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Accession Number

001882822

Author

Sergeev AV. Sherstyouk AI.

Title

Higher orders and structure of perturbation theory series for screened
Coulomb potential.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.82, no.4, April 1982,
pp.1070-8. 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 in perturbation theory for potentials of the polynomial type. It is based on the transition to the problem of perturbation theory for the Fock operator with a purely discrete spectrum. Allowance for dynamic symmetry of the unperturbed operator permits one in this case to express the corrections of any order in perturbation theory as polynomials with rational coefficients. The method is employed to calculate the bound states of the Schroedinger equation with a screened Coulomb potential. The analytical properties of the solutions are investigated. Exact values of the energy in a broad range of variation of the screening parameter is obtained by the Pade technique. The real and imaginary parts of the energies of the quasi-stationary states are calculated. (34 References).

Abstract Number

A82069056

Subject Headings

Perturbation theory
Schrodinger equation

Key Phrase Identifiers

polynomial potential; perturbation theory series; screened Coulomb potential;
higher orders; Fock operator; dynamic symmetry; bound states; Schroedinger
equation; Pade technique.

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

198200.

Accession Number

002430389

Author

Sergeev AV. Sherstyuk AI.

Institution

S.I. Vavilov State Opt. Inst., USSR.

Title

Higher-order perturbation theory for the bound states of the Dirac equation
with Yukawa-type potential.

Source

Yadernaya Fizika, vol.39, no.5, May 1984, pp.1158-64. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.39, no.5, May 1984, pp.731-4.
CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

The method of calculating higher orders of perturbation theory based on perturbation of the Fock operator with a purely discrete spectrum is generalized to the case of the Dirac equation with a potential of the Yukawa type. Corrections to any order of perturbation theory in the energy of an arbitrary bound state are given as finite polynomials which are determined through recurrence relations derived from the dynamical symmetry of the unperturbed problem. The authors propose a modified Pade approximant method which can be used to transform a divergent perturbation series into a rapidly convergent sequence for all bound and quasistationary states of the system. (19 References).

Abstract Number

A85046755

Subject Headings

Dirac equation
Meson field theory
Nuclear forces

Key Phrase Identifiers

nuclear forces; meson field theory; perturbation theory; bound states; Dirac
equation; Yukawa-type potential; Fock operator; discrete spectrum; finite
polynomials; recurrence relations; Pade approximant method.

Classification Codes

Relativistic wave equations and field theories [A1110Q]; Nuclear forces
[A2130].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/84/050731-04$03.80.

Publication Type

Journal Paper.

Update Code

198500.

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

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.

Accession Number

003195961

Author

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

Institution

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

Title

The hydrogen atom in a strong electric field.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.93, no.2, Aug. 1987,
pp.450-62. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.66, no.2, Aug. 1987, pp.258-64. CODEN:
SPHJAR. ISSN: 0038-5646.

Abstract

A calculation is reported of Stark shifts and widths of the ground and first excited states of the hydrogen atom in a strong electric field E up to values of E comparable with the field strength on an atomic orbit. Two independent methods are used, namely, summation of divergent perturbation-theory series and the 1/n expansion. The two methods have a wide region of overlap (in the parameters n/sub 1/, n/sub 2/, m, and E). The calculations are confirmed by considering the Rydberg limit as n to infinity . (28 References).

Abstract Number

A88102574

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Spectral line shift
Stark effect

Non-Thesaurus Subject Headings

atomic excited states. atomic spectral line breadth.

Key Phrase Identifiers

spectral line widths; ground state; first excited state; divergent
perturbation-theory series summation; Stark shifts; 1/n expansion; H.

Classification Codes

Excited states of atoms and molecules [A3150]; Stark effect in atoms
[A3260S]; Atomic line shapes, widths, and shifts [A3270J].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/87/080258-07$04.00.

Publication Type

Journal Paper.

Update Code

198800.

Accession Number

003337778

Author

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

Institution

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

Title

The 1/n expansion in quantum mechanics.

Source

Teoreticheskaya i Matematicheskaya Fizika, vol.74, no.3, March 1988,
pp.399-411. USSR.

Country of Publication

USSR.

Translated Source

Theoretical and Mathematical Physics (USA), vol.74, no.3, March 1988,
pp.269-78. CODEN: TMPHAH. ISSN: 0040-5779.

Abstract

The classical approximation (l=n-1 to infinity ) for the energy in /sup (0)/ and the semiclassical expansion in quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to in /sup (0)/, this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and 'funnel' potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers. (25 References).

Abstract Number

A89039261

Subject Headings

Convergence
Hydrogen neutral atoms
Quantum theory
Stark effect

Key Phrase Identifiers

Yukawa potential; funnel potential; bound states; 1/n expansion; quantum
mechanics; classical approximation; semiclassical expansion; recursive
method; quantum corrections; quasistationary states; Stark effect;
convergence; H atom.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; General
mathematical and computational developments for atoms and molecules [A3115];
Stark effect in atoms [A3260S]; Semiclassical theories and applications in
quantum theory [A0365S].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

TMFZAL

Language

English.

ISSN

0564-6162.

U.S. Copyright Clearance Center Code

0040-5779/88/7403-0269$12.50.

Publication Type

Journal Paper.

Update Code

198900.

Accession Number

003576302

Author

Mur VD. Popov VS. Sergeev AV. Shcheblykin AV.

Institution

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

Title

Stark resonances and scaling in Rydberg atoms.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.96, no.1, July 1989,
pp.91-106. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.69, no.1, July 1989, pp.49-57. CODEN:
SPHJAR. ISSN: 0038-5646.

Abstract

The Stark shifts and the widths of highly excited states are calculated in a strong electric field (n/sup 4/E approximately 1, n>>1) for an arbitrary atom (the difference between the atomic field and the Coulomb field is taken into account by introducing quantum defects in a parabolic basis). A correction to the Bohr-Sommerfeld quantization rule, necessitated by the finite barrier penetration factor, is introduced. The possibility of analytic continuation into the above-barrier region is discussed. Scaling relations are obtained via a 1/n-expansion for the near-threshold Stark resonances with quantum numbers n/sub 1/>>1, n/sub 2/, and m approximately 1. The theoretical results are compared with the experimental data on the photoionization of atoms in the presence of a constant electric field E. (32 References).

Abstract Number

A90039013

Subject Headings

Stark effect

Non-Thesaurus Subject Headings

atomic excited states.

Key Phrase Identifiers

Stark shifts; highly excited states; strong electric field; quantum defects;
Bohr-Sommerfeld quantization rule; finite barrier penetration factor;
near-threshold Stark resonances; photoionization.

Classification Codes

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

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/89/070049-09$04.00.

Publication Type

Journal Paper.

Update Code

199000.

Accession Number

003683874

Author

Sergeev AV.

Institution

S.I. Vavilov State Opt. Inst., USSR.

Title

1/N expansion for the three-body problem.

Source

Yadernaya Fizika, vol.50, no.4, Oct. 1989, pp.945-50. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.50, no.4, Oct. 1989, pp.589-92.
CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

An expansion in powers of 1/N, where N is the dimension of space, is used for the calculation of the energy of a quantum-mechanical three-body system. It is proved that the limit N to infinity corresponds to the classical motion of a rigid configuration of particles in four-dimensional space. The results of the summation of the series in 1/N are discussed in the case of an anharmonic oscillator the mu mu alpha muonic atom, and screened helium. (14 References).

Abstract Number

A90103720

Subject Headings

Harmonic oscillators
Helium neutral atoms
Many-body problems
Muonic atoms
Nuclear screening

Key Phrase Identifiers

muon-muon-alpha; 1/N expansion; three-body problem; energy;
quantum-mechanical three-body system; classical motion; anharmonic
oscillator; screened He.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G];
Positronium, muonium, muonic atoms and molecules [A3610D].

Treatment

Theoretical or mathematical.

Chemicals

He/el.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/89/100589-04$03.80.

Publication Type

Journal Paper.

Update Code

199000.

Accession Number

003705597

Author

Mur VD. Popov VS. Sergeev AV.

Institution

Inst. of Theor. & Experimental Phys., Moscow Eng.-Phys. Inst., USSR.

Title

The 1/N expansion in quantum mechanics.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.97, no.1, Jan. 1990,
pp.32-46. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.70, no.1, Jan. 1990, pp.16-24. CODEN:
SPHJAR. ISSN: 0038-5646.

Abstract

The authors consider the application of the 1/N expansion to the calculation of energies (of both discrete levels and quasi-stationary states) and wave functions, as well as to the problem of two Coulomb centers and the three-body problem. They show that in many cases (for example, for the cc charmonium states) the method yields high accuracy even for low quantum numbers, including the ground state. The relation of these results to the properties of minimizing-uncertainty coherent states is discussed. (33 References).

Abstract Number

A90114669

Subject Headings

Quantum theory
Wave functions

Key Phrase Identifiers

1/N expansion; quantum mechanics; discrete levels; quasi-stationary states;
wave functions; Coulomb centers; three-body problem; charmonium states;
ground state; minimizing-uncertainty coherent states.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/90/010016-09$03.00.

Publication Type

Journal Paper.

Update Code

199000.

Accession Number

003728319

Author

Krepostnov PI. Sergeev AV. Utkin AB.

Title

Optical properties of a dense xenon plasma in flashlamps.

Source

Optika i Spektroskopiya, vol.67, no.3, Sept. 1989, pp.538-41. USSR.

Country of Publication

USSR.

Translated Source

Optics and Spectroscopy (USA), vol.67, no.3, Sept. 1989, pp.315-17. CODEN:
OPSUA3. ISSN: 0030-400X.

Abstract

Theoretical calculations of the continuous and line absorption coefficients of a xenon flashlamp at T=8000-20000 K are carried out. The results are compared to experimental data and possible causes of the discrepancy between calculations and these data are discussed. (20 References).

Abstract Number

A90131741

Subject Headings

Flash lamps
Laser accessories
Light sources
Plasma diagnostics
Xenon

Key Phrase Identifiers

continuous absorption coefficient; laser pump source; flashlamps; line
absorption coefficients; 8000 to 20000 K; Xe plasma.

Classification Codes

Optical (ultraviolet, visible, infrared) plasma diagnostic techniques
[A5270K]; Optical sources and standards [A4272]; Emission, absorption, and
scattering of radiation in plasma [A5225P]; Laser systems and laser beam
applications [A4260].

Treatment

Theoretical or mathematical.

Chemicals

Xe/el.

Numeric Data

Temperature 8.0E+03 to 2.0E+04 K

CODEN

OSFMA3

Language

English.

ISSN

0030-4034.

U.S. Copyright Clearance Center Code

0030-400X/89/090315-03$05.00.

Publication Type

Journal Paper.

Update Code

199000.

Accession Number

003796907

Author

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

Institution

Int. Centre for Theor. Phys., Trieste, Italy.

Title

Strong-field Stark effect: perturbation theory and 1/n expansion.

Source

Physics Letters A, vol.149, no.9, 15 Oct. 1990, pp.418-24. Netherlands.

Country of Publication

Netherlands.

Abstract

The Stark shifts and the widths of the ground and excited states of a hydrogen atom are calculated. Two independent calculation methods are used: a summation of divergent perturbation theory series and 1/n expansion. The results of the calculations for the Rydberg (n>>1) states are in agreement with the experiment. (19 References).

Abstract Number

A91015513

Subject Headings

Hydrogen neutral atoms
Perturbation theory
Spectral line shift
Stark effect

Non-Thesaurus Subject Headings

atomic excited states. atomic spectral line breadth.

Key Phrase Identifiers

ground state; Stark widths; Rydberg states; perturbation theory; 1/n
expansion; Stark shifts; excited states; H.

Classification Codes

Stark effect in atoms [A3260S]; Excited states of atoms and molecules
[A3150]; Atomic line shapes, widths, and shifts [A3270J].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/90/$03.50.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

003796908

Author

Popov VS. Mur VD. Sergeev AV.

Institution

Inst. Centre for Theor. Phys., Trieste, Italy.

Title

1/n-expansion and scaling for the Stark effect in Rydberg atoms.

Source

Physics Letters A, vol.149, no.9, 15 Oct. 1990, pp.425-30. Netherlands.

Country of Publication

Netherlands.

Abstract

The Stark shifts and widths of atomic states in an intense electric field are calculated with the help of the 1/n-expansion. A previous theory is generalized to highly excited states of an arbitrary atom. The scaling relations for near-threshold (E approximately=0) resonances are obtained which are in good agreement with experiment. The modification of the Bohr-Sommerfeld quantization rule due to the finite barrier penetrability is also considered. (12 References).

Abstract Number

A91015514

Subject Headings

Spectral line shift
Stark effect

Non-Thesaurus Subject Headings

atomic excited states.

Key Phrase Identifiers

Stark widths; near-threshold resonances; scaling; Rydberg atoms; Stark
shifts; intense electric field; 1/n-expansion; scaling relations;
Bohr-Sommerfeld quantization rule; finite barrier penetrability.

Classification Codes

Stark effect in atoms [A3260S]; Excited states of atoms and molecules
[A3150]; Atomic line shapes, widths, and shifts [A3270J].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/90/$03.50.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

003872737

Author

Popov VS. Mur VD. Sergeev AV.

Institution

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

Title

Quantization rules with barrier penetrability.

Source

Journal of the Moscow Physical Society, vol.1, no.1, Feb. 1991, pp.15-31.
UK.

Country of Publication

UK.

Abstract

A correction to the quasiclassical quantization rules that allows for the presence of a barrier factor is found. The equation obtained in the process determines both the position of the quasistationary level E/sub r/ and the level width Gamma . The results are compared with numerical solutions of the Schrodinger equation and with those obtained from an exactly solvable model. Finally, a generalization of the Gamow formula for systems with separable variables is derived. (21 References).

Abstract Number

A91057782

Subject Headings

Quantum theory

Non-Thesaurus Subject Headings

quantisation.

Key Phrase Identifiers

quasiclassical quantization rules; barrier factor; quasistationary level;
level width; Schrodinger equation; exactly solvable model; Gamow formula.

Classification Codes

Semiclassical theories and applications in quantum theory [A0365S].

Treatment

Theoretical or mathematical.

CODEN

JMPSEC

Language

English.

ISSN

0960-0175.

U.S. Copyright Clearance Center Code

0960-0175/91/010015+17$03.50.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

003874290

Author

Vainberg VM. Popov VS. Sergeev AV.

Institution

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

Title

The 1/n expansion for a hydrogen atom in an external field.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.98, no.3, Sept. 1990,
pp.847-60. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.71, no.3, Sept. 1990, pp.470-7. CODEN:
SPHJAR. ISSN: 0038-5646.

Abstract

The authors construct a 1/n expansion for a hydrogen atom in constant electric and magnetic fields. The summation of the 1/n expansion enables them with a large degree of accuracy to find the position and the width of atomic levels in a strong field. The method is generalized to resonances in a repulsive Coulomb center and to two-electron atoms. (22 References).

Abstract Number

A91059095

Subject Headings

Hydrogen neutral atoms

Non-Thesaurus Subject Headings

atomic excited states. atomic resonant states. atomic spectral line
breadth.

Key Phrase Identifiers

electric fields; Rydberg states; external field; 1/n expansion; magnetic
fields; width; atomic levels; strong field; resonances; repulsive Coulomb
center; two-electron atoms; H atom.

Classification Codes

Excited states of atoms and molecules [A3150]; Atomic line shapes, widths,
and shifts [A3270J].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/90/090470-08$03.00.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

003993209

Author

Popov VS. Mur VD. Sergev AV.

Institution

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

Title

Generalization of the Gamow formula to the multidimensional case.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.53, no.9, May
1991, pp.433-6. USSR.

Country of Publication

USSR.

Translated Source

JETP Letters (USA), vol.53, no.9, May 1991, pp.455-8. CODEN: JTPLA2. ISSN:
0021-3640.

Abstract

The Gamow formula for a level width is generalized to the case of multidimensional systems with separable variables. A condition for the applicability of this approximation is found. (6 References).

Abstract Number

A91133134

Subject Headings

Hydrogen neutral atoms
Stark effect

Key Phrase Identifiers

Stark effect; Gamow formula; multidimensional case; level width; H atom.

Classification Codes

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

0021-3640/91/090455-04$01.00.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

003996451

Author

Popov VS. Mur VD. Sergeev AV.

Institution

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

Title

Quantization rules for quasistationary states.

Source

Physics Letters A, vol.157, no.4-5, 29 July 1991, pp.185-91. Netherlands.

Country of Publication

Netherlands.

Abstract

The modification of the Bohr-Sommerfeld quantization rules, which is due to the barrier penetrability, is found. The equation obtained is valid for an arbitrary analytical potential U(x), obeying the quasiclassical conditions. It determines both the position E/sub r/ and the width Gamma of the quasistationary state. A generalization of the Gamow formula for multidimensional systems with separable coordinates is derived. A comparison with exactly solvable models as well as with numerical solutions of the Schrodinger equation for the Stark problem is performed. (15 References).

Abstract Number

A91131584

Subject Headings

Schrodinger equation
Stark effect
Tunnelling

Non-Thesaurus Subject Headings

quantisation.

Key Phrase Identifiers

Bohr-Sommerfeld quantization rules; barrier penetrability; arbitrary
analytical potential; quasiclassical conditions; position; width;
quasistationary state; Gamow formula; multidimensional systems; separable
coordinates; exactly solvable models; numerical solutions; Schrodinger
equation; Stark problem.

Classification Codes

Foundations, theory of quantum measurement, miscellaneous quantum theories
[A0365B]; Solutions of wave equations: bound state in quantum theory
[A0365G]; Stark effect in atoms [A3260S].

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/91/$03.50.

Publication Type

Journal Paper.

Update Code

199100.

Accession Number

004049528

Author

Popov VS. Mur VD. Sergeev AV.

Institution

Moscow Eng. Phys. Inst., USSR.

Title

Quantization rules with allowance for barrier penetration.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.100, no.1, July 1991,
pp.20-44. USSR.

Country of Publication

USSR.

Translated Source

Soviet Physics - JETP (USA), vol.73, no.1, July 1991, pp.9-22. CODEN: SPHJAR.
ISSN: 0038-5646.

Abstract

The semiclassical quantization rules are corrected with allowance for barrier penetration. The resulting equation determines both the position E/sub r/ and the width Gamma of the quasistationary level. A comparison is made with numerical solutions of the Schrodinger equation and with exactly solvable models. The generalization of the Gamov formula for systems with separating variables is found. The possibility of generalizing the results obtained to the relativistic case is discussed. (39 References).

Abstract Number

A9202-0365-067

Subject Headings

Schrodinger equation
Tunnelling
Wave functions

Non-Thesaurus Subject Headings

quantisation.

Key Phrase Identifiers

barrier penetration; semiclassical quantization rules; quasistationary level;
numerical solutions; Schrodinger equation; exactly solvable models; Gamov
formula.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/91/070009-14$03.00.

Publication Type

Journal Paper.

Update Code

199200.

Accession Number

004136369

Author

Mur VD. Popov VS. Sergeev AV.

Institution

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

Title

Generalization of the Gamow formula to the multidimensional case.

Source

Yadernaya Fizika, vol.54, no.4, Oct. 1991, pp.950-61. USSR.

Country of Publication

USSR.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.54, no.4, Oct. 1991, pp.575-81.
CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

A generalization of the Gamow formula for the width Gamma of a quasistationary level (with energy E=E/sub r/-i Gamma /2) is given for the case of multidimensional systems with separable variables. The condition for applicability of this approximation is obtained, and some examples are considered. (30 References).

Abstract Number

A9211-2430-004

Subject Headings

Nuclear resonances
Nuclear structure theory

Key Phrase Identifiers

Gamow formula; quasistationary level; multidimensional systems.

Classification Codes

Resonance nuclear reactions and scattering [A2430]; Nuclear-structure models
and methods [A2160].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/91/100575-07$03.00.

Publication Type

Journal Paper.

Update Code

199200.

Accession Number

004159755

Author

Sergeev AV.

Institution

State Opt. Inst., Russia.

Title

Positron-nucleus resonances in electric and magnetic fields.

Source

Yadernaya Fizika, vol.54, no.5, Nov. 1991, pp.1225-31. Russia.

Country of Publication

Russia.

Translated Source

Soviet Journal of Nuclear Physics (USA), vol.54, no.5, Nov. 1991, pp.744-7.
CODEN: SJNCAS. ISSN: 0038-5506.

Abstract

Resonance states of a positron in the Coulomb field of a nucleus and in parallel homogeneous electric and magnetic fields are studied. In the classical description, the positron undergoes oscillatory motion along the symmetry axis, being reflecting consecutively from the nucleus and the anode. The magnetic field does not permit the positron to go around the nucleus and move to the cathode, stabilizing the resonances. The nucleus is regarded as infinitely heavy, and the problem reduces to a one-particle Schrodinger equation. The energies and widths of the resonances are determined by means of versions of perturbation theory in weak electric and strong magnetic fields, the 1/n expansion, and the quasiclassical approximation. Different methods are in good agreement with one another. (4 References).

Abstract Number

A9213-2530-003

Subject Headings

Electron-nucleus reactions
Perturbation theory
Schrodinger equation

Non-Thesaurus Subject Headings

nuclear resonance reactions and scattering.

Key Phrase Identifiers

positron-nucleus resonances; electric fields; Coulomb field; magnetic fields;
oscillatory motion; symmetry axis; anode; cathode; one-particle Schrodinger
equation; perturbation theory; 1/n expansion; quasiclassical approximation.

Classification Codes

Electron and positron reactions and scattering [A2530C]; Resonance nuclear
reactions and scattering [A2430]; Solutions of wave equations: bound state in
quantum theory [A0365G].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

0038-5506/91/110744-04$03.00.

Publication Type

Journal Paper.

Update Code

199200.

Accession Number

004351784

Author

Popov VS. Sergeev AV.

Institution

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

Title

Large orders of the 1/n expansion in quantum mechanics.

Source

Physics Letters A, vol.172, no.4, 4 Jan. 1993, pp.193-8. Netherlands.

Country of Publication

Netherlands.

Abstract

The asymptotics of large orders of the 1/n expansion in quantum mechanics has been found. It is shown that the coefficients epsilon /sup (k)/ grow as k]a/sup k/ with k to infinity , and the dependence of the parameter a on the coupling constant is investigated. (20 References).

Abstract Number

A9307-0365-036

Subject Headings

Quantum theory

Key Phrase Identifiers

1/n expansion; quantum mechanics; coupling constant.

Classification Codes

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

Treatment

Theoretical or mathematical.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/93/$06.00.

Publication Type

Journal Paper.

Update Code

199300.

Accession Number

004352533

Author

Popov VS. Sergeev AV. Shcheblykin AV.

Institution

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

Title

Structure of higher orders of the 1/n expansion.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.102, no.5, Nov. 1992,
pp.1453-68. Russia.

Country of Publication

Russia.

Translated Source

Soviet Physics - JETP (USA), vol.75, no.5, Nov. 1992, pp.787-95. CODEN:
SPHJAR. ISSN: 0038-5646.

Abstract

The asymptote of higher orders of the 1/n expansion in quantum mechanical problems is found. It is shown that the coefficients epsilon /sup (k)/ of the 1/n expansion grow factorially like k] a/sup k/ as k to infinity . The parameter a as a function of the coupling constant is studied. The derived analytic expressions agree with numerical calculations. As examples, the Yukawa, Hulthen and V funnel potentials are considered, as well as the Stark effect in the hydrogen atom and the molecular ion H/sub 2//sup +/. (33 References).

Abstract Number

A9307-3260S-001

Subject Headings

Hydrogen ions
Hydrogen neutral atoms
Positive ions
Potential energy functions
Quantum theory
Stark effect

Key Phrase Identifiers

Yukawa potentials; Hulthen potentials; 1/n expansion; quantum mechanical
problems; funnel potentials; Stark effect; H/sub 2//sup +/; H.

Classification Codes

Stark effect in atoms [A3260S]; Intramolecular energy transfer;
intramolecular dynamics; dynamics of van der Waals molecules [A3425]; Quantum
theory; quantum mechanics [A0365]; Zeeman and Stark effects in molecules
[A3345B]; Interatomic and intermolecular potentials and forces [A3420].

Treatment

Theoretical or mathematical.

Chemicals

H/el; H2/el; H/el.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

0038-5646/92/110787-09$05.00.

Publication Type

Journal Paper.

Update Code

199300.

Accession Number

004435191

Author

Popov VS. Sergeev AV.

Institution

Inst. of Theor. & Exp. Phys., Russian Acad. of Sci., Moscow, Russia.

Title

Asymptotic form of higher orders of the 1/n expansion.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.57, no.5, 10
March 1993, pp.273-6. Russia.

Country of Publication

Russia.

Translated Source

JETP Letters (USA), vol.57, no.5, 10 March 1993, pp.281-5. CODEN: JTPLA2.
ISSN: 0021-3640.

Abstract

The asymptotic form of higher orders of the 1/n expansion in quantum mechanics is factorial. The Yukawa potential and the hydrogen atom in electric and magnetic fields are discussed. (10 References).

Abstract Number

A9315-0365-028

Subject Headings

Hydrogen neutral atoms
Nuclear forces
Quantum theory
Series (mathematics)

Key Phrase Identifiers

electric fields; higher orders; asymptotic form; 1/n expansion; quantum
mechanics; Yukawa potential; magnetic fields; H atom.

Classification Codes

Formalism in quantum theory [A0365C]; Solutions of wave equations: bound
state in quantum theory [A0365G]; Nuclear forces [A2130].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/93/000281-05$10.00.

Publication Type

Journal Paper.

Update Code

199300.

Accession Number

004444854

Author

Mur VD. Popov VS. Sergeev AV.

Institution

Moscow Eng. Phys. Inst., Russia.

Title

The 1/n-expansion in quantum mechanics and quasi-stationary states.

Source

Journal of the Moscow Physical Society, vol.2, no.3, Aug. 1992, pp.189-217.
UK.

Country of Publication

UK.

Abstract

Applications of the 1/n-expansion to energy and wavefunction calculations, especially for quasi-stationary states are considered. As an illustration the authors have examined the funnel and Yukawa potentials, the Stark effect in a strong field and a hydrogen atom in electric and magnetic fields. They have found that in many cases the method ensures high accuracy, even for small quantum number, n approximately 1. The connection between these results and the properties of coherent states is briefly discussed. Finally, the behaviour of the large-order terms in the 1/n-expansion is investigated. (41 References).

Abstract Number

A9316-0365-041

Subject Headings

Hydrogen neutral atoms
Quantum theory
Stark effect
Wave functions

Key Phrase Identifiers

funnel potential; applied magnetic field; applied electric field;
1/n-expansion; quantum mechanics; quasi-stationary states; energy;
wavefunction calculations; Yukawa potentials; Stark effect; strong field;
coherent states; large-order terms; H atom.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Zeeman
effect in atoms [A3260V].

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

JMPSEC

Language

English.

ISSN

0960-0175.

U.S. Copyright Clearance Center Code

0960-0175/92/030189+29$07.50.

Publication Type

Journal Paper.

Update Code

199300.

Accession Number

004667621

Author

Popov VS. Mur VD. Sergeev AV.

Institution

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

Title

Critical fields and above-barrier Stark resonances.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.59, no.3, 10
Feb. 1994, pp.150-3. Russia.

Country of Publication

Russia.

Translated Source

JETP Letters (USA), vol.59, no.3, 10 Feb. 1994, pp.158-62. CODEN: JTPLA2.
ISSN: 0021-3640.

Abstract

Exact values of the critical field C/sub c/ are calculated for a hydrogen atom, including the case of the ground state. The widths Gamma /sub n/ of Stark resonances at C=C/sub c/, are also calculated. In the above-barrier region (C>C/sub c/ the widths Gamma /sub n/(C) are essentially linear functions of the electric field strength. (12 References).

Abstract Number

A9412-3260S-001

Subject Headings

Hydrogen neutral atoms
Stark effect

Key Phrase Identifiers

above-barrier Stark resonances; critical field; H atom; ground state;
above-barrier region; linear functions; electric field strength; H.

Classification Codes

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

0021-3640/94/030158-05$10.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

004678291

Author

Popov VS. Sergeev AV.

Institution

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

Title

Asymptotic form of higher orders of the 1/n expansion for multidimensional
problems.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.105, no.3, March 1994,
pp.568-91. Russia.

Country of Publication

Russia.

Translated Source

Journal of Experimental and Theoretical Physics (USA), vol.78, no.3, March
1994, pp.303-14. CODEN: JTPHES. ISSN: 1063-7761.

Abstract

The asymptotic form of higher orders of the 1/n expansion is analyzed for multidimensional problems of quantum mechanics and atomic physics. Problems in which variables can and cannot be separated are discussed. Examples of the former are the molecular hydrogen atom and the Stark effect; an example of the latter is the hydrogen atom in electric and magnetic fields. The asymptotic form is always factorial. Its parameters can be calculated through a calculation of electron tunneling trajectories by the "imaginary time" method. Possible types of singularities of the asymptotic parameter alpha at the collision point of the classical solutions are determined. (36 References).

Abstract Number

A9413-0365-031

Subject Headings

Hydrogen neutral atoms
Hydrogen neutral molecules
Quantum theory
Stark effect

Non-Thesaurus Subject Headings

molecular energy level calculations.

Key Phrase Identifiers

asymptotic form; higher orders; 1/n expansion; multidimensional problems;
quantum mechanics; atomic physics; molecular H atom; Stark effect; atomic H;
electric fields; magnetic fields; electron tunneling trajectories; imaginary
time method; singularities; collision point; classical solutions; H; H/sub
2/.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G];
Foundations, theory of quantum measurement, miscellaneous quantum theories
[A0365B]; Zeeman and Stark effects in molecules [A3345B]; Specific
calculations and results for atoms and molecules [A3120].

Treatment

Theoretical or mathematical.

Chemicals

H/el; H2/el; H/el.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

1063-7761/94/030303-12$10.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

004732543

Author

Popov VS. Sergeev AV. Mur VD. Shcheblykin AV.

Institution

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

Title

On the asymptotics of high-order terms of the 1/n expansion.

Source

Yadernaya Fizika, vol.57, no.6, June 1994, pp.1119-28. Russia.

Country of Publication

Russia.

Translated Source

Physics of Atomic Nuclei (Russia), vol.57, no.6, June 1994, pp.1057-65.
CODEN: PANUEO. ISSN: 1063-7788.

Abstract

Analytic and numerical methods for determining the asymptotics of high-order terms of the 1/n expansion in quantum-mechanical problems are developed. It is shown that this asymptotics is always of the factorial type. The dependence of parameters of the asymptotics on the form of the potential and on the coupling constant is especially analyzed in the vicinity of the point of collision of classical solutions. (23 References).

Abstract Number

A9418-0365-090

Subject Headings

Elementary particle coupling constants
Numerical analysis
Quantum theory

Key Phrase Identifiers

asymptotics; high-order terms; 1/n expansion; analytic methods; numerical
methods; quantum-mechanical problems; factorial type; coupling constant;
potential; classical solutions.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G];
Numerical approximation and analysis [A0260]; Quantum field theory [A1110].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

1063-7788/94/5706-1057$10.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

004788405

Author

Popov VS. Mur VD. Sergeev AV.

Institution

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

Title

Critical electric fields and Stark resonances in the hydrogen atom.

Source

Physics Letters A, vol.193, no.2, 26 Sept. 1994, pp.159-64. Netherlands.

Country of Publication

Netherlands.

Abstract

The exact values of critical electric fields E/sub c/ for different states of a hydrogen atom, including its ground state, as well as the widths Gamma /sub n/ of the Stark resonances at E=E/sub c/, are calculated (at E=E/sub c/ (n/sub 1/, n/sub 2/, m) the potential barrier for an electron in the (n/sub 1/, n/sub 2/, m) state disappears). Using the modified quantization condition with barrier penetrability included, we explain the dependence of Gamma /sub n/ on the principal quantum number n. (17 References).

Abstract Number

A9422-3260S-003

Subject Headings

Hydrogen neutral atoms
Stark effect

Non-Thesaurus Subject Headings

atomic spectral line breadth. quantisation.

Key Phrase Identifiers

critical electric fields; Stark resonances; H atom; ground state; level
widths; potential barrier; quantization condition; barrier penetrability;
principal quantum number; H.

Classification Codes

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

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/94/$07.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

004788406

Author

Popov VS. Sergeev AV.

Institution

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

Title

Large orders of 1/n-expansion for multidimensional problems.

Source

Physics Letters A, vol.193, no.2, 26 Sept. 1994, pp.165-72. Netherlands.

Country of Publication

Netherlands.

Abstract

The asymptotics of large orders of the 1/n-expansion is investigated for multidimensional problems of quantum mechanics and atomic physics, including those with separable variables (the hydrogen molecular ion H/sub 2//sup +/), and those where separation of variables is impossible (a hydrogen atom in electric and magnetic fields). It is shown that the parameters of the asymptotics can be found by means of calculating sub-barrier trajectories with the help of the "imaginary time" method, as well as by solution of the eikonal equation. (17 References).

Abstract Number

A9422-0365-056

Subject Headings

Atomic structure
Hydrogen ions
Hydrogen neutral atoms
Molecular electronic states
Quantum theory

Key Phrase Identifiers

1/n-expansion; multidimensional problems; large orders asymptotics; quantum
mechanics; atomic physics; separable variables; H molecular ion; H atom;
electric fields; magnetic fields; subbarrier trajectories; imaginary time;
eikonal equation; H/sub 2//sup +/; H/sub 2/; H.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; General
theory of structure, transitions and chemical binding in atoms and molecules
[A3110]; General mathematical and computational developments for atoms and
molecules [A3115].

Treatment

Theoretical or mathematical.

Chemicals

H2/el; H/el; H/el.

CODEN

PYLAAG

Language

English.

ISSN

0375-9601.

U.S. Copyright Clearance Center Code

0375-9601/94/$07.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

004835651

Author

Popov VS. Mur VD. Sergeev AV.

Institution

Int. Inst. of Phys., Moscow, Russia.

Title

Theory of the Stark effect in a strong field: critical fields, above-barrier
resonances, dependence on dimensionality.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.106, no.4, Oct. 1994,
pp.1001-30. Russia.

Country of Publication

Russia.

Translated Source

Journal of Experimental and Theoretical Physics (USA), vol.79, no.4, Oct.
1994, pp.547-60. CODEN: JTPHES. ISSN: 1063-7761.

Abstract

We have calculated accurate values of the critical fields E/sub c/ for various states (n/sub 1/, n/sub 2/, m) of a hydrogen atom, including the ground state. Using modified quantization rules that take into account the finite permeability of the barrier, we determine how the widths Gamma /sub n/ of the Stark resonances depend on n for E=E/sub c/. Using the 1/n expansion, along with several model problems as examples, we show that in the above-barrier (E>E/sub c/) region the Stark widths Gamma /sub n/(E) depend almost linearly on the electric field. We determine the dependence of the ground-state Stark shift of a d-dimensional "hydrogen atom" on the dimensionality D of the space. (45 References).

Abstract Number

A9502-3260S-001

Subject Headings

Stark effect

Key Phrase Identifiers

Stark effect; strong field; critical fields; above-barrier resonances;
dimensionality; ground state; finite permeability; Stark resonances.

Classification Codes

Stark effect in atoms [A3260S]; Spin-orbit coupling, Zeeman, Stark and strain
splitting (condensed matter) [A7170E].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

1063-7761/94/100547-14$10.00.

Publication Type

Journal Paper.

Update Code

199400.

Accession Number

005029796

Author

Sergeev AV.

Institution

S.I. Vavilov State Optical Inst., St. Petersburg, Russia.

Title

Summation of the eigenvalue perturbation series by multi-valued Pade
approximants: application to resonance problems and double wells.

Source

Journal of Physics A-Mathematical & General, vol.28, no.14, 21 July 1995,
pp.4157-62. UK.

Country of Publication

UK.

Abstract

Quadratic Pade approximants are used to obtain energy levels both for the anharmonic oscillator x/sup 2//2- lambda x/sup 4/ and for the double well -x/sup 2//2+ lambda x/sup 4/. In the first case, the complex-valued energy of the resonances is reproduced by summation of the real terms of the perturbation series. The second case is treated formally as an anharmonic oscillator with a purely imaginary frequency. We use the expansion around the central maximum of the potential to obtain a complex perturbation series on the unphysical sheet of the energy function. Then, we perform an analytical continuation of this solution to the neighbouring physical sheet taking into account the supplementary branch of quadratic approximants. In this way we can reconstruct the real energy by summation of the complex series. Such an unusual approach eliminates the double degeneracy of states that makes ordinary perturbation theory (around the minima of the double well potential) incorrect. (18 References).

Abstract Number

A9518-0365-020

Subject Headings

Bound states
Eigenvalues and eigenfunctions
Harmonic oscillators
Perturbation theory
Quantum theory

Key Phrase Identifiers

quadratic Pade approximants; eigenvalue perturbation series; resonance;
double wells; energy levels; anharmonic oscillator; degeneracy.

Classification Codes

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

Treatment

Theoretical or mathematical.

CODEN

JPHAC5

Language

English.

ISSN

0305-4470.

U.S. Copyright Clearance Center Code

0305-4470/95/144157+06$19.50.

Publication Type

Journal Paper.

Update Code

199500.

Copyright

Copyright 1995, IEE.

Accession Number

005195998

Author

Mur VD. Popov VS. Sergeev AV.

Institution

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

Title

Coulomb corrections to nuclear scattering lengths and effective ranges for
weakly bound systems.

Source

Yadernaya Fizika, vol.59, no.1, Jan. 1996, pp.68-77. Publisher: MAIK
Nauka/Interperiodica Publishing, Russia.

Country of Publication

Russia.

Translated Source

Physics of Atomic Nuclei (Russia), vol.59, no.1, Jan. 1996, pp.62-71. CODEN:
PANUEO. ISSN: 1063-7788.

Abstract

A procedure is considered for extracting the purely nuclear scattering length a/sub s/ and effective range r/sub s/ (which correspond to a strong-interaction potential V/sub s/ with disregarded Coulomb interaction) from the experimentally determined nuclear quantities a/sub cs/ and r/sub cs/ which are modified by Coulomb interaction. The Coulomb renormalization of a/sub s/ and r/sub s/ is especially strong if the system under study involves a level with energy close to zero (on the nuclear scale). This applies to formulas that determine the Coulomb renormalization of the low energy parameters of s scattering (l=0). Detailed numerical calculations are performed for coefficients appearing in the equations that determine Coulomb corrections for various models of the potential V/sub s/(r). This makes it possible to draw qualitative conclusions about the dependence of Coulomb corrections on the form of the strong-interaction potential and, in particular, on its small-distance behavior. A considerable enhancement of Coulomb corrections to the effective range r/sub s/ is found for potentials with a barrier. (32 References).

Abstract Number

A9607-2410-001

Subject Headings

Nuclear reaction theory

Key Phrase Identifiers

nuclear scattering lengths; Coulomb corrections; effective ranges; weakly
bound systems; effective range; strong-interaction potential; Coulomb
interaction; Coulomb renormalization; low energy parameters; small-distance
behavior.

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

1063-7788/96/5901-0062$10.00.

Publication Type

Journal Paper.

SICI

0044-0027(199601)59:1L.68;1-Z
1063-7788(199601)59:1L.62:CCNS;1-7

Update Code

199600.

Copyright

Copyright 1996, IEE.

Accession Number

005294672

Author

Popov VS. Sergeev AV.

Institution

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

Title

Effect of a magnetic field on the ionization of atoms.

Source

Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.63, no.6, 25
March 1996, pp.398-402. Publisher: AIP, Russia.

Country of Publication

Russia.

Translated Source

JETP Letters (USA), vol.63, no.6, 25 March 1996, pp.417-22. CODEN: JTPLA2.
ISSN: 0021-3640.

Abstract

The ionization probability of an atomic s state under the action of static electric and magnetic fields is calculated taking into account the Coulomb interaction between the escaping electron and the atomic core. The structure of the perturbation series for the energy of the level is investigated and the asymptotic behavior of the higher orders of the perturbation theory is found. (14 References).

Abstract Number

A9614-3450H-011

Subject Headings

Ionisation
Perturbation theory

Key Phrase Identifiers

atom ionization probability; static magnetic field; static electric fields;
Coulomb interaction; escaping electron; perturbation series; energy level.

Classification Codes

Electronic excitation and ionization (atoms and molecules) [A3450H].

Treatment

Theoretical or mathematical.

CODEN

PZETAB

Language

English.

ISSN

0370-274X.

U.S. Copyright Clearance Center Code

0021-3640/96/060417-06$10.00.

Publication Type

Journal Paper.

SICI

0370-274X(19960325)63:6L.398;1-B
0021-3640(19960325)63:6L.417:EMFI;1-L

Update Code

199600.

Copyright

Copyright 1996, IEE.

Accession Number

005458366

Author

Mur VD. Popov VS. Sergeev AV.

Institution

Eng. Phys. Inst., Acad. of Sci., Moscow, Russia.

Title

Coulomb corrections to scattering lengths and effective ranges for l not=0.

Source

Yadernaya Fizika, vol.59, no.11, Nov. 1996, pp.1958-65. Publisher: MAIK
Nauka/Interperiodica Publishing, Russia.

Country of Publication

Russia.

Translated Source

Physics of Atomic Nuclei (Russia), vol.59, no.11, Nov. 1996, pp.1888-94.
CODEN: PANUEO. ISSN: 1063-7788.

Abstract

Coulomb corrections to the low-energy scattering parameters (scattering lengths and effective ranges) of states with nonzero orbital angular momentum are studied. The greatest attention is paid to the case of the p wave. Resonance scattering is considered for a system with a shallow nuclear bound or quasistationary (resonance) p level. Coulomb corrections are calculated numerically, and their dependence on the shape of the strong-interaction potential-in particular, on its short-distance behavior-is studied in detail. (17 References).

Abstract Number

A9703-2410-001

Subject Headings

Nuclear reaction theory
Nuclear resonance scattering

Key Phrase Identifiers

scattering lengths; Coulomb corrections; effective ranges; p wave; resonance
scattering; quasistationary p level; strong-interaction potential;
short-distance behavior; nuclear scattering.

Classification Codes

Nuclear reaction and scattering models and methods [A2410]; Resonance nuclear
reactions and scattering [A2430].

Treatment

Theoretical or mathematical.

CODEN

IDFZA7

Language

English.

ISSN

0044-0027.

U.S. Copyright Clearance Center Code

1063-7788/96/5911-1888$10.00.

Publication Type

Journal Paper.

SICI

0044-0027(199611)59:11L.1958;1-E
1063-7788(199611)59:11L.1888:CCSL;1-U

Update Code

199700.

Copyright

Copyright 1997, IEE.

Accession Number

005892522

Author

Sergeev AV. Goodson DZ.

Institution

Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.

Title

Self-consistent field perturbation theory of molecular vibrations.

Source

Molecular Physics, vol.93, no.3, 20 Feb. 1998, pp.477-84. Publisher: Taylor &
Francis, UK.

Country of Publication

UK.

Abstract

Perturbation theory is used to perform non-iterative calculations of energy eigenvalues of the coupled ordinary differential equations that result from imposing separability assumptions in terms of normal coordinates on vibrational wavefunctions. Various model Hamiltonians with 2 or 3 coupled normal modes are studied and the increase of computational cost with the number of degrees of freedom is analysed. Quadratic Pade approximants of the perturbation expansions are rapidly convergent, and directly yield complex numbers for resonance eigenvalues. For a 3-mode system, results are obtained within partial separability assumptions, with a pair of modes left coupled. Large-order perturbation theory with partial separability is suggested as an alternative to low-order exact perturbation theory. (35 References).

Abstract Number

A9810-3310-020

Subject Headings

Differential equations
Eigenvalues and eigenfunctions
Perturbation theory
SCF calculations
Vibrational states
Wave functions

Key Phrase Identifiers

self-consistent field perturbation theory; molecular vibrations; noniterative
calculations; energy eigenvalues; coupled ordinary differential equations;
normal coordinates; vibrational wavefunctions; model Hamiltonians; coupled
normal modes; quadratic Pade approximants; perturbation expansions; resonance
eigenvalues; partial separability assumptions; large-order perturbation
theory; low-order exact perturbation theory.

Classification Codes

Vibrational analysis (molecular spectra) [A3310G]; Numerical approximation
and analysis [A0260]; Algebra, set theory, and graph theory [A0210]; Specific
calculations and results for atoms and molecules [A3120].

Treatment

Theoretical or mathematical.

CODEN

MOPHAM

Language

English.

ISSN

0026-8976.

U.S. Copyright Clearance Center Code

0026-8976/98/$12.00.

Publication Type

Journal Paper.

SICI

0026-8976(19980220)93:3L.477:SCFP;1-8

Update Code

199816.

Copyright

Copyright 1998, IEE.

Accession Number

005929646

Author

Sergeev AV. Goodson DZ.

Institution

Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.

Title

Summation of asymptotic expansions of multiple-valued functions using
algebraic approximants: application to anharmonic oscillators.

Source

Journal of Physics A-Mathematical & General, vol.31, no.18, 8 May 1998,
pp.4301-17. Publisher: IOP Publishing, UK.

Country of Publication

UK.

Abstract

The divergent Rayleigh-Schrodinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pade approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree. Different branches of the approximants converge to different branches of the function. The success of the high-degree approximants is attributed to their ability to model the function on multiple sheets of the Riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter. An efficient recursive algorithm for computing the diagonal approximant sequence is presented. (56 References).

Abstract Number

A9813-0365-048

Subject Headings

Algebra
Approximation theory
Convergence
Eigenvalues and eigenfunctions
Functions
Harmonic oscillators
Perturbation techniques

Key Phrase Identifiers

asymptotic expansions; multiple-valued functions; algebraic approximants;
anharmonic oscillators; divergent Rayleigh-Schrodinger perturbation
expansions; energy eigenvalues; cubic oscillators; quartic oscillators;
sextic oscillators; octic oscillators; generalized Pade approximants;
diagonal staircase approximant sequence; convergence; high-degree
approximants; singularity structure; Riemann surface; efficient recursive
algorithm; diagonal approximant sequence.

Classification Codes

Solutions of wave equations: bound state in quantum theory [A0365G]; Function
theory, analysis [A0230]; Algebra, set theory, and graph theory [A0210].

Treatment

Theoretical or mathematical.

CODEN

JPHAC5

Language

English.

ISSN

0305-4470.

U.S. Copyright Clearance Center Code

0305-4470/98/184301+17$19.50.

Document Number

S0305-4470(98)87859-1.

Publication Type

Journal Paper.

SICI

0305-4470(19980508)31:18L.4301:SAEM;1-X

Update Code

199822.

Copyright

Copyright 1998, IEE.

Accession Number

005979869

Author

Popov VS. Sergeev AV.

Institution

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

Title

Ionization of atoms in weak fields and the asymptotic behavior of
higher-order perturbation theory.

Source

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.113, no.6, June 1998,
pp.2047-55. Publisher: AIP, Russia.

Country of Publication

Russia.

Translated Source

Journal of Experimental and Theoretical Physics (USA), vol.86, no.6, June
1998, pp.1122-6. CODEN: JTPHES. ISSN: 1063-7761.

Abstract

Using the imaginary time method, we study the structure of the perturbation series for the hydrogen atom in electric E and magnetic H fields. It is shown that there is a "critical" value of the ratio gamma =H/E at which the perturbation series for the ground state changes from having a fixed sign (for gamma < gamma /sub c/) to having a variable sign (for gamma > gamma /sub c/). This conclusion is confirmed by direct higher-order perturbation calculations. The change in the asymptotic regime is explained by competition among the contributions of the various complex trajectories that describe the subbarrier motion of the electrons. Here the parameter gamma /sub c/ depends on the angle theta between the electric and magnetic fields. (41 References).

Abstract Number

A9817-3450H-001

Subject Headings

Field ionisation
Ground states
Perturbation theory

Key Phrase Identifiers

weak fields; asymptotic behavior; higher order perturbation theory; imaginary
time method; perturbation theory series; ground state; complex trajectories;
atomic ionisation.

Classification Codes

Electronic excitation and ionization (atoms and molecules) [A3450H].

Treatment

Theoretical or mathematical.

CODEN

ZETFA7

Language

English.

ISSN

0044-4510.

U.S. Copyright Clearance Center Code

1063-7761/98/061122-5$15.00.

Document Number

S1063-7761(98)01006-3.

Publication Type

Journal Paper.

SICI

0044-4510(199806)113:6L.2047;1-B
1063-7761(199806)86:6L.1122:IAWF;1-L

Update Code

199830.

Copyright

Copyright 1998, IEE.

Accession Number

006050968

Author

Elout MO. Goodson DZ. Elliston CD. Shi-Wei Huang. Sergeev AV. Watson DK.

Institution

Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.

Title

Improving the convergence and estimating the accuracy of summation
approximants of 1/D expansions for Coulombic systems.

Source

Journal of Mathematical Physics, vol.39, no.10, Oct. 1998, pp.5112-22.
Publisher: AIP, USA.

Country of Publication

USA.

Abstract

The convergence of large-order expansions in delta =1/D, where D is the dimensionality of coordinate space, for energies E( delta ) of Coulomb systems is strongly affected by singularities at delta =1 and delta =0. Pade-Borel approximants with modifications that completely remove the singularities at delta =1 and remove the dominant singularity at delta =0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F( delta )= Sigma jE/sub j/'/j], where E/sub j//sup '/ are the the expansion coefficients of the energy with singularity structure removed at delta =1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H/sub 2//sup +/ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using F/sub m/( delta )= Sigma jE/sub j/'/ Gamma (j+1-m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy. (47 References).

Abstract Number

A9822-3115-003

Subject Headings

Atomic structure
Convergence
Ground states
Helium neutral atoms
Hydrogen ions
Molecular electronic states
Perturbation theory
Positive ions

Key Phrase Identifiers

convergence; large-order expansions; Coulomb systems; singularities;
Pade-Borel approximants; renormalization; interelectron repulsion; Borel
function; summation convergence; ground-state energies; He; H/sub 2//sup +/;
shifted Borel summation; 1/D expansions; H.

Classification Codes

General mathematical and computational developments for atoms and molecules
[A3115].

Treatment

Theoretical or mathematical.

Chemicals

He/el; H/el.

CODEN

JMAPAQ

Language

English.

ISSN

0022-2488.

U.S. Copyright Clearance Center Code

0022-2488/98/39(10)/5112(11)/$15.00.

Document Number

S0022-2488(98)04210-8.

Publication Type

Journal Paper.

SICI

0022-2488(199810)39:10L.5112:ICEA;1-S

Update Code

199841.

Copyright

Copyright 1998, IEE.

Accession Number

006093699

Author

Sergeev AV. Goodson DZ.

Institution

Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.

Title

Semiclassical self-consistent field perturbation theory for the hydrogen atom
in a magnetic field.

Source

International Journal of Quantum Chemistry, vol.69, no.2, 5 Aug. 1998,
pp.183-92. Publisher: Wiley, USA.

Country of Publication

USA.

Abstract

A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. (45 References).

Abstract Number

A9901-3120B-001

Subject Headings

Hydrogen neutral atoms
Magnetic field effects
Perturbation theory
SCF calculations

Key Phrase Identifiers

semiclassical self-consistent field perturbation theory; H atom; magnetic
field; self-consistent field equations; summable large-order expansions;
field strength; quantum state; adiabatic approximations; adiabatic
hypothesis; H.

Treatment

Theoretical or mathematical.

Chemicals

H/el.

CODEN

IJQCB2

Language

English.

ISSN

0020-7608.

U.S. Copyright Clearance Center Code

0020-7608/98/020183-10.

Publication Type

Journal Paper.

SICI

0020-7608(19980805)69:2L.183:SSCF;1-A

Update Code

199847.

Copyright

Copyright 1998, IEE.

Accession Number

006255458

Author

Goodson DZ. Sergeev AV.

Institution

Dept. of Chem., Southern Methodist Univ., Dallas, TX, USA.

Title

On the use of algebraic approximants to sum divergent series for Fermi
resonances in vibrational spectroscopy.

Source

Journal of Chemical Physics, vol.110, no.16, 22 April 1999, pp.8205-6.
Publisher: AIP, USA.

Country of Publication

USA.

Abstract

Pade summation of large-order perturbation theory can often yield highly accurate energy eigenvalues for molecular vibrations. However, for eigenstates involved in Fermi resonances the convergence of the Pade approximants can be very slow. This is because the energy is a multivalued function of the perturbation parameter while Pade approximants are single valued, and Fermi resonances occur when a branch point lies close to the physical value of the parameter. Algebraic approximants are multivalued generalizations of Pade approximants. Using the (200) state of H/sub 2/S and the (400) state of H/sub 2/O as examples of Fermi resonances, it is demonstrated here that algebraic approximants greatly improve the summation convergence. (10 References).

Abstract Number

A1999-13-3310-003

Subject Headings

Eigenvalues and eigenfunctions
Fermi resonance
Perturbation theory
Spectroscopy
Vibrational states

Key Phrase Identifiers

algebraic approximants; sum divergent series; Fermi resonances; vibrational
spectroscopy; eigenstates; perturbation theory; wave functions; strong
mixing; unperturbed harmonic eigenfunctions; resonant states; branch points;
eigenvalues; Riemann sheet; harmonic energies; branch point; convergence;
Pade approximants; rational functions; multiple-valued nature; algebraic
summation approximants.

Classification Codes

Vibrational analysis (molecular spectra) [A3310G]; Algebra, set theory, and
graph theory [A0210]; Molecular rotation, vibration, and vibration-rotation
constants [A3520P]; Specific calculations and results for atoms and molecules
[A3120].

Treatment

Theoretical or mathematical.

CODEN

JCPSA6

Language

English.

ISSN

0021-9606.

U.S. Copyright Clearance Center Code

0021-9606/99/110(16)/8205(2)/$15.00.

Document Number

S0021-9606(99)01216-7.

Publication Type

Journal Paper.

SICI

0021-9606(19990422)110:16L.8205:AADS;1-N

Update Code

199921.

Copyright

Copyright 1999, IEE.