**Author****Sherstyuk A. I.**(?)**Title**- A theoretical study of the glass crystallization process by a differential thermal analysis system.
**Source**- Optiko-Mekhanicheskaya Promyshlennost, vol.33, no.2, Jan. 1966, pp.28-32. USSR.
**Abstract**- A method is discussed for the mathematical development of thermograms which make it possible to determine both the thermal effect of a reaction and also the temperature dependence of the relative rate of crystallization. The method is illustrated with a specific example.

**Author****Sherstyuk A. I.****Title**- Reduced Coulomb-Green function for the radial Schrodinger equation.
**Source**- Optika i Spektroskopiya, vol.30, no.2, Feb. 1971, pp.356-7. USSR.
**Abstract**- The application of perturbation theory to interelectronic interaction, using hydrogen-like functions as basis functions of the unperturbed problem, has recently gained popularity for computing the spectroscopic properties of atoms. In this case, it is convenient to use the Coulomb-Green function (CGF) g(x, x', E), for the computation of infinite series. An expression of the reduced CGF for calculating states with arbitrary values of principal quantum number n and azimuthal quantum number l is derived in this paper.

**Author**- Pavinskii P. P.,
**Sherstyuk A. I.** **Title**- Nuclear charge parameters for heavy ions and atoms.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.1, 1972, pp.155-6. USSR.
**Abstract**- Numerical values of the effective nuclear charges are quoted for l-shells of the atoms and ions, having eleven and twelve closed l-shells of electrons.

**Author****Sherstyuk A. I.****Title**- Perturbation of bound states of a Dirac equation for an electron in a central-symmetry field.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.62, no.4, April 1972, pp.1238-47. USSR.
**Abstract**- The correction to the wave function in the problem of perturbation of bound states of a Dirac electron in a Coulomb field by an arbitrary central-symmetry potential is represented as an expansion in the complete set of eigenfunctions of a Sturm-Liouville operator which processes only a discrete spectrum. This approach circumvents summation over continuous energy states with both negative or positive energies. Hence in a number of cases infinite sums of perturbation can be represented in a closed form. Finite expressions for first-order corrections to the electron Dirac wave function in the field of a screened Coulomb potential are obtained explicitly. The second and third order energies are expressed in terms of one of the components of the first order wave function.

**Author****Sherstyuk A. I.****Title**- Determination of closed expressions for the perturbation theory corrections to the wave functions of bound states by means of a Sturm function expansion.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.21, no.2, Nov. 1974, pp.224-32. USSR.
**Abstract**- By summation of expansions with respect to a complete system of eigenfunctions of a Sturm-Liouville type operator with only a discrete spectrum, closed expressions are obtained for the first- and second-order perturbation corrections to the wave function of an arbitrary bound state of an electron in a Coulomb field in the presence of a centrally symmetric perturbing potential.

**Author****Sherstyuk A. I.****Title**- Possibility of excluding a continuous spectrum from the calculation of electronic states of a molecular hydrogen ion. I. The Sturm expansion of the Green's function in two-centre problems.
**Source**- Optika i Spektroskopiya, vol.38, no.5, May 1975, pp.1040-2. USSR.
**Abstract**- The author shows through the development of the theory, that Sturm expansions can be used in calculations of two-centre systems. The author shows that the procedure may be developed to multicentred systems.

**Author**- Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Use of Coulomb functions with the effective orbital quantum number for the calculation of oscillator strengths in many-electron atoms.
**Source**- Optika i Spektroskopiya, vol.40, no.4, April 1976, pp.617-21. USSR.
**Abstract**- By using a modified Bates-Damgaard (BD) radial equation approximation the corresponding analytical radial function, P/sub nl/ can be obtained over the entire range of variation of r. This is used to calculate the oscillator strengths of a number of transitions in sodium and thallium atoms and this data is compared with that calculated using the unmodified BD Coulomb approximation.

**Author****Sherstyuk A. I.**, Yakovleva N. S.**Title**- Possibility of excluding the continuous spectrum from the calculation of electron states of the molecular hydrogen ion. II. Dependence of polarisability on internuclear distance.
**Source**- Optika i Spektroskopiya, vol.40, no.6, June 1976, pp.977-81. USSR.
**Abstract**- For pt.I see ibid., vol. 38, p.601 (1975). A method of independently calculating the contributions of each term in an expansion of the Green's function in partial spheroidal harmonics in the case of two Coulomb force centres is derived analytically and is applied to the calculation of the polarisability of the H/sub 2//sup +/ ion for internuclear distances in the range 0.4-3.4 atu range. Results are tabulated; figures for the dependence of the anisotropy of the polarisability on the internuclear distance are also given. It is shown that the main contribution of the polarisability comes from p-type states for all values of internuclear distance.

**Author****Sherstyuk A. I.**, Gruzdev P. F.**Title**- Sturm expansions in the Hartree-Fock method.
**Source**- Optika i Spektroskopiya, vol.42, no.6, June 1977, pp.1198-200. USSR.
**Abstract**- The possibility of forming the complete system of basis functions of a discrete spectrum for perturbation calculations of atomic steady states in the HF approximation is considered analytically.

**Author****Sherstyuk A. I.**, Yakovleva N. S.**Title**- Possibility of excluding the continuous spectrum when calculating the electronic states of the hydrogen molecular ion. III. Dynamic polarizability.
**Source**- Optika i Spektroskopiya, vol.43, no.5, Nov. 1977, pp.843-9. USSR.
**Abstract**- For pt.II see ibid., vol.40, p.560 (1976). The location of the poles of the two-center Coulombic Green's function in parameter space is investigated, and different possibilities for choosing a set of basic functions are examined. An expansion of the Green's function with respect to the complete set of Coulombic spherical functions of the purely discrete spectrum has been used to calculate exactly the dynamic dipolar polarizability tensor of the H/sub 2//sup +/ ion at different internuclear distances. The results of the calculations in the static limit are compared with the data existing in the literature.

**Author**- Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Choice of the spectrum of intermediate states in quantum-mechanical calculations.
**Source**- Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.41, no.12, 1977, pp.2477-85. USSR.
**Conference Information**- Proceedings of the All-Union Conference 'Modern Theory of Atoms and Atomic Spectra. Leningrad, USSR. 1-4 Feb. 1977.
**Abstract**- The possibility is investigated of using Sturm expansions of Green's functions for quantum mechanical systems of a sufficiently general form. The analysis presupposes that the various parameters in the initial Schrodinger equation are capable of quantisation and that this is also the case for the additional parameters that can be introduced by adding a certain self-adjoint operator to the Hamiltonian. The properties of the Green's function in the multidimensional parameter space can be used to obtain expansions over intermediate states related to a particular differential equation, and hence simple and convenient expressions for the corresponding Green's function. One-particle problem examples are treated. A new class of Sturm expansions over discrete spectrum states is found. Accurate physical variable estimation is possible.

**Author****Sherstyuk A. I.**, Shkol'nik A. M.**Title**- Analytic calculation of the bound states of a particle in a screened Coulomb potential.
**Source**- Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.41, no.12, 1977, pp.2648-54. USSR.
**Conference Information**- Proceedings of the All-Union Conference 'Modern Theory of Atoms and Atomic Spectra. Leningrad, USSR. 1-4 Feb. 1977.
**Abstract**- The application of a short range potential, in various aspects of physical science is briefly outlined. The static screened Coulomb potential is discussed, and the problem of determining the bound state energies in the field of this potential is examined. A possible method of obtaining exact analytic expressions for the energy and the wave functions of an arbitrary state, in theory, to any order of perturbation theory, is described, and a general expression for the energy of an arbitrarily bound state up to seventh order in chi is presented.

**Author****Sherstyuk A. I.**, Yakovleva N. S.**Title**- Possibility of excluding the continuous spectrum when calculating the electronic states of the hydrogen molecular ion. IV. Raman scattering.
**Source**- Optika i Spektroskopiya, vol.45, no.1, July 1978, pp.42-8. USSR.
**Abstract**- For pt.III see ibid., vol.43, p.499 (1977). The components of the tensor for Rayleigh and Raman scattering, including several of the first overtones, have been computed for a number of the lowest vibrational levels of the H/sub 2//sup +/ ion at different frequencies of the incident radiation. Corrections for anharmonicity have been taken into account in first-order perturbation theory.

**Author**- Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Relativistic generalization of the effective orbital quantum number method.
**Source**- Optika i Spektroskopiya, vol.46, no.4, April 1979, pp.625-30. USSR.
**Abstract**- Relativistic generalization of the effective orbital quantum number method is given. The method is illustrated by the calculation of oscillator strengths for the lines of the 3, 4p/sub 3/2,1/2/-3, 4d/sub 5/2,3/2/ transitions in the spectra of the atom and ions of the sodium isoelectronic sequence Na I-Mo XXXII. The results of the calculation are compared with the data available in the literature.

**Author**- Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Green's function for the Dirac equation with a nonlocal potential model.
**Source**- Optika i Spektroskopiya, vol.49, no.2, Aug. 1980, pp.216-20. USSR.
**Abstract**- The authors have obtained the Green's function for the Dirac equation with a nonlocal potential model.

**Author****Sherstyuk A. I.**, Yakovleva N. S.**Title**- Use of two-centre functions of purely discrete spectrum in adiabatic representation of three-body problem.
**Source**- Zhurnal Vychislitel'Noi Matematiki i Matematicheskoi Fiziki, vol.21, no.1, Jan. 1981, pp.113-26. USSR.
**Abstract**- A modification of the adiabatic representation in the three-body problem with Coulomb interaction is proposed, based on the use of the break-down of the three-particle wave function of the bound state into a full set of Sturn two-centre basic functions of the discrete spectrum. The advantages to be gained from the possibility of separating an edge problem in spheroidal coordinates into two independent one-dimensional Sturm-Liouville problems are discussed. The different possibilities offered by the selection of a random energy parameter are investigated.

**Author**- Yakovleva N. S.,
**Sherstyuk A. I.** **Title**- Calculation of parameters of H/sub 2//sup +/ ion interaction with external fields.
**Source**- Optika i Spektroskopiya, vol.50, no.5, May 1981, pp.823-5. USSR.
**Abstract**- The problem of the molecular hydrogen ion in the adiabatic approximation, the so-called problem of two Coulomb centers with charges Z/sub 1/=Z/sub 2/=1, is a test problem in the theory for diatomic molecules. Therefore, the most accurate calculations possible of the parameters of the H/sub 2//sup +/ ion interaction with external fields occupies a fundamental position from the point of view of testing various approximation methods for the calculations. The authors use the example of calculating various types of parameters for the interaction of the H/sub 2//sup +/ ion with external fields to demonstrate a fundamentally new method. This method is based upon the expansion of the two-center Green's function into a complete set of functions psi /sub n/ that are eigenfunctions of the operator S which arises in connection with problems dealing with two Coulomb centers.

**Author**- Rebane V. N., Rebane T. K.,
**Sherstyuk A. I.** **Title**- Possibility of observing the relaxation of higher polarization moments in electric-quadrupole radiation.
**Source**- Optika i Spektroskopiya, vol.51, no.5, Nov. 1981, pp.753-5. USSR.
**Abstract**- Shows that the study of the polarization characteristics of electric-quadrupole radiation will furnish valuable information on the magnitudes of higher polarization moments with kappa =3 and 4 and on the relaxation moments which remain hidden during the observation of dipole radiation.

**Author**- Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Relativistic Green's functions for atomic and molecular systems.
**Source**- Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.45, no.12, 1981, pp.2328-30. USSR.
**Conference Information**- Proceedings of the IV All-Union Conference on the Theory of Atoms and Atomic Spectra. Voronezh, USSR. 1-4 June 1980.
**Abstract**- The construction of the Green function for Dirac equations has been established for a wide class of one-electron potentials encountered in the theory of atoms and molecules; this has been done in the form of a spectral expansion with respect to the complete system of eigenfunctions for the generalized Dirac problem in terms of eigenvalues with a purely discrete spectrum.

**Author**- Sergeev A. V.,
**Sherstyouk A. I.** **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.
**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.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Calculation of the polarizability of the sodium atom from the Sturm virtual orbitals of the self-consistent-field method.
**Source**- Optika i Spektroskopiya, vol.53, no.1, July 1982, pp.3-5. USSR.
**Abstract**- A method for constructing a complete system of basis functions of a purely discrete spectrum was proposed previously (see Opt. Spektrosk., vol.42, p.1198, 1977, Opt. Spectrosc., vol.42, p.690, 1977) for the problem of the perturbation of the stationary states of atoms described in the Hartree-Fock approximation. The present authors report the first numerical implementation of this method. An algorithm has been developed and a program written for solving the system of integro-differential equations of the Hartree-Fock method to find the Hartree-Fock eigenvalues and eigenfunctions and also to determine the eigenvalues and virtual orbitals of the Sturm-Liouville problem. For the particular case of the sodium atom, the possibilities for obtaining purely discrete virtual orbitals is demonstrated.

**Author****Sherstyuk A. I.****Title**- Sturm expansions in many-fermion problems.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.56, no.2, Aug. 1983, pp.272-87. USSR.
**Abstract**- A generalization of the method of Sturm expansions is the basis of a systematic approach proposed for the construction of a complete system of intermediate states in the perturbation problem for stationary states of many-fermion systems. A time-independent expansion of the Green's function is constructed with respect to a complete set of antisymmetric functions, which include quasiparticle excitations of Sturm type. It is shown that in the case of single-particle perturbations one can completely avoid integration over continuum states, and in the case of perturbations that contain two-body interactions the multiplicity of the integrals can be significantly reduced. A diagram technique is developed for calculating the terms of the perturbation theory expansion.

**Author****Sherstyuk A. I.****Title**- Sturm spectral representations of Green's functions in the theory of many-fermion systems.
**Source**- Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.38, no.11, 10 Dec. 1983, pp.550-3. USSR.
**Abstract**- Spectral representations of one- and two-particle Green's functions are proposed. These representations do not involve an integration over intermediate states of the continuous spectrum.

**Author****Sherstyuk A. I.**, Yakushina IN.**Title**- Asymptotic expansion of eigenfunctions of discrete spectra in the problem of two Coulomb centres.
**Source**- Zhurnal Vychislitel'Noi Matematiki i Matematicheskoi Fiziki, vol.24, no.8, 1984, pp.1267-71. USSR.
**Abstract**- The authors use a standard equation to investigate the asymptotic expansion of eigenvalues and eigenfunctions arising in the problem of finding the base functions of discrete spectra employed in the calculation of the energy of the combined states in a three body system interacting according to Coulomb's law.

**Author**- Sergeev A. V.,
**Sherstyuk A. I.** **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.
**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.

**Author**- Soloveva G. S., Gruzdev P. F.,
**Sherstyuk A. I.** **Title**- Static polarizabilities of atoms and ions of the lithium, sodium, and potassium isoelectronic series and of neon and argon atoms calculated via SCF Sturm expansion.
**Source**- Optika i Spektroskopiya, vol.57, no.5, Nov. 1984, pp.776-9. USSR.
**Abstract**- A calculation of static polarizabilities of the ground valence states of atoms and ions for the isoelectronic series of lithium Li I-Ni XXVI, sodium Na I-Ni XVII, and potassium K I-Ni X has been carried out in second-order perturbation theory on the basis of Sturm virtual orbitals of the self-consistent Hartree-Fock field; also the polarizabilities of separate shells of neon and argon atoms were calculated.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Construction of a complete system of basis functions in terms of Sturm virtual orbitals of the self-consistent field method.
**Source**- Optika i Spektroskopiya, vol.58, no.2, Feb. 1985, pp.246-51. USSR.
**Abstract**- Various possibilities of generalizing the method of Sturm expansions of the Hartree Fock self-consistent field are considered using perturbation theory. The existence of several different representations of the single-electron Green's function of the self-consistent field method is shown. The formalism developed is used to calculate the static polarization of the ground 3s valence state of the sodium atom.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Calculation of the dynamic polarizability of the ground valence state of the atom and ions of the isoelectronic series of sodium, Na I-Ni XVIII.
**Source**- Optika i Spektroskopiya, vol.59, no.3, Sept. 1985, pp.495-500. USSR.
**Abstract**- The calculation of dynamic polarizability alpha ( omega ) has been done in the unbound variant of second-order perturbation theory over a wide range of frequencies omega for the ground valence state 3s of the atom and ions of the isoelectronic series of sodium, Na I-Ni XVIII. For the sodium atom and certain ions, the calculation of the quantities alpha ( omega ) has been done in two variants-the Sturm and the Schrodinger variants. the main tabular data of alpha ( omega ) numbers for the atom and ions of Na I-Ni XVIII has been obtained in the Schrodinger variant.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- A method of Sturm expansions of a self-congruent Hartree-Fock field and its use in calculating the static and dynamic polarizability of atoms and ions.
**Source**- Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.50, no.7, 1986, pp.1356-60. USSR.
**Conference Information**- Ninth All-Union Conference on the Theory of Atoms and Atomic Spectra. Uzhgorod, Ukrainian SSR, USSR. Sept. 1985.
**Abstract**- Following the work of A.I.
**Sherstyuk**et al. (1977) the authors use virtual Sturm orbitals to build the full system of based functions of a self-congruent Hartree-Fock field. This allows a better calculation, through the perturbation theory, of the interaction parameters between an atom or ion and an external electric or magnetic field.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Calculation of neon and argon static polarizabilities by the method of Sturm expansions of the Hartree-Fock self-consistent field.
**Source**- Optika i Spektroskopiya, vol.63, no.6, Dec. 1987, pp.1394-7. USSR.
**Abstract**- Calculates values of the static polarizability by the Sturm expansion method based on virtual orbitals of the Hartree-Fock self-consistent field. The calculation of the polarizability of neon and argon consisted of two steps. Initially the ordinary system of equations of the HF self-consistent field was solved. Further, using the wave functions P(nl; r) defined in the first step and taking into account the selection rules for calculation of the dipole polarizability of Ne and Ar, equations of the Sturm type are constructed.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Calculation of the dipole polarizability of the ground state of neon and argon atoms by the method of random phases with exchange, based on Sturm virtual orbitals of a self-consistent Hartree-Fock field.
**Source**- Optika i Spektroskopiya, vol.64, no.5, May 1988, pp.976-82. USSR.
**Abstract**- A method has been developed for using Sturm-type Hartree-Fock functions to study the reaction of a many-electron atom with an external field, account being taken of correlations of electrons in the random phase approximation with exchange.

**Author****Sherstyuk A. I.**, Yur'ev M. S., Yakovleva N. S.**Title**- Application of a continuous analogue of Newton's method for solving equations of a non-independent gas discharge.
**Source**- Zhurnal Vychislitel'Noi Matematiki i Matematicheskoi Fiziki, vol.29, no.2, 1989, pp.312-14. USSR.
**Abstract**- The spatial structure of an non-independent discharge for the whole of a discharge gap is examined without artificially fixing the boundaries of the pre-electrode layers. The method is described and results of a numerical solution of the problem are presented. Results are compared with those calculated by other authors.

**Author**- Firsova N. E.,
**Sherstyuk A. I.** **Title**- Some properties of the generalized spectral problems associated with the Schrodinger equation.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.81, no.1, Oct. 1989, pp.59-68. USSR.
**Abstract**- The manner in which the spectrum of generalized eigenvalue problems associated with a single-particle Schrodinger equation that depends on the form of the weight operator and the value of the energy parameter is investigated. Under fairly general conditions, the corresponding systems of eigenvalues realize diagonal representations of the Green's function and can be used to construct spectral expansions that are more convenient from the point of view of the nature of the spectrum.

**Author**- Afanaseva N. V.,
**Sherstyuk A. I.** **Title**- Study of alkali-atom spectra by the model-potential method.
**Source**- Optika i Spektroskopiya, vol.68, no.6, June 1990, pp.1225-31. USSR.
**Abstract**- The model potential with a linearly varying core charge is used for studying quantum defects of the Rydberg series of alkali atoms. An increase or decrease of quantum defects with a variation in the energy of the excited electron is explained by the formation characteristics of the supplementary potential well, formed by the core charge at distances R[left angle bracket]a/sub 0/, where a/sub 0/ is the radius of the core.

**Author**- Gruzdev P. F., Solov'eva G. S.,
**Sherstyuk A. I.** **Title**- Calculation of the coupling constants of many-electron atoms with external fields using expansions in a discrete basis of Sturmian-type virtual orbitals.
**Source**- Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, vol.33, no.8, Aug. 1990, pp.73-85. USSR.
**Abstract**- Based on a generalization of the method of Sturmian expansions to the case of many-electron systems, a fundamentally new approach was developed for the construction of a complete set of intermediate states in many-body perturbation theory thereby avoiding integration over states of the continuous spectrum. A complete system of eigenfunctions of the generalized eigenvalue problem for the one-electron Hartree-Fock equation with a factor before the energy operator and fixed values of the Lagrange multipliers is used as a basis of single-particle virtual orbitals for an initial approximation to the eigenfunctions of the Hartree-Fock self-consistent field method. In the case of bound states, the spectrum of the effective operator is purely discrete, thus permitting one to completely eliminate integration over continuum virtual orbitals in applying methods of many-body perturbation theory to atomic and molecular calculations for a number of cases. The possibilities of the developed approach are illustrated in application to the investigation of the interaction of many-electron atoms with external fields.

**Author**- Gruzdev P. F., Soloveva G. S.,
**Sherstyuk A. I.** **Title**- Polarizability of excited states of sodium and potassium atoms.
**Source**- Optika i Spektroskopiya, vol.71, no.6, Dec. 1991, pp.888-94. Russia.
**Abstract**- The scalar and tensor polarizabilities of a large number of nl states are calculated in the Coulomb approximation on the basis of previously obtained oscillator strengths of the transitions of a valence electron (l=0,1,. . .6). For states with l=0,1,2, satisfactory agreement with existing experimental and theoretical data is obtained. It is shown that the polarizabilities of states with l[right angle bracket]or=3 are described quite well by exact equations obtained for the hydrogen atom.

**Author**- Volkova G. A., Gerasimov G. N., Dubrovin A. N., Krylov B. E., Loginov A. V., Tveritinov M. P.,
**Sherstyuk A. I.**, Shishatskaya I. P., Yakovlev S. A. **Title**- Fundamental and applied studies of the spectra of atoms and simple molecules.
**Source**- Optiko-Mekhanicheskaya Promyshlennost, vol.60, no.11, Nov. 1993, pp.6-16. Russia.
**Abstract**- This paper presents the principal results in the area of fundamental and applied spectroscopy of atoms and diatomic molecules, achieved at the State Optical Institute during the past twenty-five years.

**Author****Sherstyuk A. I.****Title**- Expansions in a discrete basis set in a coupled variant of perturbation theory for atomic and molecular systems.
**Source**- Optika i Spektroskopiya, vol.78, no.3, March 1995, pp.357-9. Russia.
**Abstract**- To calculate the response of many-electron systems to an external perturbation, a modification of the coupled variant of perturbation theory was developed using an expansion in a complete set of the Hartree-Fock virtual orbitals of the Sturmian type. The orbitals are associated with the pure discrete spectrum of a generalized eigenvalue problem related to an effective one-particle operator that does not contain the self-action of electrons.

**Author****Sherstyuk A. I.**, Solov'eva GS.**Title**- Inner-shell correlations and Sturm expansions in coupled perturbation calculations of atomic systems.
**Source**- Optika i Spektroskopiya, vol.78, no.4, April 1995, pp.552-6. Russia.
**Abstract**- It is shown that virtual Hartree-Fock orbitals in Sturm-type expansions can be used to calculate the response of atomic systems to an external field within the framework of the coupled perturbation theory with allowance for correlation effects. The corrected electron-electron interaction in a system with field-distorted orbitals is considered by adding a nonlocal potential to a one-electron Hartree-Fock operator within each group of equivalent electrons. The remaining correlation effects are calculated by solving a system of equations for corrections to the radial functions. The system is solved iteratively, with each subsequent iteration corresponding to a correction of an increasingly higher order in the electron-electron interaction. The explicit expression derived for the polarizability contains one- and two-particle radial integrals of the Sturm functions.

**Author****Sherstyuk A. I.****Title**- Kinetics of radiative transitions in excimer systems with an additional source of narrowband radiation. The linear approximation.
**Source**- Optika i Spektroskopiya, vol.85, no.4, Oct. 1998, pp.561-5. Publisher: MAIK Nauka/Interperiodica Publishing, Russia.
**Abstract**- The frequency dependence of the gain is studied within a line of an additional narrowband radiation propagating in a medium of excimer molecules, when the radiation wavelength lies within an emission continuum of the main gas. Two cases are considered, in which an additional radiation can be produced by both an external source and an impurity gas uniformly distributed inside a gas-discharge tube.

**Author****Sherstyuk A. I.**, Bard'yan EA.**Title**- Kinetics of radiative transitions in excimer systems in the presence of additional narrow-band radiation: nonlinear effects.
**Source**- Optika i Spektroskopiya, vol.86, no.1, Jan. 1999, pp.113-15. Publisher: MAIK Nauka/Interperiodica Publishing, Russia.
**Abstract**- Amplification of intense narrow-band radiation is studied in a medium containing excimer molecules when the decay rate of radiative centers caused by induced radiation within the spectral line is comparable or greater than the nonradiative decay rate. It is shown that as the incident radiation intensity increases, the fraction of amplified spontaneous radiation in a molecular continuum decreases compared to the increased intensity of the emission line.

**Author****Sherstyuk A. I.****Title**- Generalized statement of the eigenvalue problem in the relativistic theory of atoms.
**Source**- Optika i Spektroskopiya, vol.87, no.5, Nov. 1999, pp.761-4. Publisher: MAIK Nauka/Interperiodica Publishing, Russia.
**Abstract**- A formalism is proposed for the construction of the Green function for the Dirac equation with non-Coulomb potentials in the form of spectral expansions in a discrete set of eigenfunctions of the generalized eigenvalue problem. The matrix structure of the weight operator is found, and the corresponding system of eigenfunctions is complete in the space of square integrable spinors, which makes it possible to obviate integration over the states of the upper and lower continua in the calculations made within the framework of the perturbation theory.

**Author****Sherstyuk A. I.****Title**- Spectral expansions of Green functions in the continuous spectrum in functions of Sturm type.
**Source**- Optika i Spektroskopiya, vol.87, no.5, Nov. 1999, pp.765-72. Publisher: MAIK Nauka/Interperiodica Publishing, Russia.
**Abstract**- A new method is developed for the construction of the Green function in the form of expansions in states of a purely discrete spectrum to calculate quantum processes involving states of a continuum. The approach proposed for this purpose is an extension of the method of Sturm expansions to the case of positive values of the energy parameter in the Green operator. By an example of calculation of dynamic polarizability at frequencies above the ionization threshold and processes of two-photon ionization of an atom, the expansions obtained are found to have an extremely rapid convergence.

A. I. Sherstyuk page (designed by A. Sergeev)