Proposal No APPLICATION FORM ISF LONG-TERM RESEARCH GRANTS PROGRAM. 1. Sherstyuk Aleksey Ivanovich. 2. ÿÑpßã_^ Ç½Ñ^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.

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