Proposal No
APPLICATION FORM
ISF LONG-TERM RESEARCH GRANTS PROGRAM.
1. Sherstyuk Aleksey Ivanovich.
2. ÿÑpßã_^ ǽÑ^ßÑ` êóá¡3a. 17 June 1937.
3b. Leningrad (at present St.-Petersburg).
4a.Passport Seria XIV-AK No 732463.
4b. Date of Issue:28 March 1980. Place:Leningrad.
5. Russia.
6a. Leading Researcher,Head of Research Group.
6b. All-Russian Scientific Center"S.I.Vavilov State
Optical Institute".
7a. 12 Birzevaya line,St.-Petersburg 199034,Russia.
7b. Tel.:(812)218-99-42. 7c.Fax:(812)350-99-93.
7d. E-mail:sergeev@soi.spb.su (for A.I.Sherstyuk).
8a. P.O. D-14,Box 95,St.-Petersburg 191014,Russia.
8b. Tel.:(812)279-38-02.
9a. Doctor of Physics and Mathematics
9b.1986 9d. Ph.D./Kandidat 1973.
9c. Leningrad State University. 9e.S.I.Vavilov State
Optical Institute
10. Development of new approach to atomic and molecular
processes calculations based on the generalization of
Sturmian-type expansions method to many-electron systems.
11. Physics I (mathematical physics),Physics IV(atomic and
molecular physics).
12. Requested Amount
First Year Second Year Total
$10,000 $9,300 $19,300
13.Requested duration. Two years 1994-1995.
14. By signing this application I certify that I meet all
the eligibility requirements of this announcement and
that I am prepared to honor all the conditions of this
program.
Signature:
Date: 17.09.93
15. Other Participating Researchers.
(1) a. Solov'eva Galina Semenovna
b. 5 December 1944
c. S.I.Vavilov State Optical Institute,St.Petersburg
d. Scientific Researcher
e. Passport: XXIII-AK, No 585758
f. 25 June 1993, St.Petersburg
g. Ph.D./Kandidat
h. 1987
(2) a. Bardjan Eduard Alekseevich
b. 1 June 1973
c. Precise Mechanics and Optics educational Institute
d. IV year student.
e. Passport: XX-AK, No 711266
f. 22 August 1989, Leningrad
g. Have hot degree
16. Official who will have fiduciary responsibility for
management of indirect costs
a.Gorbunov Bores Vasilievich b. Director c. Optical
Instrumentation and Photo-Engineering Research Institute,
belonging to the all-Russian Scientific
Centre "S.I.Vavilov State Optical Institute".
d.12 Birzheraya line, St. Petersburg 199034, Russia
e. Tell.:(812)218-75-26/Fax:(812)218-21-33
f. E-mail:leader@soi.spb.su
17. Abstract:The long-term scientific objective of the
project is development and improvement a new approach
to protractive calculations of various properties of
many-electron systems based on the use of spectral
expansions in the full sets of Sturmian-like Haltere-
Voc virtual orbitals belonging to pure discrete
spectrum. The specific aim of the project is extending
the scope of applicability of the method on reference
to the full consideration of electron correlation and
relativistic effects.
We are intend:1) To develop a version of Feynman-Gold-
stone diagram technique by including the expansions in
Sturm-type non Coulomb intermediate states. 2) To inves-
tigate the peculiarities of the spectrum of the genera-
lized eignvalue (Sturmian) problem connected with Dirac
Hartree-Fock equations with various weight operators.
3) To test the abilities of the method by carrying out
the concrete calculations of various physical properties
(polarizabilities,hyperpolarizabilities,multiphoton
transition probabilities etc.) of open shell systems
with accounting of the correlation and relativistic ef-
fects. 4) To investigate the connection of the genere-
lized Sturmian approach with the dynamical symmetry of
the systems meaning the application to semi-classical
calculations.
18. Suggested Expert Reviewers.
(1) Brian G. Wybourne, Professor, N. Copernicus Univer-
sity, Institute of Physics, ul. Grudziadzka 5/7,
PL-87-100,Torun,Poland. E-mail:bgw@risc.phys.torun.edu.
pl
(2) A.Dalgarno,Professor, Institute for Theoretical Ato-
mic and Molecular Physics,Harvard-Smithsonian Center for
Astrophysics, 60 Garden Street, Cambridge, Massachusetts
02138,USA
(3) Robin Shakeshaft, Professor,University of Southern
California, Los Angeles, California 90089-0484,USA
Paper:Sturmian basis calculations... J.Opt.Soc.Amer.,1990,
7,433.
(4) Donald R.Beck, Professor, Physics Department, Michi-
gan Tehnological University,Haugton,Michigan 49931, USA
Paper:Relativistic many-body results...Phys.Rev.A,1991,
44,758..
(5) Popov Vladimir Stepanovich,Professor,Institute of
Theoretical and Experimental Physics,Bol'shaya
Cheremushkinskaya 25,Moscow 117259,Russia.Tel.:
(095)123-97-61; (095)438-40-64.E-mail:popov@compnet.
npimsu.msk.su Paper: Strong field Stark effect...
Phys.Lett., 1990,149,418.
(6) Braun Mikhail A., Professor, Faculty of High-Energy
Physics and Elementary Particles St.-Petersburg State
University,St.-Petersburg 198904, Russia. Tel.:(812)
428-75-90, E-mail: braun@onti.phys.lgu.spb.su
Publication: Book:"Relativistic atomic theory",Moscow,
"nauka",1984 (in Russian).
Attachment a.
Research statement.
a. Specific Goals of the project are development and
improvement of the new approach to calculations of various
properties of many-electron systems based on the use of
spectral expansions in the discrete-basis-sets of Sturm-type
virtual orbitales. We intend to study the possibilities of the
method in reference to calculations accounting the electron
correlation and relativistic corrections.
b. Background and Significance. The advantages of Sturmian
basis calculations as applied to one-particle (hydrogen-like)
perturbation problem are wide known. But a generalization of
the method to non-Coulomb and many-particle systems is faced
with certain difficulties. Our approach to the problem is
based on the using of expansions in the eigenfunctions of the
generalized eigenvalue problem connected with a suitable
unperturbed operator,e.g.Hartree-Fock operator. With the
proper choice of a weight operator we do receive a full set of
square integrable basis functions belonging to pure discrete
spectrum and hence we avoid the troubles connected with the
integration over the continuum of the intermediate states.
c. Preliminary Studies. We used originally the hydrogen-like
discrete-basis functions (conventional Sturmian basis) for
determination of closed form expressions for perturbation
theory corrections to wave functions of bound states of atoms
in [6](here and further we use the publication list number)
and in the earlier publications. The generalization of
Sturmian expansions on the two-center (molecular) Systems has
been proposed in [7]. The possibility of employment of
Sturmian-type basis in the perturbation theory problem in
Hartree-Fock method was initially proposed by us in 1977 [8].
A systematic approach to the construction of the complete set
of the Sturmian-type intermediate states in the many-fermion
bound state perturbation calculations was suggested in
[9,10],where the conventional diagram technique was adapted
for the calculations with the use of the quasi-particle
Sturmian-like expansions. Later,on the basis of developed
approach it was carried out the calculations of various atomic
properties(mainly static and dynamic polarizabilities
[1,4,5]). The convergence of all the expansions has been
proved to be very rapid. So,the calculations become extremely
simple and hence more reliable in comparison with calculations
based on conventional approach.
The mathematical groundwork of generalized eigenvalue
problem connected with the Schredinger equation has been
presented in [2]. The topical review of modern state of the
problem has been published in my paper in "Problems of
Theoretical Physics"III,in Leningrad University Press,1988,p
90-114.
d. Research Design and Methods.
1. In the proposed project we intend to carry out an
investigation directed to expanding of the scope of
applicability of early developed generalized Sturmian approach
to the case of calculation of quantum processes in many-
electron systems with accounting of the correlation and
relativistic effects.
We are considering the generalized ½- eigenvalue problem
for the equation:(Ho-e)f=½gf, where Ho is unperturbed (in our
case usually Hartree-Fock) operator, g is a weight operator.
The character of the spectrum of such equation can be assigned
by suitable choice of g, which may in particular be any part
of Ho. The set of eigenfunctions(Sturmian-like functions)
determine the diagonal expansion of the Green's function of
Ho. The main impediment which arises when Ho is many-particle
Hamiltonian operator consist in difficulty of simultaneous
satisfaction both condition of full division of variables and
the elimination of continuous spectrum from the expansion of
full many-particle Green's function.
In the independent particle approximation the problem is
simplified. The one-particle Green's function can be always
represented as expansion in the discrete series of Sturmian-
like virtual orbitales. Two-particle Green's function has a
more complex structure. Since the perturbation calculations of
atomic and molecular processes do involve,generally
speaking,the two-particle Green's functions,our specific goal
is to formulate approximation in which such calculations do
not involve the integration over continuous spectrum at all.
To this effect we may consider a Feynman-Goldstone diagram
technique including the electron propagators expanded in
Sturmian-like intermediate states. The special attention in
this approach will be paid to the choice of appropriate
classes of diagrams(as in RPAE). On the other hand, it is
expected to be suitable in the concrete calculations to use
some modification of the coupled Hartree-Fock perturbation
theory with summations only over pure discrete intermediate
states. We intended to obtain as result a very simple and
reliable method of ab initio calculations of the atomic and
molecular processes.
Further,with the use of developed approach the various
physical properties (e.g. polarizabilities,hyperpolarizabi-
lities,van der Waals coefficients,multiphoton transition
probabilities etc.) will be calculated and received numerical
results will be compared with the existed theoretical and
experimental data. A special attention will be paid to the
convergence studies of the used expansions.
At the same time, the methods of calculation of molecular
processes with the use of two-centre Sturmian virtual orbitals
will be developed for many-electron molecules.
2. In the calculations of processes in highly ionized atoms
it is essential to use the relativistic theory. In this case
we must examine the generalized eigenvalue problem containing
a Dirac operator with an arbitrary potential energy term. The
construction of the pure discrete set of eigenfunctions in
this case is faced with difficulties connected with the choice
of such a weight operator that ensure simultaneous elimination
of the integrations over both positive and negative continuum.
We intend to overcome this difficulty by appropriate
introduction of projection operators. We also intend to
investigate the peculiarities of the spectrum of the resulting
eigenvalue problem with various weight matrix-operators.
3. We intend to investigate the connection of solutions of
Sturmian eigenvalue problem with dynamical symmetry of the
system,having in mind facilitation of the calculations of the
relevant matrix elements and subsequent construction of
generalized cogerence states essential to semi-classical
calculation.
The obtained results will be submitted to Phys. Review A,
JOSA, Journ, of Exper. and Theor.Phys.(Russian),Optics
and Spectroscopy (Russian).
Attachment b.
PROPOSAL BUDGET on 1994.
ISF LONG-TERM RESEARCH GRANTS PROGRAM.
Principal Investigator's Name: Proposal Number:
Sherstyuk A.I.
1. Individual Finansical Funds Funds
Support Requested Granted
by Proposer by ISF
A. Principal Investigator.
Amount per month: $300.
Number of months : 12.
Total A: $3600 $
B. Other investigators.
1. Solov'eva G.S.(She will be working out the procedure of
numerical soolution of the generalized eigenvalue problem
resulting from Hartree-Fock and Hartree-Fock-Dirac equations
with various type of weight operators).
Amount per month: $150.
Number of months: 12.
Total B: $1800. $
C. Student: Bardjan E.A.(He will be taking part in the
studies the connection of the solutiolns of Sturmian
eigenvalue problem with dynamical symmetry of the
system).
Amount per month: $50.
Number of months: 9.
Total C: $450 $
2. Equipment and Supplies.
Computer PC/AT 386 ($950).
Total equipment and supplies: $950 $
3. International Travel. (Travel of one participant (with
report) on 26 EGAS Annual International Conference on
Atomic Spectroscopy which will be held in
Barselona, Spain in July 1994).
Total International Travel: $550. $
4. Other Direct Costs.
a. Matherials and Supplies
(Purchase of Typewriter ($200) and
Minicalculatirs ($50))
Total A $250 $
B. Communications
(Expenses connected with preparation and sending
scientific papers. Reception of foreign scientists)
$250 $
C. Internal Travels
(Participation in the domestic conferences on atomic,
molecular physics and laser physics)
$150 $
Total Other Direct Costs $650 $
5. Total Direct Costs (1+2+3+4) $8000 $
6. Total Indirect Costs (25%*Line5) $2000 $
7. Total Direct and Indirect Costs $10000 $
PROPOSAL BUDGET on 1995.
ISF LONG-TERM RESEARCH GRANTS PROGRAM.
Principal Investigator's Name: Proposal Number:
Sherstyuk A.I.
1. Individual Finansical Funds Funds
Support Requested Granted
by Proposer by ISF
A. Principal Investigator.
Amount per month: $300.
Number of months : 12.
Total A: $3600 $
___B. Other investigators
1. Solov'eva G.S.(She will be calculating
on the base of Sturmian-like expansions
approach to precise values of various atomic
parameters (e.g. polarizabilities, multiphoton
transitions probabilities and so on) with accounting
of correlation and relativistic effects).
Amount per month $150
Number of Months 12
Total 1B $1800 $
C. Student
1. Bardjan E.A. (He will be taking part in the
investigation of properties of generalized coherent states
constructed with the aid of Sturmian eigenfunctions
and it's application to the semi-classicaL l calculation)
Amount per month $50
Number of months 9
Total 1C. $450 $
Total Individual Finansical
Support $5850 $
2. Equipment and Supplies
Facsimile machine ($600)
Total Equipment and Supplies $600 $
3. International Travel
Travel of one participant on 27 EGAS Annual International
Conference on Atomic Spectroscopy.
July 1995.
Total International Travel $450 $
4.Other Direct Costs.
A.Materials and Supplies.
(Purchase of Typewriter) $200 $
B.Communications.
(Expences connected with the preparation and
sending of scientific papers. Reception of the
foreign scientists) $200 $
C.Internal Travels.
(Participation in the domestic conferences
on atomic and molecular physics) $150 $
Total Other Direct Costs $550 $
5.Total Direct Costs (1+2+3+4) $7450 $
6.Total Indirect Costs (25%xLine5) $1862 $
7.Total Direct and Indirect
Costs (5+6) $9312 $
Attachment c.
Biographical sketch of Sherstyuk A.I.(PI)
I was born in Leningrad in 1937. Married. I have a son of
eleven years old. I was graduated as theoretical physicist
from Physics Department of Leningrad State University in 1960.
Since 1961 I am working in S.I.Vavilov State Optical
Institute in St.-Petersburg (Leningrad).
My scientific work has been devoted to theoretical investi
gations in varied directions of fundamental and applied
researches,mainly in theoretical atomic spectroscopy,optics,
magnetic resonance. At present,the main direction of my work
is development and application of new mathematical methods of
calculations of structure and physical parameters of atomic
and molecular systems, namely:1. The calculations of
various atomic and molecular properties with the use of new
approach based on the generalization of Sturmian expansion
method to many-electron systems. 2. The development of new
methods of the summation of the divergent perturbation theory
series and application of them to calculations of
quasistationary and Rydberg states of atomic systems in the
strong external fields.
Now I am Doctor of Science,leading researcher,head of
research group in the Laboratory of atomic and molecular
spectroscopy of S.I.Vavilov State Optical Institute.I am
member of scientific Council on Theoretical Physics at St.-
Petersburg State University. I have over 100 scientific
publications on various theoretical topics in atomic,molecular
and solid state physics.
Biographical sketch of Solov'eva G.S.
I was born in Leningrad in 1944. I was graduated from
Physics Department of Leningrad State University in 1967.
I am working in S.I.Vavilov State Optical Institute.
My scientific work was devoted to theoretical investigations
of electronic-vibrational spectra of molecules. Now the main
direction of my work is theoretical
calculations of structure and physical parameters of atoms
and atomic ions.
At present I am working as scientific researcher in the
Laboratory of atomic and molecular spectroscopy S.I.Vavilov
State Optical Institute. Kandidat of Physics and Mathematics
from 1987. I have 22 scientific publications in various topics
of atomic and molecular physics.
Attachment d.
List of Publications of Sherstyuk A.I. (PI).
1.Gruzdev P.F.,Solov'eva G.S.,Sherstyuk A.I. Calculation of
dipole polarizabilities of the ground states of Ne and Ar
Optika i spectroscopia,1988,64,976-982.
2.Firsova N.E.,Sherstyuk A.I.On properties of generalized
eigenvalue problems related to the Schredinger equation.
Teoreticheskaya i matematicheskaya fizika,1989,81,59-68.
3.Afavasjeva N.V.,Sherstyuk A.I. Study of Alkali atoms by
the model potential.Optika i spectroskopia,1990,68,
1225-1231.
4. Gruzdev P.F.,Solov'eva G.S.,Sherstyuk A.I.Use of the
expansions on discrete basis of the Hartree-Fock
virtual Sturmian-type orbitals for evaluation of many
electron atoms with external fields.Izvestiya vysshih
uchebnykh zavedenii seriya fizika,1990,33,73-85.
5. Gruzdev P.F.,Solov'eva G.S.,Sherstyuk A.I.The
polarizabilities of excited states of Na and K.
Optika i spektroskopiya,1991,71,888-893.
6. Sherstyuk A.I.Perturbation of bound states of a
Dirac equation for an electron in a central-symmetry
field.Zhurnal eksperimentalnoi i teoreticheskoi fiziki,
1972,62,1238-1247.
7. Sherstyuk A.I. On the possibility of elimination of
continuous spectrum in calculation of electronic states
of hydrogen molecular ion.I.Optika i spectroskopiya,1975,
38,1040-1042; III,ibid,1977,43,843-849.
8. Sherstyuk A.I.,Gruzdev P.F.On the use of Sturmian expan-
sions in Hartree-Fock method.Optika i spectroskopiya,1977
42,1198-1200.
9. Sherstyuk A.I.Sturmian spectral representations of Green's
functions in many-fermion theory. Pisma v zhurnal
eksperimental'noi i teoreticheskoi fiziki,1983,38,550-
553.
10. Sherstyuk A.I.Sturmian expansions in the many-fermion
problem.Teoreticheskaya i matematicheskaya fizika,1983,
56,272-287.
List of Publications of Solov'eva G.S.
1. Gruzdev P.F.,two co-authors.Calculation of dipol
polarizabilities of Ne and Ar in RPAE with the use of
Sturmian virtual Hartree-Fock self-consistent field
orbitales.Optika i spectroskopya,1988,64,976-982.
2. Gruzdev P.F.,two co-authors.Use of the expansions in
discrete basis of the Hartree-Fock virtual Sturmian
-type orbitals for evaluation of interaction with
external fields.Izvestiya vysshih uchebnykh zavedenii
seriya fizika,1990,33,73-85.
3. Gruzdev P.F.,two co-authors. The polarizabilities of
excited states of Na and K. Optika i spectroskopiya,
1991,71,888-893.
Attachment e.
OTHER SOURCES OF SUPPORT
Investigator's Name: Sherstyuk A.I.
1.Support:Pending.
Project: Development of novel methods for calculations of
many-electron systems in a strong external field with the use
of improved summation procedure in high-order perturbation
theory.
Source of support: American Physical Society.
Annual Rate: $500.
Period Covered: 1993.
Location of Research: S.I.Vavilov State Optical Institute.
2.Support: Pending.
Project: Mathematical investigation of the generalized
eigenvalue problem with various weight operators.
Source of Support: American Mathematical Society.
Awared Amount: $50.
Period Covered: 1993.
Location of Research: S.I.Vavilov State Optical Institute.
3.Support: Current.
Source of Support: St.Petersburg Physical Society.
Project: Squarre-integrable basis for the calculations of
above-threshold multiphoton transitions.
Award Amount: $10.
Period Covered: 1993.
Location oof Research: S.I.Vavilov State Optical Institute
4. Support: Current.
Source of Support: International Science Foundation.
Projecy: Development of novel methods of quantum mechanical
calculation and application of them to the precise
calculations of various atomic and molecular properties.
Awared Amount: $500.
Perios Covered: 1993.
Location of Research: S.I.Vavilov State Optical Institute.
Investigator's Name: Solov'eva G.S.
Have not other sources of support.
Investigator's Name: Bardjan E.A.
Have not other sources of support.
Back to A. I. Sherstyuk.
Designed by A. Sergeev.