodical fields.

Source

Yadernaya Fizika, vol.19, no.5, 1974, pp.1140-56. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The method of imaginary times is formulated for periodical fields, T(t+T)=F(t), where F(t) is an external electric field satisfying the conditions necessary for the quasiclassical approach to be consistent. Ionization of atoms by a strong light wave and pair creation from vacuum are considered as applications. Explicit expressions for the pair production probability w, applicable for any periodical field, are obtained in case of the linear polarization of the field F(t). The probability w has different forms for fermions and for bosons. Effect of the statistics of the created particles is most essential at p/sub ///=0, i.e. for particles produced in a direction transversal to the electric field. In this case boson pairs are created only if an even number of quanta is absorbed, n=2K, and fermion pairs are created only if an odd number is absorbed, n=2K+1. Properties of the exact solutions of the Klein-Gordan and Dirac's equations with a periodical field and the relation to the quasiclassical approach are discussed. Pair creation by an electric field with elliptic and circular polarizations is also considered by means of the method of imaginary times. (23 References).

Abstract Number

A74047448

Subject Headings

Bosons
Dirac equation
Fermions
Photoionisation
Quantum electrodynamics

Non-Thesaurus Subject Headings

ionisation of atoms

Key Phrase Identifiers

method of imaginary time; periodical fields; ionization of atoms; strong light wave; pair creation; fermions; bosons; Klein Gordan equation; Dirac equation.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F]; Atomic photoionization, photodetachment, photoelectron spectra [A3280F].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000656832

Author

Perelomov AM. Popov VS .

Title

Variational principle for critical charge.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.14, no.1, Jan. 1973, pp.18-26. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.14, no.1, Jan. 1973, pp.12-18. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

In order to find the critical charge Z/sub V/, the effective potential method is developed and a variational principle is formulated. (18 References).

Abstract Number

A74051696

Subject Headings

Variational techniques

Non-Thesaurus Subject Headings

theory of quantum electrodynamics

Key Phrase Identifiers

variational principle; critical charge; effective potential method.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000676438

Author

Marinov MS. Popov VS. Stolin VL .

Title

Variational calculation of the critical distance between nuclei.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.19, no.1, 5 Jan. 1974, pp.76-80. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

A variational calculation is made of the critical distance R/sub c/ between colliding nuclei, at which the fundamental term of the quasimolecule (Z,Z,e) drops to the limit of the lower continuum and spontaneous positron generation begins. (9 References).

Abstract Number

A74063209

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

variational calculation; critical distance between nuclei; spontaneous position generation; lower continuum limit.

Classification Codes

Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

ZFPRAU

Language

Russian.

Publication Type

Journal Paper.

Update Code

197400.

Accession Number

000711765

Author

Marinov MS. Popov VS .

Title

A variant of the Wentzel-Kramers-Brillouin method and calculation of the critical nuclear charge.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.67, no.4, Oct. 1974, pp.1250-62. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A modification of the WKB method is proposed which consists in exclusion of centrifugal energy from the momentum p(r) and in a corresponding alteration of the constant gamma in the quantization condition gamma = gamma (l,a), where l is the orbital moment and V(r) approximately r/sup - alpha / for r to 0. The accuracy of the approximation and application of the WKB method for a strong coulomb field with a charge Z>137 are considered in detail. (20 References).

Abstract Number

A75005504

Subject Headings

Nuclear charge
Quantum theory

Non-Thesaurus Subject Headings

nuclear theory

Key Phrase Identifiers

Wentzel Kramers Brillouin method; critical nuclear charge; WKB method.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F]; Hartree-Fock and random-phase approximations in nuclei [A2160J].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000723791

Author

Marinov MS. Popov VS .

Institution

Inst. Theoretical & Experimental Phys., USSR.

Title

On the production of e/sup +/e/sup -/ pairs from the vacuum under the influence of an electric field.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.17, no.1, Oct. 1973, pp.34-46. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.17, no.1, Oct. 1973, pp.967-76. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

A study is made of the problem of pair production of particles with spin 1/2 in an external homogeneous electric field E(t). The Heisenberg equations of motion are found for the operators of creation and annihilation, a solution for which has the form of a linear canonical transformation. A system of differential equations that determine the coefficients U(t) and V(t) of this transformation are obtained. The probabilities of pair creation are expressed in terms of the eigenvalues of the matrix VV/sup +/. The case of particles with anomalous magnetic moment is also considered. (21 References).

Abstract Number

A75012055

Subject Headings

Electric field effects
Electron pair production

Non-Thesaurus Subject Headings

theory of quantum electrodynamics

Key Phrase Identifiers

creation operators; annihilation operators; QED; production of e/sup +/e/sup -/ pairs; vacuum; electric field; Heisenberg equations of motion; linear canonical transformation; differential equations; eigenvalues; anomalous magnetic moment.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000730409

Author

Marinov MS. Popov VS .

Title

On energy spectrum of positrons produced in nuclear interactions at R

Source

Yadernaya Fizika, vol.20, no.6, 1974, pp.1223-8. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The energy spectrum positrons produced in the collision of heavy nuclei with charges Z/sub 1/+Z/sub 2/>Z/sub c/ is calculated when the ground level of the discrete spectrum dives into the lower continuum. The spectrum positron has a sharp peak near the upper boundary T=T/sub max/. (11 References).

Abstract Number

A75017730

Subject Headings

Beta-decay

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

nuclear interactions.

Classification Codes

Nuclear matrix elements and nuclear structure inferred from beta decay [A2340H]; Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000751159

Author

Marinov MS. Popov VS .

Title

Critical distance in heavy ion collisions.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.62, no.2, Feb. 1975, pp.421-31. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A variational calculation is carried out for the critical distance R/sub cr/ between colliding ions. Values of R/sub cr/ are calculated in the 90

Abstract Number

A75032271

Non-Thesaurus Subject Headings

atomic collision processes
nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

heavy nuclei Coulomb collisions; spontaneous positron production; critical distance; heavy ion collisions; variational calculation.

Classification Codes

Nuclear reaction and scattering models and methods [A2410]; Other topics in nuclear reactions and scattering, general [A2490]; Other topics in nuclear reactions and scattering: specific reactions [A2590]; Elastic scattering of atoms and molecules [A3440]; Inelastic scattering of atoms and molecules [A3450].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000787103

Author

Mur VD. Popov VS .

Title

Pole model of the scattering amplitude with a highest possible growth of the cross section.

Source

Yadernaya Fizika, vol.21, no.4, 1975, pp.868-77. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

According to the known Froissart inequality, the total cross section sigma /sub t/ at s to infinity cannot grow more rapidly than ln/sup 2/ s. The pole models of partial amplitudes of the cross-channel leading to the highest possible growth sigma /sub t/ approximately ln/sup 2/ s and consistent with the unitarity condition in the s channel are considered. It is shown that in the region of the parameter rho approximately ln s' an automodel regime is being settled, i.e. the partial amplitudes of the s channel asymptotically depend only upon the ratio rho /ln s. General features of the amplitudes as well as the cases sigma /sub t/ approximately ln s are briefly discussed. (17 References).

Abstract Number

A75053427

Subject Headings

Complex angular momentum plane

Non-Thesaurus Subject Headings

elementary particle inclusive reactions

Key Phrase Identifiers

scattering amplitude; Froissart inequality; pole models of partial amplitudes; unitarity condition; automodel regime.

Classification Codes

Complex angular momentum plane; Regge poles and cuts (Reggeons) [A1240M]; Hadron induced inclusive reactions, including total cross sections, (energy > 10 GeV) [A1385K].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000830547

Author

Popov VS .

Title

Spontaneous positron production in collisions between heavy nuclei.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.65, no.1, July 1973, pp.35-53. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

It is shown that in collisions between a completely stripped (bare) nucleus (Z/sub 2/) and the atoms of a heavy target (Z/sub 1/), vacancies are formed in the K-shell of the united atom, providing Z/sub 2/>or=Z/sub 1/. Therefore such collisions, as well as those between two bare nuclei, will result in spontaneous production of electron-positron pairs in a static Coulomb field of the colliding nuclei if the nuclei approach each other at a distance R

Abstract Number

A75080228

Subject Headings

Electron pair production
Positrons

Non-Thesaurus Subject Headings

nuclear reactions and scattering due to nuclei of z>2

Key Phrase Identifiers

spontaneous production of positrons; positron energy spectrum; heavy nuclei collisions.

Classification Codes

Electrons and positrons [A1460C]; Heavy ion induced reactions and scattering [A2570].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197500.

Accession Number

000840190

Author

Marinov MS. Popov VS .

Institution

Inst. for Theoretical & Experimental Phys., Moscow, USSR.

Title

A modification of the Bohr-Sommerfeld quantization condition.

Source

Journal of Physics A-Mathematical & General, vol.8, no.10, Oct. 1975, pp.1575-85. UK.

Country of Publication

UK.

Abstract

The Bohr-Sommerfeld quasiclassical quantization condition for a central potential is modified in such a way that the constant gamma becomes dependent on the angular momentum l and on the potential behaviour at small distances. This form of the quantization condition is especially simple in the case l=0. When applied to some particular potentials, taken as examples, the present approximation provides more accurate values of the level energies than the conventional form of the quantization condition. Application of the quasiclassical approach to singular potentials with 'collapse' and to the superstrong Coulomb field induced by a charge Z>137 is also considered. (23 References).

Abstract Number

A76000474

Subject Headings

Quantum theory

Key Phrase Identifiers

central potential; Bohr Sommerfeld quantisation.

Classification Codes

Quantum theory; quantum mechanics [A0365].

Treatment

Theoretical or mathematical.

CODEN

JPHAC5

Language

English.

ISSN

0305-4470.

Publication Type

Journal Paper.

Update Code

197600.

Accession Number

000840514

Author

Marinov MS. Popov VS .

Title

Phase shift technique for the Dirac equation and the calculation of the critical nuclear charge.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.65, no.6, Dec. 1973, pp.2141-54. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A simple method for solving the Dirac and Schroedinger equations with an arbitrary potential V(r) is developed which is convenient for qualitative analysis of the problem and for numerical calculations. The idea of the method is that the equation under consideration is replaced by first order nonlinear equation for the phase function theta (r). Application of the method to the problem of appearance of a bound level and its application for calculation of the critical charge Z/sub c/ are considered. The effect of screening of the nuclear Coulomb field by the electron shell on Z/sub c/ is estimated. Variational calculations of Z/sub c/ for a system of colliding nuclei (relativistic two-center problem) are performed. (34 References).

Abstract Number

A76000920

Subject Headings

Dirac equation
Nuclear charge
Schrodinger equation

Key Phrase Identifiers

Dirac equation; critical nuclear charge; system of colliding nuclei; phase shift technique; Schrodinger equation; screening of nuclear Coulomb field.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197600.

Accession Number

000848664

Author

Marinov MS. Popov VS. Stolin VL .

Institution

Inst. for Theoretical & Experimental Phys., Moscow, USSR.

Title

Variational approach to the relativistic two-center problem: Critical internuclear distance.

Source

Journal of Computational Physics, vol.19, no.3, Nov. 1975, pp.241-56. USA.

Country of Publication

USA.

Abstract

As shown recently, if the distance between two heavy nuclei becomes less than its critical value, R/sub cr/, their electric potential is strong enough to create electron-positron pairs from the vacuum. This process may occur when the ground level of the quasimolecule (Z,Z,e) is lower than -m/sub e/c/sup 2/. In order to find R/sub cr/ the Dirac equation with two Coulomb centres is considered. By means of a proper choice of coordinates and using the variational principle the problem is reduced to a set of ordinary linear differential equations with singular coefficients. To solve the boundary problem the Riccati equation for the logarithmic derivative matrix was considered. The computations are carried out and R/sub cr/ is found as a function of the nuclear charges. By virtue of the variational principle the obtained quantity is a sure lower limit for R/sub cr/. (16 References).

Abstract Number

A76004340

Subject Headings

Dirac equation
Electron pair production
Mathematical analysis
Special relativity
Variational techniques

Non-Thesaurus Subject Headings

theory of quantum electrodynamics

Key Phrase Identifiers

Dirac equation; two Coulomb centres; variational principle; Riccati equation; logarithmic derivative matrix.

Classification Codes

Special relativity [A0330]; Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F].

Treatment

Theoretical or mathematical.

CODEN

JCTPAH

Language

English.

ISSN

0021-9991.

Publication Type

Journal Paper.

Update Code

197600.

Accession Number

000899651

Author

Marinov MS. Popov VS .

Title

Two-center problem for the Dirac equation.

Source

Yadernaya Fizika, vol.23, no.2, 1976, pp.479-87. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The two-center problem for the Dirac equation is considered in view of an experiment on the spontaneous production of positrons in collisions of heavy nuclei. The positrons are created when the internuclear distance is less than its critical value R/sub cr/. The critical distance R/sub cr/ is calculated by means of the variational approach for all the nuclear charges Z<137. It is shown that at Z to 137 the function R/sub cr/(Z) has a finite limit. Formulae necessary for numerical calculations of the critical distance by means of the variational approach are presented. (15 References).

Abstract Number

A76038738

Subject Headings

Dirac equation
Positrons
Variational techniques

Key Phrase Identifiers

Dirac equation; collisions of heavy nuclei; variational approach; critical distance; spontaneous positron production.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Relativistic wave equations and field theories [A1110Q].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197600.

Accession Number

000977788

Author

Migdal AB. Voskresenskii DN. Popov VS .

Title

On the distribution of vacuum charge near supercharged nuclei.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.24, no.3, 5 Aug. 1976, pp.186-8. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

A supercritical nucleus, surrounded by a vacuum shell, which remains around the nucleus after the departure of the positrons to infinity, is investigated. The behaviour of the potential and of the density of the electron cloud, near the edge of the supercharged nucleus, at Ze/sup 3/>>1, is determined. The analysis is performed in the Thomas-Fermi approximation. (0 References).

Abstract Number

A76089881

Subject Headings

Nuclear charge
Nuclear structure

Non-Thesaurus Subject Headings

theory of quantum electrodynamics

Key Phrase Identifiers

distribution of vacuum charge; supercharged nuclei; supercritical nucleus; vacuum shell; positrons; potential; electron cloud density; Thomas Fermi approximation.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Experimental tests of quantum electrodynamics [A1220F]; Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

ZFPRAU

Language

Russian.

Publication Type

Journal Paper.

Update Code

197600.

Accession Number

000992915

Author

Eletskii VL. Popov VS .

Title

Critical charge for abnormal nuclei.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.24, no.4, 20 Aug. 1976, pp.253-6. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

Results are presented of analysis and calculation of the critical charge Z/sub c/ for abnormal nuclei, specifically, a relationship is obtained for Z/sub c/ as a function of density of the nuclear substance and Z/A ratio. The results indicate that Z/sub c/ falls with rising n/sub p/ and, in the range n/sub p/>>n/sub p//sup (o)/, approaches 137 value (critical charge for a point nucleus). (8 References).

Abstract Number

A77000273

Subject Headings

Nuclear charge
Nuclear density

Key Phrase Identifiers

abnormal nuclei; critical charge; density; atomic number.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F].

Treatment

Theoretical or mathematical.

CODEN

ZFPRAU

Language

Russian.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

000996891

Author

Popov VS. Eletskii VL. Mur VD .

Title

Properties of deep-lying levels in a strong electrostatic field.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.71, no.3, Sept. 1976, pp.856-71. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Properties of deep levels (real, virtual and quasistationary) lying near the boundary of the lower continuum are considered. The effective radius expansion is extended to the case of the Dirac equation. It is employed for investigating the level motion near the boundary epsilon =-mc/sup 2/ for various values of the moments j and l. In the limiting cases of R<>h(cross)/mc (R is the range of forces) the formulas can be simplified. The case of a wide potential well R>>h(cross)/mc, in particular, can be reduced to the determination of the spectrum of bound and quasistationary states in the Schrodinger equation with a power potential. The asymptotic behavior of the critical nuclear charge Z/sub cr/ in the region R/sub N/>>h(cross)/mc (R/sub N/ is the nuclear radius) is found and Z/sub cr/ is calculated for the muon for various distributions of electric charge in the nucleus. Differences in the behavior of the levels near epsilon =-mc/sup 2/ for scalar and spinor particles and the inapplicability of the Klein-Gordon single particle equation for Z>or=Z/sub cr/ are discussed. (24 References).

Abstract Number

A77002910

Subject Headings

Dirac equation
Nuclear charge
Nuclear energy levels
Schrodinger equation

Key Phrase Identifiers

strong electrostatic field; lower continuum; effective radius expansion; Dirac equation; quasistationary states; Schrodinger equation; muon; Klein Gordon single particle equation; deep lying levels; bound states; critical nuclear charge.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F]; Nuclear level density and structure [A2110M].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001055179

Author

Migdal AB. Popov VS. Voskresenskii DN .

Title

Distribution of a vacuum charge near super-charged nuclei.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.72, no.3, March 1977, pp.834-50. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The distribution of a vacuum charge near super-critical nuclei (Ze/sup 2/>>1) is found. The calculation is performed in the Thomas-Fermi approximation extended to the relativistic case. For Ze/sup 3/>or approximately=1 the electron shell penetrates the nucleus and almost completely screens its charge. For Ze/sup 3/>>1 the supercharged nucleus is an electrically neutral plasma with equal concentrations of electrons, protons and neutrons (when N=Z). The potential within the nucleus is constant and equals -V/sub 0/=-(3 pi /sup 2/n/sub p/)/sup 1/3/ approximately=-1.94 m/sub pi /c/sup 2/. Near the boundary of the nucleus there is a transition region with a width which is independent of Z. The electric field and surface charge are located in this region. The Coulomb energy of the nucleus, which impedes its stability, is reduced as a result of screening and the E/sub Q/ varies as Z/sup 5/3/ dependence is replaced by a Z/sup 2/3/ dependence. The Thomas-Fermi equation for a neutral atom is also considered. (25 References).

Abstract Number

A77041876

Subject Headings

Nuclear charge
Nuclear screening

Key Phrase Identifiers

supercharged nucleus; electrically neutral plasma; electric field; surface charge; Coulomb energy; screening; neutral atom; relativistic Thomas Fermi equation; vacuum charge distribution; nuclear potential.

Classification Codes

Nuclear Coulomb effects [A2110S].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001064704

Author

Mur VD. Popov VS .

Institution

Moscow Engng. Phys. Inst., Moscow, USSR.

Title

Bound states near the limit of the lower continuum (fermion case).

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.27, no.2, May 1976, pp.204-16. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.27, no.2, May 1976, pp.429-38. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The effective range approximation is generalized to the case of the Dirac equation. Formulas are obtained that express the parameters in the expansion of the S-matrix as epsilon to -mc/sup 2/ in terms of the wave function of the level at the critical point. These formulas are used to investigate the entry of levels of the discrete spectrum into the lower continuum. The critical charge of the nucleus for muons is calculated (the case R>>h(cross)/mc). (14 References).

Abstract Number

A77049638

Subject Headings

Dirac equation
Quantum electrodynamics

Key Phrase Identifiers

lower continuum; fermion case; effective range approximation; Dirac equation; S-matrix; discrete spectrum; bound states; nuclear critical charge for muons.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Specific calculations and limits of quantum electrodynamics [A1220D].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001064899

Author

Mur VD. Popov VS .

Institution

Moscow Engng. Phys. Inst., Moscow, USSR.

Title

Bound states near the limit of the lower continuum (boson case).

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.27, no.1, April 1976, pp.81-93. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.27, no.1, April 1976, pp.346-54. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The well-known effective range approximation in nonrelativistic scattering theory is generalized to the case of scalar particles satisfying the Klein-Gordon equation. Exact expressions are obtained for the parameters of the expansion of the S-matrix and the energy of levels near the limit of the lower continuum in terms of the wave function at the point at which a bound state arises for antiparticles (i.e., at epsilon =-mc/sup 2/). These expressions are used to investigate the motion of the levels near the limit epsilon =-mc/sup 2/ for different values of the angular momentum l. It is shown that the p-level curve can 'bend' for potentials with sharp edge; this was known previously only for s-levels. A number of exactly solvable examples is considered. In particular, the exact solution of the Klein-Gordon equation for the s levels in the Hulthen potential is investigated in detail, together with the passage to the limit of unscreened Coulomb potential. (14 References).

Abstract Number

A77049885

Subject Headings

Boson systems
Quantum electrodynamics
Quantum statistical mechanics
S-matrix theory

Key Phrase Identifiers

effective range approximation; nonrelativistic scattering theory; scalar particles; S-matrix; lower continuum; p-level curve; Hulthen potential; unscreened Coulomb potential; Klein Gordon equation.

Classification Codes

Boson systems (quantum statistical mechanics) [A0530J]; Specific calculations and limits of quantum electrodynamics [A1220D].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001065314

Author

Eletskii VL. Popov VS .

Title

Critical nuclear charge for higher levels. (Numerical calculations and the quasiclassical approach).

Source

Yadernaya Fizika, vol.25, no.5, 1977, pp.1107-12. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Numerical results are presented for the critical nuclear charges corresponding to all the electronic levels crossing the boundary of the lower continuum at Z alpha <9. Quasi-classical formulae for the number of states in the lower continuum are obtained and compared with the numerical calculation. Integral representations are obtained for the Macdonald function with an imaginary index and its derivative, that are appropriate for numerical computations at any values of the argument and the index. (20 References).

Abstract Number

A77050338

Subject Headings

Atomic structure

Key Phrase Identifiers

quasiclassical approach; critical nuclear charges; lower continuum; Macdonald function; numerical computations; superheavy elements; atomic structure.

Classification Codes

General theory of structure, transitions and chemical binding in atoms and molecules [A3110].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001097577

Author

Lisin VI. Marinov MS. Popov VS .

Institution

Inst. for Theoretical & Experimental Phys., Moscow, USSR.

Title

Critical distance for the electron two-center problem.

Source

Physics Letters B, vol.69B, no.2, 1 Aug. 1977, pp.141-2. Netherlands.

Country of Publication

Netherlands.

Abstract

Critical distance R/sub cr/ for the spontaneous positron creation in heavy-ion collisions is calculated precisely for point-like nuclei with 85

Abstract Number

A77071553

Subject Headings

Electron pair production
Heavy ion-nucleus scattering

Key Phrase Identifiers

spontaneous positron creation; U-U collision; heavy ion collisions; critical distance.

Classification Codes

Nuclear Coulomb effects [A2110S]; Coulomb excitation in heavy ion induced reactions [A2570K].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001112412

Author

Popov VS. Eletskii VL. Turbiner AV .

Title

Summing asymptotic series in quantum field theory.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.26, no.3, 5 Aug. 1977, pp.193-7. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

Examines a method of summing series in the perturbation theory with factorially increasing coefficients a/sub k/. A connection is established between the asymptote of a/sub k/ when k to infinity and the nature of the special characteristics of the sum of the series. The boundaries of the range of applicability of the improved perturbation theory are found. The results obtained are tested on a number of physics problems for which exact solutions are known. (12 References).

Abstract Number

A77082683

Subject Headings

Perturbation theory
Quantum field theory

Key Phrase Identifiers

quantum field theory; perturbation theory; asymptotic series summing.

Classification Codes

Asymptotic problems and properties in quantum field theories [A1110J].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

Russian.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197700.

Accession Number

001138922

Author

Popov VS .

Title

New expressions for the invariant operators of the unitary groups.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.29, no.3, Dec. 1976, pp.357-69. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.29, no.3, Dec. 1976, pp.1122-30. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The invariant operators or (Casimir operators) for the unitary groups U(n) and SU(n) are considered. The eigenvalues of these operators for arbitrary irreducible representation are expanded with respect to standard power sums S/sub k/. Expansion are obtained for the coefficients ( beta )/sub nu /( nu ); they hold for arbitrary rank n-1 of the group and arbitrary order p of the invariant operator. These expressions considerably simplify the calculation of the eigenvalues of the invariant operators (especially for large p), which is demonstrated by a number of examples. (25 References).

Abstract Number

A78008555

Subject Headings

Eigenvalues and eigenfunctions
Elementary particle symmetry
Lie groups

Non-Thesaurus Subject Headings

SU / sub n/ theory

Key Phrase Identifiers

invariant operators; unitary groups; Casimir operators; U(n); SU(n); eigenvalues; arbitrary irreducible representation; standard power sums.

Classification Codes

Group theory [A0220]; Symmetry and conservation laws [A1130].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001139103

Author

Popov VS. Eletskii VL. Marinov MS .

Title

Critical charge for anomalous nuclei.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.73, no.4, Oct. 1977, pp.1241-57. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The dependence of the critical charge of nuclei on the proton density is found. The values of Z/sub cr/ for anomalous nuclei are obtained. The calculations of Z/sub CR/ are carried out by taking into account the diffusion of the nuclear boundary and also the effect of screening of the Coulomb nuclear potential by the electron shell. The Thomas-Fermi statistical method is employed for describing the electron density in the shell. Two cases are considered: 1) screening by an ordinary electron shell formed by electrons occupying levels of the discrete spectrum (-m< epsilon

Abstract Number

A78008736

Subject Headings

Nuclear charge
Nuclear structure
Thomas-Fermi model

Key Phrase Identifiers

anomalous nuclei; critical charge; proton density; screening; Coulomb nuclear potential; electron shell; vacuum shell; electron states; ionized atom; nuclear boundary diffusion; Thomas Fermi statistical method.

Classification Codes

Nuclear shape, charge, radius, form factors and structure functions [A2110F]; Nuclear Coulomb effects [A2110S].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001151263

Author

Popov VS. Eletsky VL. Turbiner AV .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

Borel summation of perturbation series in quantum mechanics and field theory.

Source

Physics Letters B, vol.72B, no.1, 5 Dec. 1977, pp.99-102. Netherlands.

Country of Publication

Netherlands.

Abstract

The Borel summation of factorial divergent perturbation series is considered. The relation between the asymptotics of the coefficients in the series and the character of the exact function singularity is established. The applicability limits for the improved perturbation theory are obtained. The results are tested on a number of physical problems for which the exact solutions are available. (16 References).

Abstract Number

A78016683

Subject Headings

Perturbation theory
Quantum field theory
Quantum theory
Series (mathematics)

Key Phrase Identifiers

quantum mechanics; Borel summation; asymptotics; exact function singularity; quantum field theory.

Classification Codes

Function theory, analysis [A0230]; Functional analytical methods in quantum theory [A0365D]; Quantum field theory [A1110].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001151954

Author

Eletsky VL. Voskresensky DN. Popov VS .

Title

Quasiclassical approximation and the Thomas-Fermi method for Z>137.

Source

Yadernaya Fizika, vol.26, no.5, 1977, pp.994-1004. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The quasiclassical approximation is applied to solve the problem of the electron in the Coulomb field of the nucleus with the charge Z when Ze/sup 2/>1 and to describe the multielectronic shell of the supercritical (Ze/sup 2/>>1) atom. An approximate method based on the condition R<

Abstract Number

A78017547

Subject Headings

Atomic structure
Relativistic corrections

Key Phrase Identifiers

quasiclassical approximation; multielectronic shell; short nuclear range approximation; electron states; supercritical atom; electron in nuclear Coulomb field; energy close to lower continuum boundary; Thomas Fermi relativistic equation.

Classification Codes

General theory of structure, transitions and chemical binding in atoms and molecules [A3110]; Radiative and relativistic effects (atoms and molecules) [A3130J].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001174089

Author

Eletskii VL. Popov VS .

Title

The Thomas-Fermi method for Z>137.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.73, no.6, Dec. 1977, pp.2046-59. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A solution is obtained for the relativistic Thomas-Fermi equation for the electron cloud density near supercritical (Ze/sup 2/>>1) nuclei. The cases of a vacuum ion (supercritical nucleus surrounded by a vacuum shell), neutral atom and positive ion are considered. The angular momentum distribution of the vacuum shell electrons is found. For Ze/sup 3/<<1 (weak screening) the electron shell of the supercritical atom consists of two parts which almost do not overlap. These are the vacuum shell with a radius r/sub a/ approximately Ze/sup 2//2 and the outer shells with a radius r/sub e/ approximately (Z/sup 1/3/e/sup 2/)/sup -1/. Here r/sub a//r/sub e/ approximately (Ze/sup 3/)/sup 4/3/<<1. 'Falling to the center' is investigated in the relativistic Thomas-Fermi equation. The nature of the singularities of the equation solutions at r to 0 is determined by the renormalization group technique. A differential equation for the Gell-Mann-Low function beta ( mu ) is obtained and its asymptotic values for mu to 0 and mu to infinity are found. A numerical solution is obtained for all values of the effective coupling constant mu . (23 References).

Abstract Number

A78029748

Subject Headings

Atomic structure
Elements (chemical)
Thomas-Fermi model

Key Phrase Identifiers

electron cloud density; vacuum ion; neutral atom; positive ion; angular momentum distribution; weak screening; renormalization group technique; differential equation; effective coupling constant; relativistic Thomas Fermi method; Z>137; supercritical nuclei; Gell Mann Low function.

Classification Codes

Nuclear-structure models and methods [A2160]; Other statistical model calculations (atoms and molecules) [A3120L].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001186019

Author

Popov VS. Yeletskii VL. Turbiner AV .

Title

Higher orders in perturbation theory and the summation of series in quantum mechanics and field theory.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.74, no.2, Feb. 1978, pp.445-65. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The Borel method for summation of the perturbation theory series with factorially increasing coefficients is considered. The relation between the asymptotic value of the coefficients of the series a/sub k/, for k to infinity , and the singularity of the sum is established. An improved perturbation theory is developed and the limits of its applicability are found. The results are verified for a number of physical problems for which the coefficients of the perturbation theory series exhibit factorial growth and the exact solutions are known. By applying the improved perturbation theory to the scalar field theory g phi /sup 4//4] it is possible to determine the behavior of the Gell-Mann-Low function psi (g) for 0

Abstract Number

A78036886

Subject Headings

Perturbation theory
Quantum field theory
Quantum theory

Key Phrase Identifiers

perturbation theory; summation of series; quantum mechanics; field theory; Borel method; factorially increasing coefficients; scalar field theory; Lagrange function; nonlinear electrodynamics of vacuum; electron energy levels; superheavy nucleus Coulomb field; nuclear charge screening; supercritical atom vacuum shell; Stark effect; H atom; Gell Mann Low function.

Classification Codes

Quantum theory; quantum mechanics [A0365]; Theory of quantized fields [A0370].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001199231

Author

Mur VD. Popov VS. Voskresenskii DN .

Title

On levels in the lower continuum.

Source

Yadernaya Fizika, vol.27, no.2, 1978, pp.529-41. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Quasistationary levels belonging to the lower (negative) continuum of solutions of the Dirac equation are considered. Application of the WKB approximation enables one to solve the problem of the real part of the level energy completely. Explicit formulae are obtained for the level spectrum with the energy epsilon <-mc/sup 2/, their numbers and the angular momentum distribution are found. Comparison with the numerical calculation shows that the WKB method has a reasonable accuracy even at zeta =Ze/sup 2//h(cross)c>or approximately=2. The change of the asymptotics (r to infinity ) of the solutions of the Dirac equation at crossing the boundary of the lower continuum is explicated. (20 References).

Abstract Number

A78045826

Subject Headings

Dirac equation
WKB calculations

Non-Thesaurus Subject Headings

electron energy states (condensed matter)

Key Phrase Identifiers

lower continuum; Dirac equation; WKB approximation; level spectrum; angular momentum distribution; numerical calculation; accuracy; asymptotics; quasistationary levels; level width.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; General theories and computational techniques for electron states in condensed matter [A7110].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001249249

Author

Mur VD. Popov VS. Voskresenskii DN .

Title

The WKB method for Z>137.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.28, no.3, 5 Aug. 1978, pp.140-4. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

WKB approximation formulae are obtained for Dirac's equations in a strong (>2 M/sub e/C/sup 2/ electron binding energy) external field, and used to calculate the energies and widths of the quasistationary states in the lower continuum. A preexponential factor for the probability of spontaneous positron production is also found. (7 References).

Abstract Number

A78078123

Subject Headings

Quantum electrodynamics
WKB calculations

Key Phrase Identifiers

WKB approximation formulae; Dirac's equations; preexponential factor; spontaneous positron production; Z greater than 137.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Other special atoms and molecules [A3690].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

Russian.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001252748

Author

Eletskii VL. Popov VS .

Title

Calculation of the Gell-Mann-Loy function in scalar field theory.

Source

Yadernaya Fizika, vol.28, no.1, 1978, pp.268-70. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Lipatov's work (1976, 1977) suggests a quasi-classical method of calculating functional integrals in perturbation theory, and analyses the coefficients of the Gell-Mann-Loy function in scalar field theory. It is proposed that Lipatov's method of calculating the asymptotic coefficients should be used in conjunction with the Pade-Borel approximation for accurate and economical computation of the Gell-Mann-Loy function. An example is presented where the function is calculated for a scalar field g phi /sup 4//4]. (10 References).

Abstract Number

A78082116

Subject Headings

Axiomatic field theory

Key Phrase Identifiers

functional integrals in perturbation theory; scalar field theory; Lipatov's method; asymptotic coefficients; quasiclassical calculation method; Gell Mann Loy function; Pade Borel approximation; g-phi/sup 4//4 factorial field.

Classification Codes

Axiomatic field theories [A1110C].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001261726

Author

Eletsky VL. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

On the Pade-Borel summation of perturbation series.

Source

Physics Letters B, vol.77B, no.4-5, 28 Aug. 1978, pp.411-14. Netherlands.

Country of Publication

Netherlands.

Abstract

Pade-Borel summation of perturbation series with factorially growing coefficients is considered. Application of this method to scalar field theory g phi /sup 4//4] allows one to compute the Gell-Mann-Low function psi (g) at 0

Abstract Number

A78086416

Subject Headings

Perturbation theory
Quantum field theory
Series (mathematics)

Key Phrase Identifiers

perturbation series; factorially growing coefficients; scalar field theory; coupling constant; Pade Borel summation; Gell Mann Low function.

Classification Codes

Theory of quantized fields [A0370]; Quantum field theory [A1110].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001264395

Author

Mur VD. Popov VS .

Title

Semiclassical approximation for the Dirac equation in strong fields.

Source

Yadernaya Fizika, vol.28, no.3, 1978, pp.837-49. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

A consistent scheme of the semiclassical approximation for the Dirac equation in strong external field is developed. The approximate wave function is found both in classically allowed region and in the forbidden region and the joining conditions in the turning point are obtained. Equations are obtained for the energies of quasistationary levels lying in the lower continuum of solutions of the Dirac equation. The method is applied to relativistic corrections to the Bohr-Sommerfeld quantization rule, to calculation of the preexponential factor in probability of the position spontaneous production by the Coulomb field of a nucleus with charge Z>Z/sub cr/. Semiclassical formulae are obtained for the number of levels dropped into the lower continuum. (14 References).

Abstract Number

A78089645

Subject Headings

Dirac equation

Non-Thesaurus Subject Headings

quantisation

Key Phrase Identifiers

Dirac equation; strong fields; semiclassical approximation; approximate wave function; forbidden region; quasistationary levels; relativistic corrections; preexponential factor; position spontaneous production; Coulomb field; Bohr Sommerfeld quantisation rule.

Classification Codes

Algebraic methods in quantum theory [A0365F]; Specific calculations and limits of quantum electrodynamics [A1220D].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197800.

Accession Number

001283232

Author

Eletskii VL. Popov VS .

Title

Summing of perturbation theory series by Pade and Pade-Borel methods.

Source

Yadernaya Fizika, vol.28, no.4, 1978, pp.1109-22. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The series in the perturbation theory and quantum mechanics often have coefficients which increase as factorials a/sub k/ approximately const.(k alpha )]a/sup k/k/sup beta /, k to infinity . Therefore the convergence radius of these series is zero. The Pade and Pade-Borel methods allow to find the sum of the perturbation theory series psi (g)= Sigma a/sub k/(-g)/sup k/ (in a certain g interval) using the first coefficients a/sub k/ and their asymptotic behaviour at k to infinity . These methods (especially the Pade-Borel method) have essential advantages as compared to the ordinary and improved perturbation theory. The results are illustrated by a number of physical problems for which the coefficients a/sub k/ increase as factorials and at the same time the exact solutions are known. Application of the Pade-Borel method to the scalar field theory with the interaction H/sub int/=(g/4]) integral phi /sup 4/d/sup 4/x allows to find the Gell-Mann-Low function psi (g) at 0

Abstract Number

A79002663

Subject Headings

Perturbation theory
Quantum theory
Series (mathematics)

Key Phrase Identifiers

quantum mechanics; scalar field theory; summing of perturbation theory series; Pade method; Pade Borel method; Gell Mann Low function.

Classification Codes

Algebra, set theory, and graph theory [A0210]; Algebraic methods in quantum theory [A0365F].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001294771

Author

Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., USSR.

Title

Superheavy atoms.

Source

Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.41, no.12, 1977, pp.2577-84. USSR.

Country of Publication

USSR.

Translated Source

Bulletin of the Academy of Sciences of the USSR, Physical Series (USA), vol.41, no.12, 1977, pp.101-8. CODEN: BUPSAA. ISSN: 0001-432X.

Conference Information

Proceedings of the All-Union Conference 'Modern Theory of Atoms and Atomic Spectra. Leningrad, USSR. 1-4 Feb. 1977.

Abstract

A review is given of the present state of the theory of superheavy (atomic number greater than 137) atoms. Problems reviewed include the critical charge of the nucleus, entry of discrete levels into the lower (negative) continuum, properties of the electron shells of supercritical atoms and spontaneous creation of positrons in slow collisions between heavy ions. (29 References).

Abstract Number

A79009603

Subject Headings

Electron pair production
Heavy ion-nucleus scattering
Quantum electrodynamics
Superheavy nuclei

Key Phrase Identifiers

electron shells; supercritical atoms; slow collisions; superheavy atoms; heavy ion collisions; spontaneous positron creation; critical nuclear charge; lower negative continuum discrete levels entry; quantum electrodynamics.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D]; Heavy ion induced reactions and scattering [A2570]; Properties of nuclei with 220

Treatment

Theoretical or mathematical.

CODEN

IANFAY

Language

English.

ISSN

0367-6765.

Publication Type

Conference Paper.

Update Code

197900.

Accession Number

001297312

Author

Dolgov AD. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

Modified perturbation theories for an anharmonic oscillator.

Source

Physics Letters B, vol.79B, no.4-5, 4 Dec. 1978, pp.403-5. Netherlands.

Country of Publication

Netherlands.

Abstract

A simple method of higher-order calculations in perturbation theory (PT) for an arbitrary gv(r) anharmonic oscillator is presented. The method is based on using the Riccati equation instead of the Schrodinger one. The structure of the perturbation series for the energy eigenvalues is investigated. If v(r) to exp(br/sup v/) as r to infinity , then the perturbation series is not Borel summable for 0or=2 the PT expansion in powers of g does not exist. A new convergent version of PT valid for any g, 0

Abstract Number

A79012644

Subject Headings

Eigenvalues and eigenfunctions
Harmonic oscillators
Perturbation theory

Key Phrase Identifiers

anharmonic oscillator; perturbation theory; Riccati equation; energy eigenvalues.

Classification Codes

Algebra, set theory, and graph theory [A0210]; Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001307395

Author

Popov VS. Eletsky VL. Mur VD. Voskresensky DN .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

WKB approximation for the Dirac equation at Z>137.

Source

Physics Letters B, vol.80B, no.1-2, 18 Dec. 1978, pp.68-72. Netherlands.

Country of Publication

Netherlands.

Abstract

The WKB formulae are obtained for the Dirac equation in a strong external field, i.e. a field in which the electron binding energy exceeds 2m/sub e/c/sup 2/ and the energy levels cross the lower continuum boundary. The energy and the width of the quasistationary states in the lower continuum are calculated as well as the preexponential factor in the probability of spontaneous positron production by the Coulomb field. A simple quasiclassical expression for the number of levels immersed into the lower continuum is obtained. Other applications of the WKB method to the theory of supercritical atoms are briefly discussed. (12 References).

Abstract Number

A79017650

Subject Headings

Dirac equation
Quantum electrodynamics
WKB calculations

Key Phrase Identifiers

WKB approximation; Dirac equation.

Classification Codes

Specific calculations and limits of quantum electrodynamics [A1220D].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001310939

Author

Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., USSR.

Title

Invariant operators for the classical groups.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.32, no.3, Sept. 1977, pp.344-7. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.32, no.3, Sept. 1977, pp.784-6. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The eigenvalues of invariant operators of arbitrary order for all classical groups are calculated. The eigenvalues are represented as polynomials of the power sums S/sub k/. (12 References).

Abstract Number

A79021585

Subject Headings

Eigenvalues and eigenfunctions
Group theory
Lie groups
Quantum theory

Key Phrase Identifiers

classical groups; eigenvalues; invariant operator; polynomials.

Classification Codes

Group theory [A0220]; Algebraic methods in quantum theory [A0365F].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001320627

Author

Dolgov AD. Popov VS .

Title

Higher orders and the structure of perturbation theory for an anharmonic oscillator.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.75, no.6, Dec. 1978, pp.2010-26. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A simple method is developed for the calculation of the higher orders in perturbation theory (PT) in powers of g for a D-dimensional isotropic oscillator with arbitrary anharmonicity gv(r). The method is based on a transition from the Schrodinger equation to the Riccati equation. In the important particular case of power law anharmonicity when v(r)=r/sup 2N/, N=2, 3, 4, ..., all the xi /sub n/(r) terms of the PT series become polynomials and hence calculation of the higher orders of perturbation theory is considerably simplified. A new variant of PT is proposed which converges for all values of the coupling constant g, 0

Abstract Number

A79025904

Subject Headings

Harmonic oscillators
Perturbation theory

Key Phrase Identifiers

perturbation theory; anharmonic oscillator; Schrodinger equation; Riccati equation; coupling constant.

Classification Codes

Quantum theory; quantum mechanics [A0365].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001350824

Author

Kudryavtsev AE. Popov VS .

Title

On the theory of the nuclear shift of proton-antiprotonic atom levels.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.29, no.5, 5 March 1979, pp.311-16. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

A formula is obtained, expressing the shift in coulomb levels of hadronic atoms in terms of nuclear potential scattering length (without a small shift presumption). Experimental data on the pp-atom 1s-level shift point to a possible bound state with a binding energy of about 0.9 MeV and width <200 keV in the pp system. (7 References).

Abstract Number

A79045870

Subject Headings

Atomic structure
Hadronic atoms

Key Phrase Identifiers

nuclear shift; coulomb levels; hadronic atoms; nuclear potential scattering length; bound state; binding energy; proton antiprotonic atom.

Classification Codes

Exotic atoms and molecules (containing mesons, muons, and other abnormal particles) [A3610].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

Russian.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001353996

Author

Popov VS. Voskresenskii DN. Eletskii VL. Mur VD .

Title

The WKB method for Z>137 and its application to the theory of supercritical atoms.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.76, no.2, Feb. 1979, pp.431-59. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Formulas for the Dirac equation in a strong external field are obtained in the WKB approximation. A field is considered strong if the electron coupling energy exceeds 2m/sub e/c/sup 2/ and the discrete spectrum levels may be lowered into the continuum. The wave functions in the classically allowed and forbidden regions are found and the conditions for matching them on transition through the turning point are obtained. The WKB method is applied to the following problems: 1) generalization of the Bohr-Sommerfeld quantization conditions with allowance for relativistic effects and the spin; 2) calculation of the pre-exponential factor in the probability for spontaneous positron production; 3) the energy and width of the levels in the relativistic two-center problem; 4) effect of screening on the critical distance R/sub cr/ between the colliding nuclei; 5) tunneling through a nonspherical barrier and the positron angular distribution; 6) allowance for the finite velocity of nuclei. Some other problems which lie outside the limits of applicability of the WKB method are also discussed e.g. the electron spectrum Ze/sup 2/=1 and the deep levels in the lower continuum (Ze/sup 2/>>1, j

Abstract Number

A79049587

Subject Headings

Nuclear structure theory
Superheavy nuclei
WKB calculations

Key Phrase Identifiers

WKB method; supercritical atoms; Dirac equation; electron coupling energy; relativistic effects; spin; spontaneous positron production; energy; width; levels; screening; Z greater than 137.

Classification Codes

Nuclear-structure models and methods [A2160]; Properties of nuclei with 220

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001418023

Author

Dolgov AD. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

The anharmonic oscillator and its dependence on space dimensions.

Source

Physics Letters B, vol.86B, no.2, 24 Sept. 1979, pp.185-8. Netherlands.

Country of Publication

Netherlands.

Abstract

The perturbation series (PS) in powers of g for the D-dimensional gr/sup 4/ anharmonic oscillators is considered. High-order terms of the ground-state-energy E(g,D) expansion are explicitly calculated with the help of recurrence relations among integers. The rate of approach of the PS coefficients to the asymptotic value as a function of D is investigated. For the case of D=0 explicit solutions are obtained and analytic properties of E(g,0) are briefly discussed. For D>>1 the first terms in the expansion of E(g,D) in powers of D/sup -1/ are found. (6 References).

Abstract Number

A79092983

Subject Headings

Harmonic oscillators

Key Phrase Identifiers

dependence on space dimensions; perturbation series; D-dimensional gr/sup 4/ anharmonic oscillators; recurrence relations.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001429510

Author

Alliluev SP. Eletsky WL. Popov VS .

Institution

Moscow Phys. Tech. Inst., Moscow, USSR.

Title

The high orders of perturbation theory for the Stark effect in hydrogen.

Source

Physics Letters A, vol.73A, no.2, 3 Sept. 1979, pp.103-6. Netherlands.

Country of Publication

Netherlands.

Abstract

An effective method is developed to calculate the high orders of the perturbation series (PS) for the Stark shift of the energy levels in the hydrogen atom. The method is based on the use of the Riccati equation instead of the Schrodinger equation. The PS coefficients alpha /sub k/ (hyperpolarizabilities) are given by simple recurrence relations among integers. For the ground state alpha /sub k/ are calculated exactly for k

Abstract Number

A79098025

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Stark effect

Key Phrase Identifiers

high orders; perturbation theory; Stark effect; Riccati equation; Schrodinger equation; hyperpolarizabilities; H.

Classification Codes

Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

Publication Type

Journal Paper.

Update Code

197900.

Accession Number

001476243

Author

Popov VS. Kudryavtsev AE. Mur VD .

Title

Nuclear level shift and radiative transitions in a proton-antiproton atom.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.77, no.5, 1979, pp.1727-50. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

A formula for the Coulomb level shifts in a proton-antiproton atom is derived in terms of the scattering length for a strong potential V/sub s/. The rearrangement of the atomic spectrum when a bound state in the V/sub s/ potential appears is discussed on the basis of the formula. The relation between the level shift and effective radius expansion is pointed out. The mean radius of the s-state for an arbitrary value of the shift and the probabilities for radiative E1 transitions between p- and s-levels are calculated. From the experimental data on the 1s-level shift in the pp-atom it is concluded that a bound Qs-state (quasinuclear meson) with a binding energy epsilon approximately=1 MeV and width Gamma

Abstract Number

A80028121

Subject Headings

Exotic atoms
Nuclear energy level transitions
Protons

Key Phrase Identifiers

radiative transitions; Coulomb level shifts; scattering length; strong potential; atomic spectrum; bound state; effective radius expansion; quasinuclear meson; proton antiproton atom; nuclear level shift; s-state mean radius.

Classification Codes

Lifetimes and transition probabilities of nuclei [A2320C]; Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001514623

Author

Mur VD. Popov VS .

Title

The theory of a nuclear shift of levels in heavy atoms.

Source

Yadernaya Fizika, vol.31, no.3, 1980, pp.617-25. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The results of Kudryavtsev et al. (1979) are generalized to the case of the relativistic Coulomb problem when the parameter zeta =Za approximately=Z/137 is not supposed to be small. The method of matching derivatives is used, the Klein-Gordon and Dirac equations being solved exactly outside the nucleus (r>r/sub N/). For mr/sub N/<<1 the nuclear shift of the levels is written in an explicit analytical form. The derived formulae are applied to calculate the critical distance in heavy ion collisions (taking into account finite size of the colliding nuclei). (20 References).

Abstract Number

A80052586

Subject Headings

Heavy ion-nucleus reactions
Nuclear energy levels

Non-Thesaurus Subject Headings

nuclear reaction and scattering theory

Key Phrase Identifiers

nuclear shift of levels; heavy atoms; relativistic Coulomb problem; Dirac equations; heavy ion collisions; Klein Gordon equations.

Classification Codes

Nuclear level density and structure [A2110M]; Nuclear reaction and scattering models and methods [A2410]; Heavy ion induced reactions and scattering [A2570]; Fragmentation and relativistic heavy ion induced collisions [A2570N].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

Russian.

ISSN

0044-0027.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001521881

Author

Lisin VI. Marinov MS. Popov VS .

Institution

Inst. for Theoretical & Experimental Phys., Moscow, USSR.

Title

Critical electron state in heavy-ion collisions.

Source

Physics Letters B, vol.91B, no.1, 24 March 1980, pp.20-2. Netherlands.

Country of Publication

Netherlands.

Abstract

The results of a calculations of the electron wave function for the critical state epsilon =-m/sub e/c/sup 2/) and of some related quantities are presented. The effect of the finite nuclear size on the critical internuclear distance R/sub cr/ is taken into account. The calculations are performed by means of the variational method for nuclei with charges 85

Abstract Number

A80057796

Subject Headings

Heavy ion-nucleus reactions

Non-Thesaurus Subject Headings

nuclear reaction and scattering theory

Key Phrase Identifiers

electron wave function; critical state; finite nuclear size; critical internuclear distance; variational method; WKB method; strong Coulomb fields; heavy ion collisions.

Classification Codes

Nuclear reaction and scattering models and methods [A2410]; Reaction mechanisms in heavy ion induced reactions [A2570B].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001538857

Author

Mur VD. Kudryavtsev AE. Popov VS .

Title

On the influence of the nn-channel on the properties of a proton-antiproton atom.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.31, no.7, 5 April 1980, pp.429-33. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The influence of the second channel (nn) on nuclear level shifts and the probabilities of radiation transitions in a pp atom are studied. The obtained formulae can also be used on other hadronic atoms ( Sigma /sup -/p, K/sup -/p etc.) (6 References).

Abstract Number

A80069270

Subject Headings

Hadronic atoms

Key Phrase Identifiers

second channel; nuclear level shifts; radiation transitions; proton antiproton atom.

Classification Codes

Exotic atoms and molecules (containing mesons, muons, and other abnormal particles) [A3610].

CODEN

PZETAB

Language

Russian.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001566860

Author

Eletskii VL. Mur VD. Popov VS .

Title

On the WKB method for Z>137.

Source

Doklady Akademii Nauk SSSR, vol.249, no.1-3, Nov. 1979, pp.329-33. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.24, no.11, Nov. 1979, pp.906-8. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The authors study the WKB method for a strong external field (in the Coulomb problem this corresponds to the region Z>137). For the relativistic wavefunctions they obtain approximations that can be used in the neighborhood of a turning point and also consider the question of the accuracy of the WKB method. (11 References).

Abstract Number

A80086598

Subject Headings

Relativistic quantum field theory
Wave functions
WKB calculations

Key Phrase Identifiers

WKB method; Z>137; relativistic wavefunctions; turning point.

Classification Codes

Semiclassical theories and applications in quantum theory [A0365S]; Relativistic wave equations and field theories [A1110Q].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001567312

Author

Alliluev SP. Eletsky VL. Popov VS. Weinberg VM .

Institution

Moscow Phys. Tech. Inst., Moscow, USSR.

Title

Stark effect in hydrogen: high orders of perturbation theory for excited states.

Source

Physics Letters A, vol.78A, no.1, 7 July 1980, pp.43-6. Netherlands.

Country of Publication

Netherlands.

Abstract

The method proposed previously by the authors (1978-79) for computation of high order terms of perturbation series (PS) is generalized to excited states with wave-functions having nodes. The computation of the PS coefficients E/sub k/ for the Stark shift in hydrogen is reduced to solving a system of recurrence relations. With these relations exact values of E/sub k/ are calculated up to k=12 for all states with the principal quantum number n=2 as well as for the states with n/sub 1/=n/sub 2/=0, mod m mod =n-1 and n

Abstract Number

A80087079

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Stark effect

Non-Thesaurus Subject Headings

atomic excited states

Key Phrase Identifiers

Stark effect; perturbation theory; excited states; recurrence relations; principal quantum number; power corrections; H.

Classification Codes

Excited states of atoms and molecules [A3150]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001573950

Author

Eletsky VL. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

On perturbation theory for the gr/sup 2N/ anharmonic oscillator.

Source

Physics Letters B, vol.94B, no.1, July 1980, pp.65-8. Netherlands.

Country of Publication

Netherlands.

Abstract

Perturbation series (PS) in powers of the coupling constant g for D-dimensional anharmonic oscillator with power anharmonicity gr/sup 2N/ is considered. The high order PS coefficients epsilon /sub k/ for the ground state energy are calculated explicitly with the help of recurrence relations among integers. The rate of approach of epsilon /sub k/ to their asymptotics epsilon /sub k/ as a function of space dimension D is discussed. (13 References).

Abstract Number

A80090712

Subject Headings

Harmonic oscillators
Perturbation theory

Key Phrase Identifiers

perturbation theory; gr/sup 2N/ anharmonic oscillator; coupling constant; power anharmonicity; ground state energy.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B].

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

Publication Type

Journal Paper.

Update Code

198000.

Accession Number

001634012

Author

Eletskii VL. Popov VS .

Title

The divergence of the perturbation theory series for the Stark effect and summation of the series.

Source

Doklady Akademii Nauk SSSR, vol.250, no.1-3, Jan. 1980, pp.74-7. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.25, no.1, Jan. 1980, pp.27-9. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

Effective methods for calculating the higher orders of perturbation theory have been found in recent years in quantum mechanics and field theory. A number of problems of quantum mechanics are known for which the perturbation-theory coefficients possess a factorial increase and at the same time one can obtain (analytically or numerically) an exact solution of the Schrodinger equation. The anharmonic oscillator and the Stark effect are classical examples. The results for the Stark effect (a hydrogen atom in a uniform electric field) are described. (15 References).

Abstract Number

A81018076

Subject Headings

Harmonic oscillators
Perturbation theory
Stark effect

Key Phrase Identifiers

perturbation theory; Stark effect; quantum mechanics; field theory; Schrodinger equation; anharmonic oscillator; H atom.

Classification Codes

Functional analytical methods in quantum theory [A0365D]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

Publication Type

Journal Paper.

Update Code

198100.

Accession Number

001645275

Author

Dolgov AD. Eletskii VL. Popov VS .

Title

A new approach to perturbation theory for a discrete spectrum (anharmonic oscillator).

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.79, no.5, Nov. 1980, pp.1704-18. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

An effective method is developed for calculating the higher orders of perturbation theory (PT) for discrete spectrum. The method is based on the transition from the Schrodinger equation to the Riccati equation for the logarithmic derivative of the wave function. For the polynomial potentials (and in particular for the case of an anharmonic oscillator with a gr/sup 2N/ nonlinearity, N=2, 3, 4,...) the calculation of higher orders of PT is reduced to simple recurrence relations. Using these relations the coefficients in the PT series for the energy levels are found exactly for k

Abstract Number

A81023053

Subject Headings

Harmonic oscillators
Perturbation theory
Schrodinger equation

Key Phrase Identifiers

perturbation theory; discrete spectrum; anharmonic oscillator; Schrodinger equation; Riccati equation; logarithmic derivative; wave function; polynomial potentials; recurrence relations.

Classification Codes

Functional analytical methods in quantum theory [A0365D]; Solutions of wave equations: bound state in quantum theory [A0365G].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

198100.

Accession Number

001713773

Author

Popov VS. Kudryavtsev AE. Lisin VI. Mur VD .

Title

On the theory of nuclear level shifts in hadronic atoms.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.80, no.4, 1981, pp.1271-87. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Due to strong short range interaction the Coulomb levels of hadronic atoms experience shifts and broadening. The presence in the problem of a small parameter r/sub e//a/sub B/ makes it possible to develop an analytic theory of the phenomenon (r/sub e/ is an effective range of the strong potential and a/sub B/=h(cross)/sup 2//m/sup e2/ is the Bohr radius). Terms of the order of r/sub e/, the proton form factor and also the effect of the second channel (which is close in energy) are taken into account in the equation for the level shifts. The shifts and broadening of the s-levels and the restructuring of the atomic spectrum are investigated in the presence of absorption, i.e. for a complex scattering length. The region of applicability of perturbation theory in terms of the scattering amplitude is determined. The theory is extended to states with nonvanishing angular momenta. (31 References).

Abstract Number

A81068347

Subject Headings

Hadronic atoms
Nuclear energy level transitions

Non-Thesaurus Subject Headings

atomic spectra

Key Phrase Identifiers

nuclear level shifts; hadronic atoms; short range interaction; Coulomb levels; proton form factor; atomic spectrum; complex scattering length; perturbation theory; nonvanishing angular momenta.

Classification Codes

Electromagnetic transitions [A2320]; Exotic atoms and molecules (containing mesons, muons, and other abnormal particles) [A3610].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

198100.

Accession Number

001755106

Author

Eletsky VL. Popov VS. Weinberg VM .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

Logarithmic perturbation theory for the screened Coulomb potential.

Source

Physics Letters A, vol.84A, no.5, 3 Aug. 1981, pp.235-8. Netherlands.

Country of Publication

Netherlands.

Abstract

Logarithmic perturbation theory (PT) is formulated for the screened Coulomb potential in powers of the screening parameter mu . Recurrence relations are obtained which allow one to compute successively the PT series coefficients E/sub k/ for the ground state energy E=E( mu ). On a number of examples the authors demonstrate that Pade summation of the PT series makes it possible to obtain the energy in the strong coupling region. (16 References).

Abstract Number

A81094697

Subject Headings

Perturbation theory
Potential scattering

Key Phrase Identifiers

screened Coulomb potential; ground state energy; Pade summation; logarithmic perturbation theory.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Nonrelativistic scattering in quantum theory [A0365N].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

Publication Type

Journal Paper.

Update Code

198100.

Accession Number

001781093

Author

Alliluev SP. Vainberg VM. Eletskii VL. Popov VS .

Title

Logarithmic perturbation theory for excited levels.

Source

Doklady Akademii Nauk SSSR, vol.254, no.4-6, Oct. 1980, pp.1392-6. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.25, no.10, Oct. 1980, pp.851-3. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

A significant simplification of higher-order perturbation-theory (PT) calculations in quantum mechanics has recently been achieved. For perturbations of the form V(x)= Sigma /sub -2

Abstract Number

A82003426

Subject Headings

Perturbation theory
Quantum theory
Stark effect

Non-Thesaurus Subject Headings

numerical methods

Key Phrase Identifiers

logarithmic perturbation theory; anharmonic oscillator; H; excited levels; quantum mechanics; recurrence relations; numerical calculation; Stark effect; wave functions; nodes.

Classification Codes

Functional analytical methods in quantum theory [A0365D]; Excited states of atoms and molecules [A3150]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

Publication Type

Journal Paper.

Update Code

198200.

Accession Number

001781979

Author

Kudryavtsev AE. Lisin VI. Popov VS .

Title

Coulomb systems with short-action distance: Sigma /sup -/p atom and the resonance states of light nuclei.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.34, no.5, 5 Sept. 1981, pp.292-6. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The equation connecting the shift and breadth of atomic levels with strong scattering length, is generalised for the case of complex pulses k and arbitrary values of momentum l and zeta =-Z/sub 1/Z/sub 2/. Estimates are presented for the shift and breadth of the s-levels for Sigma /sup -//sub p/ atom. The connection between the position and width of resonances in the case of Coulombic scattering is investigated. (12 References).

Abstract Number

A82004420

Subject Headings

Exotic atoms

Non-Thesaurus Subject Headings

atomic resonant states

Key Phrase Identifiers

Sigma/sup -/p atom; nuclear resonance states; atomic level shift; atomic level breadth; short-action distance; s-levels; Coulombic scattering.

Classification Codes

Exotic atoms and molecules (containing mesons, muons, and other abnormal particles) [A3610].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

Russian.

ISSN

0370-274X.

Publication Type

Journal Paper.

Update Code

198200.

Accession Number

001810202

Author

Veinberg VM. Eletskii VL. Popov VS .

Title

Logarithmic perturbation theory for screened Coulomb potential and charmonium potential.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.81, no.5, 1981, pp.1567-82. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

Logarithmic perturbation theory (PT) for screened Coulomb potential is considered. Calculation of higher PT orders of the level energy E/sub k/ is reduced to recurrent relations which are valid for any type of screening and are very convenient for computer calculations. They are employed to calculate the PT coefficient of E/sub k/ up to k=100 for a number of physically interesting cases such as the Yukawa potential, quarkonium potential etc. The approach of E/sub k/ at k to infinity to the asymptotics. E/sub k/, defined by the quasiclassical approximation, is discussed. The problem of summation of the divergent PT series is considered. By employing the Pade approximants and the asymptotics E/sub k/ it is possible to determine with a high accuracy the energy level E(g) for the potentials mentioned above in a range which considerably exceeds the range of applicability of PT, including the strong coupling region. (34 References).

Abstract Number

A82023958

Subject Headings

Elementary particle interaction models
Perturbation theory
Potential scattering

Key Phrase Identifiers

logarithmic perturbation theory; screened Coulomb potential; charmonium potential; Yukawa potential; quarkonium potential; quasiclassical approximation; Pade approximants; energy level.

Classification Codes

Potential models of strong interactions [A1240Q].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

198200.

Accession Number

001852677

Author

Alliluev SP. Veinberg VM. Eletskii VL. Popov VS .

Title

Logarithmic perturbation theory and its application to the Stark effect in the hydrogen atom.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.82, no.1, 1982, pp.77-90. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The technique considered by S.P. Alliluev et al. (see Phys. Lett. A, vol.78, p.43, 1980) for calculating of higher orders in perturbation theory (PT) in quantum mechanics is extended to excited states whose wave functions have nodes. Calculation of the E/sub k/ coefficients of the PT series for the level energies reduces to recurrent relations which are convenient for numerical computation. As an example the Stark effect in the hydrogen atom is considered for states with n=1 or 2 and also for all states with n/sub 1/=n/sub 2/=0. The asymptotic value for E/sub k/ for k to infinity which depends on the level width in weak fields is obtained. Summation of the divergent PT series makes it possible to determine the Stark shift and the level width in a strong electric field. The asymptotic value of the energy E(E) in extremely strong fields is found for a model which can be solved exactly (Stark effect for a one-dimensional delta -potential). (29 References).

Abstract Number

A82049333

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Stark effect

Key Phrase Identifiers

H atom; Stark effect; hydrogen atom; perturbation theory; quantum mechanics; excited states.

Classification Codes

Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

Russian.

ISSN

0044-4510.

Publication Type

Journal Paper.

Update Code

198200.

Accession Number

001917665

Author

Popov VS. Weinberg VM .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

On summation of perturbation series in quantum mechanics.

Source

Physics Letters A, vol.90A, no.3, 28 June 1982, pp.107-9. Netherlands.

Country of Publication

Netherlands.

Abstract

Summation of a divergent perturbation series for a funnel-like potential is considered. It is done by the Pade-Borel method with the transformation of the variable which moves the nearest singularity of the Borel transform to infinity. The method makes it possible to compute the energy E(g) with a good accuracy for all physical values of the coupling constant g, including the behaviour of E(g) as g to infinity . (10 References).

Abstract Number

A82089562

Subject Headings

Perturbation theory
Quantum theory

Key Phrase Identifiers

perturbation series; quantum mechanics; funnel-like potential; Pade-Borel method; Borel transform.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

Publication Type

Journal Paper.

Update Code

198200.

Accession Number

002008545

Author

Vainberg VM. Popov VS .

Title

The summation of perturbation series.

Source

Doklady Akademii Nauk SSSR, vol.264, no.1-3, May 1982, pp.330-3. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.27, no.5, May 1982, pp.386-8. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The authors consider the summation of the perturbation series for the potential V(r)=-r/sup -1/+gr, h(cross)=m=e=1, They show that, if one knows exactly the first few coefficients of the perturbation series and their asymptotic form E/sub k/ for k to infinity , one can determine the energy E(g) not only for g to 0 but also in the strong coupling regime. (13 References).

Abstract Number

A83030703

Subject Headings

Perturbation theory
Quantum theory

Key Phrase Identifiers

perturbation series; strong coupling regime.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/82/050386-03$02.20.

Publication Type

Journal Paper.

Update Code

198300.

Accession Number

002067343

Author

Popov VS. Kudryavtsev AE. Lisin VI. Mur VD .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

Relation between scattering lengths and effective radii in the charged and neutral channels.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.36, no.6, 20 Sept. 1982, pp.207-10. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.36, no.6, 20 Sept. 1982, pp.257-60. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The Coulomb correction to the strong scattering length a/sub l//sup (s)/ and the effective radius r/sub l//sup (s)/ are calculated for states with arbitrary angular momentum l. This allows relating the position and width near threshold resonances in charged and neutral channels for the lightest nuclei (/sup 5/He and /sup 5/Li, etc.). The Coulomb correction to a/sub l//sup (s)/ is especially large for the s wave, while the correction to r/sub l//sup (s)/ is large for the p wave, when they contain the large logarithm ln(a/sub B//r/sub 0/), where a/sub B/ is the Bohr radius and r/sub 0/ is the range of nuclear forces. (9 References).

Abstract Number

A83065242

Non-Thesaurus Subject Headings

nuclear reaction and scattering theory

Key Phrase Identifiers

charged channel; effective radii; neutral channels; Coulomb correction; strong scattering length; threshold resonances.

Classification Codes

Nuclear reaction and scattering models and methods [A2410].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/82/180257-04$01.00.

Publication Type

Journal Paper.

Update Code

198300.

Accession Number

002081563

Author

Alliluev SP. Vainberg VM. Popov VS .

Title

Higher orders of perturbation theory for the screened Coulomb potential.

Source

Doklady Akademii Nauk SSSR, vol.265, no.1-3, July 1982, pp.597-601. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.27, no.7, July 1982, pp.560-2. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The calculation of the higher orders of perturbation theory in quantum mechanics has been significantly advanced recently by the development of logarithmic perturbation theory. The authors consider its application to the screen Coulomb potential. (9 References).

Abstract Number

A83074321

Subject Headings

Perturbation theory
Quantum theory
Schrodinger equation

Key Phrase Identifiers

Schrodinger equation; perturbation theory; screened Coulomb potential; quantum mechanics; logarithmic perturbation theory.

Classification Codes

Algebraic methods in quantum theory [A0365F]; Solutions of wave equations: bound state in quantum theory [A0365G].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/82/07-0560-03$02.20.

Publication Type

Journal Paper.

Update Code

198300.

Accession Number

002179108

Author

Kudryavtsev AE. Mur VD. Popov VS .

Institution

Moscow Engng. Phys. Inst., Moscow, USSR.

Title

Possible bound state of a K/sup -/ meson with a /sup 4/He nucleus.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.37, no.8, 20 April 1983, pp.412-14. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.37, no.8, 20 April 1983, pp.489-92. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The analytic theory of nuclear level shifts developed in some earlier papers is applied to the /sup 4/He K/sup -/ atom. The experimental data on the shift of the 2p level indicate that there may be a weakly bound state in the /sup 4/He K/sup -/ system. The binding is 'weak' on the nuclear scale; the binding energy is epsilon approximately 100 keV. The probabilities for nonradiative transitions to this level are calculated. (6 References).

Abstract Number

A84014613

Subject Headings

Kaons
Mesic atoms

Non-Thesaurus Subject Headings

helium atoms

Key Phrase Identifiers

bound state; K/sup -/ meson; /sup 4/He nucleus; nuclear level shifts; /sup 4/He K/sup -/ atom; binding energy; nonradiative transitions.

Classification Codes

Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/83/080489-04$01.00.

Publication Type

Journal Paper.

Update Code

198400.

Accession Number

002261059

Author

Mur VD. Kudryavtsev AE. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., State Comm. on Use of Atomic
Energy, USSR.

Title

Coulomb corrections to scattering length and effective range.

Source

Yadernaya Fizika, vol.37, no.6, June 1983, pp.1417-28. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.37, no.6, June 1983, pp.844-9. CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The authors consider the problem of determination of the purely nuclear scattering length a/sub s/ (pertaining to a strong-interaction potential V/sub s/ with the Coulomb interaction switched off) from the nuclear-Coulomb scattering length a/sub cs/ that is directly measured in experiment. The difference between a/sub s/ and a/sub cs/ is especially large if the potential V/sub s/ has a level (real or virtual) with energy close to zero. For such a case they have obtained the formulae relating the scattering lengths a/sub s/ and a/sub cs/ and the effective ranges r/sub s/ and r/sub ss/. The results are generalized to states with arbitrary angular momentum l. They show that the Coulomb correction to the coefficient of k/sup 2l/ in the effective-range expansion is especially large because of the large logarithm ln(a/sub B//r/sub 0/). The Coulomb renormalization of the other terms in the effective-range expansion is of the order r/sub 0//a/sub B/, where r/sub 0/ is the range of the nuclear force and a/sub B/ is the Bohr radius. The formulae obtained are illustrated for several model potentials V/sub s/ used in nuclear physics. (15 References).

Abstract Number

A84064108

Non-Thesaurus Subject Headings

nuclear reaction and scattering theory

Key Phrase Identifiers

Coulomb corrections; scattering length; effective range.

Classification Codes

Nuclear reaction and scattering models and methods [A2410].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/83/060844-06$03.80.

Publication Type

Journal Paper.

Update Code

198400.

Accession Number

002312641

Author

Vainberg VM. Popov VS .

Title

Summing the perturbation series for the Yukawa potential.

Source

Doklady Akademii Nauk SSSR, vol.272, no.1-3, Sept. 1983, pp.335-40. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.28, no.9, Sept. 1983, pp.762-4. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

Over the last few years, significant progress has been made in computing higher orders of perturbation theory (PT) in quantum mechanics and field theory. Very high orders of PT for a screened Coulomb potential have been computed-in particular, for the Yukawa potential V(r)=-e/sup - mu r/r/sup -1/ (up to k=100). Since the PT series for the energy levels E/sup (nl)/( mu )= Sigma /sub k=0//sup infinity /E/sub k//sup (nl)/ mu /sup k/ has zero radius of convergence, the computation of higher orders of the PT does not by itself solve the problem of finding the energy eigenvalues E/sup (nl)/ in the strong-coupling region. The authors consider the summation of the divergent series, taking the Yukawa potential as an example. (14 References).

Abstract Number

A84095910

Subject Headings

Meson field theory
Nuclear forces
Perturbation theory
Quantum theory

Key Phrase Identifiers

perturbation series; Yukawa potential; quantum mechanics; field theory; screened Coulomb potential; energy levels; energy eigenvalues; strong-coupling region; divergent series.

Classification Codes

Quantum theory; quantum mechanics [A0365]; Nuclear forces [A2130].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/83/090762-03$02.20.

Publication Type

Journal Paper.

Update Code

198400.

Accession Number

002329461

Author

Kudrjavtsev AE. Mur VD. Popov VS .

Institution

Inst. of Theoretical & Experimental Phys., Moscow, USSR.

Title

Possible existence of K/sup -/-light nucleus bound states.

Source

Physics Letters B, vol.143B, no.1-3, 9 Aug. 1984, pp.41-4. Netherlands.

Country of Publication

Netherlands.

Abstract

Experimental data on the shift of the K/sup -/ /sup 4/He atom 2p-level evidence a possible existence of a loosely bound nuclear p-state in this system, its binding energy and width being epsilon approximately J approximately 0.5 MeV. The probabilities of radiative transitions to this state and its production cross section in nuclear reaction on /sup 6/Li are calculated. (11 References).

Abstract Number

A84102830

Subject Headings

Mesic atoms
Nuclear energy level transitions
Nuclear energy levels
Nuclei with mass number 6 to 19

Key Phrase Identifiers

kaon/sup -/-light nucleus bound states; kaon/sup -/-/sup 4/He atom; /sup 6/Li(K/sup -/,d)K/sup -4/He; 2p-level; nuclear p-state; binding energy; radiative transitions; production cross section; nuclear reaction.

Classification Codes

Nuclear level density and structure [A2110M]; Nuclear gamma transitions and level energies [A2320L]; Properties of nuclei with 6

Treatment

Theoretical or mathematical.

CODEN

PYLBAJ

Language

English.

ISSN

0370-2693.

U.S. Copyright Clearance Center Code

0370-2693/84/$03.00.

Publication Type

Journal Paper.

Update Code

198400.

Accession Number

002435624

Author

Popov VS. Weinberg VM .

Institution

Inst. of Theor. & Exp. Phys., Moscow, USSR.

Title

On summation of perturbation series for screened Coulomb potentials.

Source

Physics Letters A, vol.107A, no.8, 25 Feb. 1985, pp.371-5. Netherlands.

Country of Publication

Netherlands.

Abstract

Higher orders of perturbation theory (PT) in quantum mechanics and field theory rise factorially at k to infinity (k is the PT order). The authors discuss the computation results of higher orders of PT and summation methods for divergent perturbation series (PS) for quantum mechanical problems: the Yukawa and Hulthen potentials, the funnel-shaped potential, etc. Criteria of PS summability by Pade approximants are examined. (27 References).

Abstract Number

A85052007

Subject Headings

Perturbation theory
Quantum theory

Key Phrase Identifiers

summation; perturbation series; screened Coulomb potentials; quantum mechanics; field theory; Pade approximants.

Classification Codes

Quantum theory; quantum mechanics [A0365].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

Publication Type

Journal Paper.

Update Code

198500.

Accession Number

002583424

Author

Popov VS. Vainberg VM. Mur VD .

Institution

Inst. of Theor. & Exp. Phys., USSR.

Title

Diverging perturbation-theory series and classical mechanics.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.41, no.10, 25 May 1985, pp.439-42. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.41, no.10, 25 May 1985, pp.539-43. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

A summation of the diverging perturbation-theory series yields expressions for the energies of levels (real, virtual, and quasistationary) in terms of the coefficients of the perturbation theory, E/sub k/. Taking the limit of classical mechanics reveals the asymptotic behavior of the highly excited levels with l=n-1>>1, confirming the results of the summation of the perturbation-theory series. (10 References).

Abstract Number

A86013368

Subject Headings

Perturbation theory

Non-Thesaurus Subject Headings

classical mechanics of discrete systems

Key Phrase Identifiers

diverging perturbation theory series summation; excited energy levels; classical mechanics limit; asymptotic behavior.

Classification Codes

Classical mechanics of discrete systems: general mathematical aspects [A0320]; Semiclassical theories and applications in quantum theory [A0365S].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/85/100539-05$01.00.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002585268

Author

Vainberg VM. Popov VS .

Title

Summation of divergent series in perturbation theory for screened Coulomb potentials.

Source

Doklady Akademii Nauk SSSR, vol.279, no.1-3, Nov. 1984, pp.59-63. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.29, no.11, Nov. 1984, pp.895-7. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

As a rule, the higher orders of perturbation theory (PT) in quantum mechanics and field theory increase factorially as k to infinity , and so the PT series diverge however small the coupling constant g (the Dyson phenomenon). The authors consider the summation of the PT series for the screened Coulomb potential: V(r)=-r/sup -1/f(ur). In the limit mu to 0 the energies of the levels can be expanded in formal power series: E/sup (nl)/( mu )= Sigma /sub k=0//sup infinity /E/sub k//sup (nl)/ mu /sup k/. The method of 'logarithmic perturbation theory', which has been developed in recent years, can be used effectively to calculate the PT coefficients E/sub k/. Using this method the authors have calculated E/sub k/ for various screened potentials. In a number of cases (the Yukawa, Hulthen, and funnel potentials) the terms of PT series alternate in sign, while in other cases its structure is more complicated. Because of the factorial growth of the higher orders of PT, the point mu =0 is an essential singularity for the energy E( mu ). This restricts the use of the usual polynomials of PT to the region of very small mu . (11 References).

Abstract Number

A86013411

Subject Headings

Perturbation theory
Potential energy functions
Quantum field theory
Quantum theory

Key Phrase Identifiers

divergent series summation; Yukawa potential; logarithmic method; Hulthen potential; level energies; funnel potential; perturbation theory; screened Coulomb potentials; quantum mechanics; field theory; coupling constant; Dyson phenomenon; power series; factorial growth; polynomials.

Classification Codes

Quantum theory; quantum mechanics [A0365]; Theory of quantized fields [A0370].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/84/110895-03$02.20.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002594358

Author

Karnakov BM. Mur VD. Popov VS .

Institution

Eng. Phys. Inst., Moscow, USSR.

Title

Atomic-spectrum restructuring when I not=0.

Source

Doklady Akademii Nauk SSSR, vol.279, no.1-3, Nov. 1984, pp.345-9. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.29, no.11, Nov. 1984, pp.938-40. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The authors discuss the restructuring of the atomic spectrum for states with l>or=1. They give simple formulas that describe the shifts of l-level everywhere, including the region of intersection of terms. This analysis is, in the authors' opinion, of interest in itself, since 'atomic-spectrum restructuring' has a general quantum mechanical nature and can manifest itself not only in hadronic atoms. The phenomenon of restructuring of an atomic spectrum (for states with an arbitrary angular momentum l) is called the Zel'dovich effect. (8 References).

Abstract Number

A86020191

Subject Headings

Hadronic atoms
Spectral line shift

Non-Thesaurus Subject Headings

atomic spectra

Key Phrase Identifiers

atomic l-levels; atomic spectrum restructuring; l-level shifts; quantum mechanical nature; hadronic atoms; angular momentum; Zel'dovich effect.

Classification Codes

Atomic line shapes, widths, and shifts [A3270J]; Exotic atoms and molecules (containing mesons, muons, and other abnormal particles) [A3610].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/84/110938-03$02.20.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002603670

Author

Popov VS .

Title

Fast-converging perturbation theory.

Source

Doklady Akademii Nauk SSSR, vol.279, no.4-6, Dec. 1984, pp.1362-7. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.29, no.12, Dec. 1984, pp.1037-9. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The authors analyse nonstandard perturbation theory (NPT). A detailed study of the convergence of the higher approximations of the NPT is presented. As an example, they consider the NPT for a funnel potential. (12 References).

Abstract Number

A86024112

Subject Headings

Convergence
Perturbation theory

Key Phrase Identifiers

nonstandard perturbation theory; convergence; NPT; funnel potential.

Classification Codes

Function theory, analysis [A0230]; Functional analytical methods in quantum theory [A0365D].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/84/1037-03$02.20.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002613942

Author

Popov VS. Kudryavtsev AE. Lisin VI. Mur VD .

Institution

Inst. of Theor. & Exp. Phys., USSR.

Title

Shallow nuclear levels and radiative transitions in hadronic atoms.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.88, no.3, March 1985, pp.715-27. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.61, no.3, March 1985, pp.420-6. CODEN: SPHJAR. ISSN: 0038-5646.

Abstract

The position of a nuclear level perturbing the Coulomb spectrum can be calculated in the analytic theory of nuclear level shifts from the level shift of a hadronic atom. The is illustrated by the example of the K/sup -4/He atom. Experimental 2p-level shifts suggest that this system may have a weakly-bound p-state with binding energy and width epsilon approximately gamma approximately 0.5 MeV. The probabilities of radiative transitions to this level and the cross section for its creation in nuclear reactions on /sup 6/Li are calculated. The possible existence of states in which K/sup -/ and p are weakly bound to other light nuclei is examined. An exact solution is obtained for a model Coulomb problem with short-range interaction, and is used to determine the range of validity of the initial approximations. (28 References).

Abstract Number

A86032047

Subject Headings

Mesic atoms
Nuclear energy levels

Non-Thesaurus Subject Headings

helium atoms

Key Phrase Identifiers

shallow nuclear levels; creation cross-section calculations; radiative transitions; hadronic atoms; Coulomb spectrum; level shift; K/sup -4/He atom; 2 p-level shifts; weakly-bound p-state; binding energy; short-range interaction.

Classification Codes

Nuclear level density and structure [A2110M]; Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/85/030420-07$04.00.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002624152

Author

Karnakov BM. Mur VD. Popov VS .

Institution

Moscow Eng.-Phys. Inst., USSR.

Title

Zel'dovich effect for states with l=0.

Source

Yadernaya Fizika, vol.41, no.5, May 1985, pp.1258-71. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.41, no.5, May 1985, pp.804-11. CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

In systems bound by Coulomb potential distorted at short distances (r approximately r/sub 0/<or=1 they are very accurate. (28 References).

Abstract Number

A86038111

Subject Headings

Atomic forces
Potential energy functions
Spectral line shift

Non-Thesaurus Subject Headings

atomic spectra

Key Phrase Identifiers

nuclear energy levels; Zel'dovich effect; Coulomb potential; strong interaction; atomic level shifts.

Classification Codes

Other topics in the theory of atoms and molecules [A3190]; Molecular spectra grouped by wavelength ranges [A3320]; Molecular line and band widths, shapes, and shifts [A3370J]; Interatomic and intermolecular potentials and forces [A3420].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/85/050804-08$03.80.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002741331

Author

Mur VD. Popov VS .

Institution

Inst. of Theor. & Exp. Phys., State Comm. for Use of Atomic Energy, Moscow,
USSR.

Title

Coulomb problem with short-range forces (exact solution).

Source

Yadernaya Fizika, vol.42, no.6, Dec. 1985, pp.1470-9. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.42, no.6, Dec. 1985, pp.930-5. CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The nonrelativistic Coulomb problem with short-range interaction is considered. The model chosen for the strong potential V/sub s/(r) is the delta -function interaction on a sphere r-r/sub 0/, and this makes it possible to solve the Schrodinger equation exactly and to find explicit analytical expressions for the scattering lengths, effective ranges, phase shifts, etc. Detailed comparison of the exact solutions with approximate formulas obtained previously for an arbitrary potential V/sub s/ makes it possible to establish the limits of the range of applicability of these approximations. (19 References).

Abstract Number

A86106542

Subject Headings

Hadronic atoms
Mesic atoms
Nuclear resonances
Nuclear structure theory
Schrodinger equation

Key Phrase Identifiers

hadronic atoms; nuclear resonances; short-range forces; nonrelativistic Coulomb problem; short-range interaction; delta -function interaction; Schrodinger equation; scattering lengths; effective ranges; phase shifts.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Nuclear-structure models and methods [A2160]; Resonance nuclear reactions and scattering [A2430]; Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/85/120930-06$03.80.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002741860

Author

Mur VD. Popov VS .

Institution

Moscow Eng. Phys. Inst., USSR.

Title

Coulomb problem with short-range interaction: exactly solvable model.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.65, no.2, Nov. 1985, pp.238-49. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.65, no.2, Nov. 1985, pp.1132-40. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The nonrelativistic Coulomb problem with short-range interaction is considered. The strong potential V/sub s/(r) is modeled by a delta-function interaction on a sphere r=r/sub 0/. Exact solutions to the Schrodinger equation are obtained for states with arbitrary angular momentum l together with explicit analytic expressions for the scattering lengths, effective ranges, etc. Comparison of the exact solutions with the approximate formulas established earlier for arbitrary short-range potential V/sub s/(r) makes it possible to determine the limits of applicability of these approximations. (30 References).

Abstract Number

A86106085

Subject Headings

Hadronic atoms
Schrodinger equation

Key Phrase Identifiers

hadronic atoms; exactly solvable model; nonrelativistic Coulomb problem; short-range interaction; strong potential; delta-function interaction; Schrodinger equation; arbitrary angular momentum; scattering lengths; effective ranges.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

U.S. Copyright Clearance Center Code

0040-5779/85/6502-1132$09.50.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002772303

Author

Mur VD. Popov VS .

Institution

Moscow Eng. Phys. Inst., USSR.

Title

Coulomb correction to low-energy scattering.

Source

Doklady Akademii Nauk SSSR, vol.284, no.1-3, Sept. 1985, pp.586-91. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.30, no.9, Sept. 1985, pp.782-4. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The calculation of the Coulomb corrections to low-energy scattering parameters (scattering length a/sub l/, effective radius r/sub l/, etc.) is important in applications and has been widely discussed in the literature. The authors demonstrate that the renormalization of the coefficients in the expansion of the effective radius generally contains a 'Coulomb logarithm' lna/sub B//r/sub 0/, with the singular term being independent of the strong potential V/sub s/(r) and calculable in explicit form. This circumstance is of interest in quantum scattering theory, and is also applicable to cases where r/sub 0/<

Abstract Number

A86124436

Subject Headings

Quantum theory
Renormalisation
Scattering

Key Phrase Identifiers

Coulomb logarithm; Coulomb correction; low-energy scattering; scattering length; effective radius; renormalization; quantum scattering theory.

Classification Codes

Nonrelativistic scattering in quantum theory [A0365N]; General theory of scattering [A0380].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/85/090782-03$02.20.

Publication Type

Journal Paper.

Update Code

198600.

Accession Number

002862263

Author

Vainberg VM. Mur VD. Popov VS. Sergeev AV .

Institution

Inst. of Theor. & Exp. Phys., USSR.

Title

Strong-field Stark effect.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.44, no.1, 10 July 1986, pp.9-12. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.44, no.1, 10 July 1986, pp.9-13. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The Stark shifts and the widths of the ground and excited states of the hydrogen atom are calculated. Two independent calculation methods are used: a summation of a divergent perturbation-theory series and a 1/n expansion. (12 References).

Abstract Number

A87050008

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Stark effect

Non-Thesaurus Subject Headings

atomic excited states
atomic spectral line breadth

Key Phrase Identifiers

ground state width; excited states width; Stark shifts; divergent perturbation-theory series; H atom.

Classification Codes

Stark effect in atoms [A3260S]; Atomic line shapes, widths, and shifts [A3270J].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/86/130009-05$01.00.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

002930205

Author

Karnakov BM. Kudryavtsev AE. Mur VD. Popov VS .

Institution

Moscow Phys. Eng. Inst., USSR.

Title

Zel'dovich effect in quantum mechanics.

Source

Nuovo Cimento della Societa Italiana di Fisica B-General Physics Relativity Astronomy & Mathematical Physics & Methods, vol.98B, ser.2, no.1, 11 March 1987, pp.63-86. Italy.

Country of Publication

Italy.

Abstract

In systems bound by the Coulomb potential with a short-range distortion, the reconstruction of the atomic spectrum (or Zel'dovich effect) can appear. Some peculiarities of this phenomenon for the state of nonzero angular momentum are discussed. The analytical properties of the basic equation appearing in the presence of absorption are investigated. The values of absorption at which the reconstruction of atomic levels is replaced by an oscillation regime are given. Some applications of the Zel'dovich effect for hadronic atoms and mesomolecules are considered. (44 References).

Abstract Number

A87089028

Subject Headings

Hadronic atoms
Mesic molecules
Quantum theory

Key Phrase Identifiers

Zel'dovich effect; quantum mechanics; Coulomb potential; short-range distortion; atomic spectrum; nonzero angular momentum; absorption; atomic levels; oscillation regime; hadronic atoms; mesomolecules.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories [A0365B]; Mesonic atoms and molecules, hyperonic atoms and molecules [A3610G].

Treatment

Theoretical or mathematical.

CODEN

NIFBAP

Language

English.

ISSN

0369-3554.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

002942886

Author

Popov VS. Vainberg VM. Mur VD .

Institution

Inst. of Theor. & Exp. Phys., State Comm. on Use of Atomic Energy, USSR.

Title

Higher orders of perturbation theory, classical mechanics, and the 1/n expansion.

Source

Yadernaya Fizika, vol.44, no.4, Oct. 1986, pp.1103-13. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.44, no.4, Oct. 1986, pp.714-20. CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The higher orders of perturbation theory in quantum mechanics and field theory increase as k] for k to infinity , where k is the order. The authors discuss the results of calculations of higher orders of perturbation theory and techniques of summing divergent perturbation series for a large class of quantum mechanical problems (including the Yukawa and Hulthen potentials, the V-funnel potential, and so on). It is shown that in this way it is possible to obtain very accurate values of the energy levels (real, virtual, and quasistationary) using the perturbation series coefficients E/sub k/. By going to classical mechanics the authors find the asymptotic form of the energies of highly excited states and calculate their quantum corrections. These calculations confirm the results of summation of the perturbation series. (31 References).

Abstract Number

A87095409

Subject Headings

Perturbation theory
Quantum field theory
Quantum theory

Key Phrase Identifiers

Yukawa potential; perturbation theory; quantum mechanics; field theory; perturbation theory; Hulthen potentials; V-funnel potential; energy levels; asymptotic form; excited states; quantum corrections.

Classification Codes

Quantum theory; quantum mechanics [A0365]; Quantum field theory [A1110].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/86/100714-07$03.80.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

002954363

Author

Vainberg VM. Popov VS .

Title

Summation of perturbation theory series and classical mechanics.

Source

Doklady Akademii Nauk SSSR, vol.289, no.4-6, Aug. 1986, pp.1095-9. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.31, no.8, Aug. 1986, pp.620-2. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The problem of calculating virtual and resonance levels is constantly encountered in atomic and nuclear physics, scattering, theory, etc. The authors present an approach to this problem based on the summation of perturbation theory (PT) series. They use the results of higher-order calculations for screened Coulomb potentials. (14 References).

Abstract Number

A87102145

Subject Headings

Perturbation theory

Non-Thesaurus Subject Headings

classical mechanics of discrete systems

Key Phrase Identifiers

virtual levels; perturbation theory series; classical mechanics; resonance levels; summation; higher-order calculations; screened Coulomb potentials.

Classification Codes

Classical mechanics of discrete systems: general mathematical aspects [A0320].

Treatment

Theoretical or mathematical.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/86/080620-03$02.20.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

003015457

Author

Mur VD. Popov VS .

Institution

Inst. of Theor. & Exp. Phys., USSR.

Title

1/n expansion and wave functions.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.45, no.7, 10 April 1987, pp.323-6. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.45, no.7, 10 April 1987, pp.410-13. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The 1/n expansion is used to calculate wave functions. Analytic expressions are derived. They are valid for an arbitrary smooth potential V(r), in particular, for the asymptotic coefficients in the limits r to 0 and r to infinity . Comparison with numerical calculations shows that the wave function is calculated very accurately at the origin. (14 References).

Abstract Number

A87140437

Subject Headings

Wave functions

Key Phrase Identifiers

1/ n expansion; wave functions; arbitrary smooth potential; asymptotic coefficients.

Classification Codes

Function theory, analysis [A0230].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/87/070410-04$01.00.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

003017180

Author

Popov VS. Mur VD. Shcheblykin AV. Weinberg VM .

Institution

Inst. of Theor. & Exp. Phys., Moscow, USSR.

Title

1/n-expansion for the Stark effect in strong field.

Source

Physics Letters A, vol.124, no.1-2, 14 Sept. 1987, pp.77-80. Netherlands.

Country of Publication

Netherlands.

Abstract

Stark shifts and widths of the ground and excited states of the hydrogen atom in a strong field E have been computed using the 1/n-expansion (up to E values comparable to the field on an electron orbit, i.e. E>or approximately=n/sup -4/, and for n=1-30). Computation results for the states with parabolic quantum numbers n/sub 1/=n/sub 2/=0, m=n-1 are given and the Rydberg limit, n to infinity , is also considered. (13 References).

Abstract Number

A87141521

Subject Headings

Hydrogen neutral atoms
Stark effect

Non-Thesaurus Subject Headings

atomic excited states

Key Phrase Identifiers

1/ n-expansion; Stark effect; strong field; shifts; widths; ground; excited states; H.

Classification Codes

Excited states of atoms and molecules [A3150]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/87/$03.50.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

003019174

Author

Vainberg VM. Orlov YuV. Popov VS. Tupovtsev VV .

Title

Virtual and resonance levels in the Yukawa potential.

Source

Ukrainskii Fizicheskii Zhurnal, vol.32, no.8, Aug. 1987, pp.1125-9. Ukrainian SSR, USSR.

Country of Publication

Ukrainian SSR, USSR.

Abstract

Two methods for computation of real, virtual and resonance energy eigenvalues are considered: summation of divergent perturbation series and solution of integral equations for t-matrix on physical and unphysical sheets of energy. It is shown on the example of the Yukawa potential that the energy eigenvalues given by both methods coincide with high precision. As an illustration the positions of real (deuteron) and virtual (singlet deuteron) poles of the neutron-proton scattering amplitude were calculated. (13 References).

Abstract Number

A87140913

Subject Headings

Elementary particle interaction models
Perturbation theory

Key Phrase Identifiers

resonance levels; Yukawa potential; real; virtual; energy eigenvalues; summation; divergent perturbation series; integral equations; t-matrix; deuteron; neutron-proton scattering amplitude.

Classification Codes

Potential models of strong interactions [A1240Q].

Treatment

Theoretical or mathematical.

CODEN

UFIZAW

Language

Russian.

ISSN

0503-1265.

Publication Type

Journal Paper.

Update Code

198700.

Accession Number

003115430

Author

Popov VS. Vainberg VM. Mur VD. Shcheblykin AV .

Institution

Inst. of Theor. & Exper. Phys., Moscow, USSR.

Title

1/n expansion in quantum mechanics (H atom Stark effect).

Source

Doklady Akademii Nauk SSSR, vol.293, no.4-6, April 1987, pp.851-5. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - Doklady (USA), vol.32, no.4, April 1987, pp.295-7. CODEN: SPHDA9. ISSN: 0038-5689.

Abstract

The authors consider the 1/n expansion in quantum mechanics by including the Stark effect in the H atom. They limit the discussion to the Bohr-atom model. (10 References).

Abstract Number

A88052565

Subject Headings

Hydrogen neutral atoms
Quantum theory
Stark effect

Key Phrase Identifiers

1/n expansion; quantum mechanics; Stark effect; Bohr-atom model; H atom.

Classification Codes

Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

DANKAS

Language

English.

ISSN

0002-3264.

U.S. Copyright Clearance Center Code

0038-5689/87/040295-03$02.20.

Publication Type

Journal Paper.

Update Code

198800.

Accession Number

003123826

Author

Vainberg VM. Mur VD. Popov VS. Sergeev AV .

Institution

Inst. of Theor. & Exp. Phys., Moscow, USSR.

Title

Stark effect for the Rydberg states of the hydrogen atom.

Source

Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.46, no.5, 10 Sept. 1987, pp.178-82. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.46, no.5, 10 Sept. 1987, pp.225-30. CODEN: JTPLA2. ISSN: 0021-3640.

Abstract

The Stark shifts and the widths of highly excited (n=15-30) states of a hydrogen atom in a strong electric field, which is higher than the classical ionization threshold of an atom, are calculated. The results of the calculations are in agreement with the experiment. (11 References).

Abstract Number

A88060313

Subject Headings

Hydrogen neutral atoms
Stark effect

Non-Thesaurus Subject Headings

atomic excited states
ionisation of atoms

Key Phrase Identifiers

excited state width; Rydberg states; Stark shifts; strong electric field; classical ionization threshold; atom; H.

Classification Codes

Excited states of atoms and molecules [A3150]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/87/170225-06$01.00.

Publication Type

Journal Paper.

Update Code

198800.