**Author****Demkov****YuN**. Subramanyan R.**Title**- Motion of a particle in a linear periodic array of small radius potential wells in quantum mechanics.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.57, no.2, Aug. 1969, pp.698-702. USSR.
**Abstract**- The problem of motion of a particle in a one dimensional periodic array of small radius potential wells is considered. Closed expressions are obtained for the energy band, band width and effective mass of a particle moving in such a field. It is shown that for a well of arbitrarily small depth a negative energy state should exist. The wave function obtained is in fact a Green function and can be employed for solving the general problem of motion of a particle in the field of a linear periodic array in three dimensional space.

**Author****Demkov****YuN**. Monozon BS. Ostrovskii VN.**Title**- Energy levels of the hydrogen atom in crossed electric and magnetic fields.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.57, no.4, Oct. 1969, pp.1431-4. USSR.
**Abstract**- First and second perturbation theory approximation values of the energy level splitting of the hydrogen atom in uniform electric and magnetic fields of arbitrary mutual orientation are obtained. Symmetry of the four-dimensional Fock rotational group is used. Relativistic corrections and the spin-orbit interaction are not introduced. In a first approximation the result is the same as that obtained by the earlier Bohr theory. Cases are considered when degeneracy is not completely removed. In particular the case of mutually perpendicular electric and magnetic fields is analyzed.

**Author****Demkov****YuN**. Drukarev GF. Kuchinskii VV.**Title**- Negative ion decomposition in the short range potential approximation.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.58, no.3, March 1970, pp.944-51. USSR.
**Abstract**- The cross section for electron detachment in collisions between negative ions A- and atoms A are considered by the short range potential method. The adiabatic approximation is employed for quasi-stationary states; nonzero probability for survival of the A/sub 1//sup -/ systems is taken into account and correspondingly allowance is made for the energy dependence of the cross section. The energy distribution of the emitted electrons is calculated in the same approximation. The case of different atoms and ions (A/sup -/+B) can be reduced to the case (A/sup -/+A) by renormalizing the parameters of the problem. The results are illustrated by the process H/sup -/+H to H+H+e and are compared with the experiments and with other calculations.

**Author****Demkov****YuN**. Rudakov VS.**Institution**- Leningrad State Univ., USSR.
**Title**- Elastic scattering of electrons by molecules: partial wave method and zero-range approximation.
**Source**- 6th International conference on the physics of electronic and atomic collisions (abstracts). MIT Press. 1969, pp.851-3. Cambridge, MA, USA.
**Conference Information**- Cambridge, MA, USA. IPPS. Air Force Office of Sci. Res. Army Res. Office, Durham. Office Naval Res. Nat. Sci. Foundation. 28 July-2 Aug. 1969.
**Abstract**- Abstract only given substantially as follows. Neglecting the inelastic processes the authors consider the scattering of electrons by a molecule as a scattering of a plane wave by a nonspherical potential. They consider a special instance when the nonspherical potential is a sum of zero-range potentials. This problem can be solved exactly. A method of eigenfunctions of the scattering operator S, which is a natural extension of the usual partial wave method for spherically symmetrical potentials, is used.

**Author****Demkov**Yu N. Ostrovsky VN.**Institution**- Leningrad State Univ. USSR, USSR.
**Title**- Scattering of electrons by J/sub 2/ molecule, zero range potentials approximation and the trajectories of the S-matrix poles.
**Source**- 6th International conference on the physics of electronic and atomic collisions (abstracts). MIT Press. 1969, pp.1004-7. Cambridge, MA, USA.
**Conference Information**- Cambridge, MA, USA. IPPS. Air Force Office of Sci. Res. Army Res. Office, Durham. Office Naval Res. Nat. Sci. Foundation. 28 July-2 Aug. 1969.
**Abstract**- Abstract only given substantially as follows. The zero range potential model has been applied recently in the theory of electron detachment in collisions of negative ions with atoms and inelastic scattering of electrons by molecules. The authors extend this model using the multi-component wave function psi =( psi /sub 1/, psi /sub 2/, ..., psi /sub n/). Such extension allows them to take into consideration the inelastic processes.

**Author****Demkov****YuN**. Ostrovskii VN.**Title**- Zero range potential approximation and inelastic scattering of electrons by molecules. e+H/sub 2/ scattering.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.59, no.5, pp.1765-74. USSR.
**Abstract**- The zero range potential approximation is extended to the multi-channel case. By taking into account phenomenologically splitting of singlet and triplet molecular terms one can calculate in this approximation the cross section for excitation of the triplet state of a molecule by electron impact. The calculations are performed for the e+H/sub 2/ system. The term energies and widths for the H/sub 2/-molecular ion are calculated. Trajectories of the S-matrix poles on the complex energy surface are investigated as functions of internuclear distance.

**Author****Demkov****YuN**. Rudakov VS.**Title**- Partial wave method for a nonspherical scatterer.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.59, no.6, 1970, pp.2035-47. USSR.
**Abstract**- The S-representation for a nonspherical scatterer, which generalizes the ordinary phase shift method for the spherically symmetric problem, is considered. It is shown that for a low incident particle energy the phase behavior is analogous to that in the spherically symmetric case. The phases can be classified with respect to the azimuthal quantum number l, there being 2l+1 phases eta /sub l/ approximately E/sup l/+/sup 1///sub 2/. For a symmetric scatterer the partial waves and phases can be classified with respect to the symmetry group representations, degeneracy being defined by the dimension of the representation. The Hulthen-Schwinger variational principles, perturbation theory, virial theorem, Neuman-Wigner theorem on nonintersection of eta (E) curves related to a single representation of the symmetry group are formulated. The Levinson theorem which relates the phase behavior with the number of bound states is discussed. For the case when the scatterer can be represented as a superposition of n zero range potentials the problem reduces to a purely algebraic problem, to inversion of an n-th order matrix.

**Author****Demkov****YuN**. Ostrovskii VN. Berezina NB.**Title**- Uniqueness of the Firsov inversion technique and focusing potentials.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.60, no.5, 1971, pp.1604-10. USSR.
**Abstract**- By applying the Firsov inversion formula one can set up spherically symmetric systems possessing ideal focusing properties from the standpoint of geometric optics. The equivalent mechanical problem leads to force fields focusing particles with a given energy E. In particular the cut-off potential of a three dimensional harmonic oscillator focusses in the well edge a parallel beam of particles with an energy equal to the well depth. For particles with energies half the cut-off energy, the cut-off coulomb field potential is reflective. If the trajectory changes discontinuously with variation of impact parameter, the problem of determining the potential is non-unique; by prescribing almost arbitrarily the refractive index n(r) in one region the focusing conditions can be satisfied by selecting n(r) in another region. This arbitrariness can be exploited for elimination chromatic aberrating, selecting the region of variation of n etc.

**Author****Demkov****YuN**. Ostrovskii VN.**Title**- Intrinsic symmetry of the Maxwell 'fish-eye' problem and the Fock group for the hydrogen atom.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.60, no.6, 1971, pp.2011-18. USSR.
**Abstract**- As a particular case of the focusing potentials studied previously, a system is obtained which Maxwell called 'fish-eye'. The wave equation for this problem can be reduced to the Laplace equation on a four-dimensional sphere. Thus the symmetry group for this problem coincides with the hydrogen atom symmetry group found by Fock for a discrete spectrum. It is shown that the Maxwell potential possesses focusing properties in the wave sense, i.e. when diffraction is taken into account exactly. The Green function is found and generalizations of the fish-eye problem are considered.

**Author**- Adamov MN.
**Demkov****YuN**. Ob'edkov VD. Rebane TK. **Institution**- Leningrad Univ., USSR.
**Title**- Model of a small-radius potential for molecular systems.
**Source**- Teoreticheskaya i Eksperimental'Naya Khimiya, USSR.
**Abstract**- The problem of particle mobility in a field of an arbitrary number of force centers with a small action radius and in homogeneous electric or magnetic field is considered. An exact solution of the problem within the framework of the first-order perturbation over the wave function was obtained. The results may be used for the calculation of the polarizability and diamagnetic susceptibility of many- atom molecules.

**Author**- Devdariani AZ.
**Demkov****YuN**. **Title**- Quadratic approximation in the theory of electron detachment in the collision of a negative ion with an atom.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.3, 1971, pp.23-34. USSR.
**Abstract**- An accurate solution of the nonstationary problem of the ionisation of the bound state when the discrete level of time depending on energy operator reaches the boundary of the continuous spectrum only at the sole time moment has been obtained. In this case the approximation of zero range potential with the quadratic dependence of boundary condition from time may be used. The probability that electron remains in the bound state after interaction and distribution on the impulses of the detached electrons has been found. For the same case an accurate solution of the problem on scattering was obtained which made it possible to form complete S-matrix. The possibility of comparing the results obtained with those of experiments on the electron detachment at the collision of the negative ion with neutral atom has been considered.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Leningrad State Univ., USSR.
**Editor**- Branscomb LM; Erhardt H; Geballer R; de Heer FJ; et al.
**Title**- Adiabatic approximation for the electron detachment in slow atomic collisions.
**Source**- Abstracts of papers of the 7th international conference on the physics of electronic and atomic collisions. North-Holland. 1971, pp.1176-9. Amsterdam, Netherlands.
**Conference Information**- Amsterdam, Netherlands. IUPAP. UNESCO. N.V. Philips' Gloeilampenfabrieken. et al. 26-30 July 1971.
**Abstract**- The adiabatic approximation for the bound electronic states which is extensively used in the theory of slow automatic collisions is extended to include the case of quasistationary electronic states with complex E=E/sub 0/-/sup 1///sub 2/ Gamma . A consistent and general formulation is derived.

**Author****Demkov****YuN**. Ostrovskii VN.**Institution**- Leningrad State Univ., USSR.
**Title**- n+1 filling rule in the periodic system and focusing potentials.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, USSR.
**Abstract**- The Klechkovskii rule of filling of one-electron states in the periodic table is considered; according to this rule, levels with lowest values of N=n+l (sum of principal and orbital quantum numbers) are consecutively filled up, and for equal values of N the levels with smallest values of n are filled up. It is shown that for the potential U(r) approximately r/sup -1/(r+R)/sup -2/ which possesses special focusing properties and which closely resembles the Thomas-Fermi potential, additional degeneracy occurs for levels with identical values of N and an energy E=0. The degeneracy is lifted at E[left angle bracket]0 and the sequence of split levels corresponds to the second part of the rule. Good agreement is observed between values Z=Z/sub N/ for which levels with a given N appear in the model potential, and values of Z for which electrons with the same N values first appear in atoms in the periodic system.

**Author****Demkov****YuN**. Nikitin SI.**Institution**- Leningrad State Univ., USSR.
**Editor**- Cobic BC; Kurepa MV.
**Title**- Autoionizational decay of highly excited states of helium atom.
**Source**- 8th International Conference on the Physics of Electronic and Atomic Collisions (Extended abstracts). Inst. Phys. Part II, 1973, pp.531-2. Beograd, Yugoslavia.
**Conference Information**- Beograd, Yugoslavia. IUPAP. 16-20 July 1973.
**Abstract**- The authors consider the doubly excited states of helium atom with one electron in the state with n=2 and another electron in a highly excited state. Then due to the spacial separation of electrons the exchange can be neglected and the Coulomb electron-electron interaction can be taken into account by a dipole approximation.

**Author****Demkov****YuN**.**Institution**- Leningrad State Univ., USSR.
**Editor**- Cobic BC; Kurepa MV.
**Title**- Generalized Massey parameter for the exchange collisions.
**Source**- 8th International Conference on the Physics of Electronic and Atomic Collisions (Extended abstracts). Inst. Phys. Part II, 1973, pp.799-800. Beograd, Yugoslavia.
**Conference Information**- Beograd, Yugoslavia. IUPAP. 16-20 July 1973.
**Abstract**- Two heavy particles A and B exchanging a light one (with the mass m) during the collision are considered. The motion of A and B is considered as a classical one with the constant relative velocity v. Using the nonstationary perturbation theory the exchange amplitude is obtained. The generalized Massey parameter is determined using the method of steepest descent. Relativistic effects are considered.

**Author****Demkov****YuN**. Berezina NB.**Institution**- Leningrad State Univ., USSR.
**Editor**- Cobic BC; Kurepa MV.
**Title**- Low energy resonance scattering of electrons on Thomas-Fermi atoms.
**Source**- 8th International Conference on the Physics of Electronic and Atomic Collisions (Extended abstracts). Inst. Phys. Part I, 1973, pp.471-2. Beograd, Yugoslavia.
**Conference Information**- Beograd, Yugoslavia. IUPAP. et al. 16-20 July 1973.
**Abstract**- The Thomas-Fermi approximation is used. In the case of the nonzero orbital quantum number l the presence of the centrifugal barrier results in the appearance of the quasistationary states. They exhibit themselves in the resonance occuring at low energy. Using perturbation theory technique for the low-bound states i, the formula for the Thomas-Fermi quasilevels widths is obtained.

**Author****Demkov****YuN**. Devdariani AZ.**Institution**- Leningrad State Univ., USSR.
**Editor**- Cobic BC; Kurepa MV.
**Title**- The destruction of negative ions near the reaction threshold.
**Source**- 8th International Conference on the Physics of Electronic and Atomic Collisions (Extended abstracts). Inst. Phys. Part II, 1973, pp.840-1. Beograd, Yugoslavia.
**Conference Information**- Beograd, Yugoslavia. IUPAP. 16-20 July 1973.
**Abstract**- The collisions of slow negative ions with atoms are considered in the case when the potential curve of the molecular ion AB/sup -/ at some critical internuclear distance R/sub o/ crosses the potential curve of AB, i.e. at R[left angle bracket]R/sub o/ the AB/sup -/ state becomes unstable. For the description of the behavior of the AB/sup -/ system at R approximately=R/sub 0/ it seems reasonable to use the model of a small radius potential. In contrast with this, very slow collisions are considered here so that the kinetic energy of atoms is comparable with that of the detached electron and therefore the former cannot be considered as an infinite source of energy. Therefore the relative atomic motion must be considered together with the motion of an electron in the same quantum mechanical equation.

**Author****Demkov****YuN**. Berezina NB.**Title**- Energy levels in a Thomas-Fermi potential and their relation to atomic spectra.
**Source**- Optika i Spektroskopiya, vol.34, no.5, May 1973, pp.841-5. USSR.
**Abstract**- The Schroedinger equation was solved for most atoms in the periodic table for various bound states to give a graph of energy as a function of nuclear charge in the range 0-100 for all values of n and l. Indications of the behaviour of the energy curves near E=0 were obtained using the Tietz potential. The results are compared with those obtained from Hartree and Hartree-Fock methods. Results using Latter's method differ in the range of small mod E mod since he uses the Coulomb potential in conjunction with the Thomas-Fermi potential.

**Author****Demkov****YuN**. Los J.**Institution**- Leningrad State Univ., USSR.
**Title**- The giant glory effect in atomic collisions.
**Source**- Physics Letters A, vol.46A, no.1, 19 Nov. 1973, pp.13-14. Netherlands.
**Abstract**- The effect of total backscattering in elastic collisions from cut-off Coulomb potentials is discussed.

**Author****Demkov****YuN**. Kuchinskii VV.**Title**- Calculation of the distribution over vibrational and rotational states in the reaction A/sup -/+A to A/sub 2/+e by means of the generalized Franck-Condon principle.
**Source**- Optika i Spektroskopiya, vol.35, no.5, Nov. 1973, pp.804-8. USSR.
**Abstract**- Approximate formulae are derived for calculating energy and width of quasi-stationary terms of A/sub 2//sup -/ ions, cross-section for A/sup -/+A=A/sub 2/+e and electron distribution. First order perturbation theory for atoms with spin is considered and the method of calculation of population of vibrational-rotational states of the A/sub 2/ molecule discussed. Maps of population of vibrational-rotational states for H atom reaction are presented. Probability of dissociative breakaway of an electron in the H reaction is shown graphically.

**Author****Demkov****YuN**. Ostrovskii VN. Solov'ev EA.**Title**- Transitions between degenerate states of excited hydrogenlike ions in distant collisions with charged particles.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.66, no.1, Jan. 1974, pp.125-34. USSR.
**Abstract**- Transitions between n/sup 2/ degenerate states of an excited hydrogen-like ion (n is the principal quantum number) is considered for distant collisions between the ion and a heavy charged particle. The nuclei are assumed to move along classical trajectories, the interaction between them at large distances being close to Coulomb interaction. The nonstationary Schrodinger equation for electrons in the basis of n/sup 2/ degenerate states is solved exactly by employing the four-dimensional symmetry group for a non-relativistic hydrogen-like atom and the dipole approximation for interaction between an atomic electron and charged particle. The dynamic terms are found and also the corresponding quasi-molecule dynamic wave functions between which transitions do not occur during the collision. Interference between the states results in oscillations in the angular dependences of the transition probabilities between states with spherical quantum numbers. The limits of applicability of the theory are discussed. As an example the H/sup +/+He/sup +/(2s) to H/sup +/+He/sup +/(2p) reaction is considered in detail.

**Author****Demkov****YuN**. Ostrovskii VN. Solov'ev EA.**Title**- Scattering of electrons by long linear molecules. The effect of approximate translational symmetry.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.66, no.2, Feb. 1974, pp.501-8. USSR.
**Abstract**- A general theory is considered of scattering of electrons by a long linear chain in three-dimensional space; the chain consists of a large number of identical cells. This type of system possesses translational symmetry which is unusual in scattering problems; however, the symmetry is only approximate due to finite length of the chain. Scattering by finite chains consisting of N cells (polymer molecules) can be observed, the cross section being averaged over the chain orientations. For N to infinity the averaged differential cross section changes abruptly at angles theta /sub m/=2 arcsin ( pi m/kd) (k is the momentum, d the cell length and m is an integer). The magnitude of the discontinuity is of the same order as the cross section itself at theta /sub m/. For long but finite chains the singularities become less pronounced and the discontinuity is replaced by a sharp increase, the derivative of the differential cross section with respect to angle growing linearly with increase of N.

**Author**- Berezina NB.
**Demkov****YuN**. **Title**- Low-energy resonant scattering of electrons by Thomas-Fermi atoms.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.68, no.3, March 1975, pp.848-54. USSR.
**Abstract**- Scattering of electrons by atoms in the energy range from a fraction of an electron-volt to the first excitation potential is considered within the framework of the statistical model. It is of interest to elucidate the effect of energy levels entering the continuous spectrum with decrease of the atomic nucleus charge on the scattering process. The quasistationary states which are formed and whose width is calculated may be the cause of the appearance of a number of broad resonances in the slow electron scattering cross section. Curves of the dependence of the resonance scattering cross section on incident electron energy are presented for a number of atoms (22z[left angle bracket]or=[left angle bracket]or=26). These curves yield information on variation of the shape and positions of the resonances on variation of the nuclear charge. The behavior of the scattering length near the point of contact of the s-levels and the boundary of the continuous spectrum is analyzed.

**Author****Demkov****YuN**. Ostrovskii VN.**Title**- Asymptotic charge exchange theory for arbitrary velocities.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.69, no.5, Nov. 1975, pp.1582-93. USSR.
**Abstract**- An asymptotic (with respect to impact parameter) charge exchange theory is developed for arbitrary collision velocities. The dominant asymptotic amplitude term is calculated in the general nonresonant case for transitions between atomic s-states. The result is compared with data of various approximate methods. Concrete examples of resonance (p+H to H+p) and nonresonance (Li/sup +/+Na to Li+Na/sup +/) charge exchange processes are considered.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Editor**- Risley JS; Geballe R.
**Title**- Nonadiabatic asymptotical theory of charge transfer.
**Source**- International Conference on Physics of Electronic and Atomic Collisions. (Extended abstracts only received). Univ. Washington Press. Part I, 1975, pp.181-2. Seattle, WA, USA.
**Conference Information**- Seattle, WA, USA. IUPAP. US Nat. Sci. Found. et al. 24-30 July 1975.
**Abstract**- The asymptotical theory of generally non-resonant charge transfer is developed for large impact parameters rho . The formulation of the theory includes three important steps. 1. The exact identity for the charge transfer amplitude F( rho ) is obtained. 2. The integral is calculated for large rho by the stationary phase method for multidimensional integrals. 3. In the stationary phase point the corrections to the wave function are calculated by the method similar to semiclassical one.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Editor**- Risley JS; Geballe R.
**Title**- On the scattering from an inverse square potential.
**Source**- International Conference on Physics of Electronic and Atomic Collisions. (Extended abstracts only received). Washington Univ. Press. Part II, 1975, pp.656-7. Seattle, WA, USA.
**Conference Information**- Seattle, WA, USA. IUPAP. Nat. Sci. Found. et al. 24-30 July 1975.
**Abstract**- The small-angle scattering on the inverse square potential is considered as a simplified model for the scattering of charged particles on the systems with dipole moment. A formula is obtained which connects the quasiclassical region with the region of applicability of perturbation theory.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Editor**- Risley JS; Geballe R.
**Title**- The giant glory semiclassical calculations.
**Source**- International Conference on Physics of Electronic and Atomic Collisions. (Extended abstracts only received). Washington Univ. Press. Part II, 1975, pp.1017-18. Seattle, WA, USA.
**Conference Information**- Seattle, WA, USA. IUPAP. Nat. Sci. Found. et al. 24-30 July 1975.
**Abstract**- In atomic scattering, the cut off Coulomb potential, in the first approximation, describes the adiabatic interaction between halogen and alkali atoms. In real collisions where nonadiabatic transitions are negligible, e.g. Na+I, the deviation of the interaction potential from the Coulomb law has to be taken into account, along with quantum effects. The high frequency oscillations connected with glory are modulated by low frequency rainbow type oscillations in the differential cross-sections.

**Author**- Devdariani AZ.
**Demkov****YuN**. **Institution**- A.A. Zhdanov Leningrad State Univ., USSR.
**Title**- Dissociation and formation of negative ions in slow collisions with atoms. Allowance for the quantum-mechanical nature of the motion of atoms in the case of horizontal position of the boundary of the continuous spectrum.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.21, no.1, Oct. 1974, pp.74-85. USSR.
**Abstract**- In the framework of the method of the short-range potential, a study is made of the dissociation of negative ions in a collision, A+B/sup -/, and their creation in scattering, A+B+e. In contrast to earlier papers, the motion of the atoms is treated quantum-mechanically. If one makes the natural assumption that the term of the system AB depends weakly on the internuclear distance, the problem reduces to the solution of Helmholtz's equation on a half-plane with mixed boundary condition that depends linearly on the coordinate. An exact analytic solution of this problem is found. A formula is derived for the dissociation cross section near the reaction threshold. The conditions are investigated under which the formulas go over into those previously obtained for classical motion of the atoms.

**Author****Demkov****YuN**.**Title**- Some current problems in the theory of atomic collisions.
**Source**- Voprosy Teorii Atomnykh Stolknoveniya, no.1, 1975, pp.5-9. USSR.
**Abstract**- Presents a survey of the theoretical treatment of detachment of the electrons during slow atomic collisions. The discussion deals with the behaviour of quasi-steady-state terms in the complex energy plane, the energy spectrum of escaping slow electrons, approximation of small-radius potentials, isotopic effect for the dissociative capture, and with other problems. Particular attention is paid to the contributions from the theoretical group of Leningrad University.

**Author****Demkov****YuN**.**Title**- Electron detachment during slow collisions between atoms and ions.
**Source**- Voprosy Teorii Atomnykh Stolknoveniya, no.1, 1975, pp.87-102. USSR.
**Abstract**- Presents the results of examining several important characteristic aspects of processes taking place during collisions of slow atomic particles. A theory of these processes is formulated. Simple modelling representations are discussed, with the object of obtaining a clear description and understanding of the most significant factors, governing the dynamics of slow collisions of the atomic particles.

**Author****Demkov****YuN**. Ostrovskii VN.**Title**- Exchange excitation of atoms by high angular momentum electrons.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.73, no.3, Sept. 1977, pp.854-8. USSR.
**Abstract**- A parameter is found which describes the exponential decrease of the partial amplitudes for exchange scattering of high angular momentum electrons by atoms (involving, in general, the excitation of the atoms). The decrease slows down with increase of the collision energy. The contribution of the respective partial waves to the differential cross section contains a peak in forward scattering. The effective parameters describing the peak are discussed as well as the dependence of the peak shape on the properties of the wave functions of the initial and final atomic states.

**Author****Demkov****YuN**. Zaretskii DF. Karpeshin FF. Listengarten MA. Ostrovskii VN.**Title**- Distribution of muons among muonic atom fission fragments.
**Source**- Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.28, no.5, 5 Sept. 1978, pp.287-90. USSR.
**Abstract**- The probability of occurrence of muons in the light and heavy fragments following spontaneous fission of a muonic atom is calculated.

**Author****Demkov****YuN**. Ostrovskii VN. Solov'ev EA.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Title**- Two-state approximation in the adiabatic and sudden-perturbation limits.
**Source**- Physical Review a (General Physics), vol.18, no.5, Nov. 1978, pp.2089-96. USA.
**Abstract**- The properties of the two-state approximation are considered from the point of view of atomic collision theory in the limit of large and small values of a characteristic collision time T. For large T (the adiabatic limit) asymptotically exact expressions are obtained for the elastic-scattering phase shifts and for the nonadiabatic transition probability due to the pseudocrossing of terms. This approximation is carried out under fairly general assumptions about the Hamiltonian, enabling us to consider such processes as transitions between Sigma - Pi terms caused by rotation of an internuclear axis. Such general problems of the adiabatic approximation as the applicability of adiabatic perturbation theory, the introduction of a dynamical basis, and the properties of the electronic wave functions in the pseudocrossing region are discussed. For small T (the sudden-perturbation limit) the evolution operator to zeroth and first order in T is calculated. The authors introduce a general and unambiguous definition of an adiabatic basis as a basis of eigenvectors of the evolution matrix to zeroth order in T.

**Author****Demkov****YuN**. Kunasz CV. Ostrovskii VN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Title**- United-atom approximation in the problem of Sigma - Pi transitions during close atomic collisions.
**Source**- Physical Review a (General Physics), vol.18, no.5, Nov. 1978, pp.2097-106. USA.
**Abstract**- The authors consider a very simple approximation, in which the splitting of the energy of a P state in a united atom into Sigma and Pi quasimolecular terms for small internuclear distances R depends quadratically on R, and the colliding atoms pass one another along a straight or a hyperbolic trajectory. In this case the transition probability for a given scattering angle or impact parameter depends on only one parameter-the Massey parameter. This probability is computed numerically along with the elastic scattering phase shifts. Approximate formulas are obtained for both the adiabatic limit (in which the parameter is large and the flight is slow) and the sudden-perturbation limit for which the parameter is small, the flight is fast, and the process reduces to a sudden rotation of the internuclear axis. They also obtain, in the adiabatic case, the first term in the expansion of the factor in front of the exponential. In the intermediate range of the parameter, simple analytic approximations, ensuring transition to the limiting cases, are proposed. Analytic expressions for the total transition cross sections are obtained in the limits of large and small collision velocities. The results of the calculations are applicable to Sigma - Pi transitions of electrons and holes in both outer and inner shells for close collisions in a broad energy range, where, owing to a scale transformation, all cases reduce to one. Reasonable agreement is found with other more complicated calculations for the collisions of specific atoms.

**Author****Demkov****YuN**. Komarov IV.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Title**- Hypergeometric partial solutions in the problem of two Coulomb centers.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.38, no.2, Feb. 1979, pp.263-6. USSR.
**Abstract**- It is shown that for m=1, lambda =(z/sub 1/+or-z/sub 2/)R the Coulomb spheroidal functions can be expressed in terms of Whittaker functions. New partial solutions are constructed in the problem of two Coulomb centers.

**Author****Demkov**YN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Editor**- Damburg R.
**Title**- The development of ideas of V. Fock in atomic physics.
**Source**- Atomic Physics 6. Plenum. 1979, pp.65-76. New York, NY, USA.
**Conference Information**- Riga, USSR. 17-22 Aug. 1978.
**Abstract**- The influence of V. Fock's ideas and achievements on the development of atomic physics and quantum theory is reviewed.

**Author**- Varsimashvili KV.
**Demkov****YuN**. Ostrovskii VN. **Title**- An inverse scattering problem in the eikonal approximation.
**Source**- Yadernaya Fizika, vol.31, no.3, 1980, pp.816-20. USSR.
**Abstract**- The eikonal approximation for small-angle scattering is applied to express explicitly the interaction potential through the angle-dependent scattering amplitude at a fixed collision energy. The transition of the found solution of the inverse scattering problem to the classical scattering limit and to the perturbation theory (Born approximation) is investigated. The restraint on the angular and energy dependence of the amplitude is formulated to provide energy independence of the potential.

**Author****Demkov****YuN**.**Institution**- Phys. Dept., Leningrad State Univ., Leningrad, USSR.
**Editor**- Oda N; Takayanagi K.
**Title**- Zero range Fermi approach in negative ion detachment.
**Source**- Electronic and Atomic Collisions. Invited Papers and Progress Reports. Proceedings of the XIth International Conference on the Physics of Electronic and Atomic Collisions. North-Holland. 1980, pp.645-53. Amsterdam, Netherlands.
**Conference Information**- Kyoto, Japan. 29 Aug.-4 Sept. 1979.
**Abstract**- The zero range potential method is a natural approach to describe the processes involving negative ions. The low energy part of the detached electrons energy distribution obtained by this method agrees reasonably well with the experimental results. Some generalizations of the method are possible, allowing one to consider the relative motion of colliding atoms and ions quantum-mechanically, to treat the weakly-bound p-electrons and to apply the theory to the associative detachment processes.

**Author****Demkov****YuN**. Ostrovskii VN.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Title**- Analog of the Watson transformation for angular variables and scattering on the potential a/r/sup 2/.
**Source**- Teoreticheskaya i Matematicheskaya Fizika, vol.42, no.2, Feb. 1980, pp.223-31. USSR.
**Abstract**- A new representation is introduced for the angle-dependent amplitude of scattering on a spherical potential. This complements Watson's representation of the complex angular momentum and includes integration over the complex scattering angle. The proposed representation is particularly convenient for investigating questions associated with the quasiclassical limit. The properties of the representation are illustrated by the example of scattering on a potential inversely proportional to the square of the distance. The part played by orbiting and 'complex paths' is discussed, and a new closed expression is obtained for the amplitude in the eikonal approximation. The latter is also derived by an approximate summation of a partial-wave series.

**Author****Demkov****YuN**.**Title**- Classical problem of conformal small angle scattering.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.80, no.1, Jan. 1981, pp.127-43. USSR.
**Abstract**- On classical scattering of high energy particles or waves by a nonspherical scatterer into small angles, the mapping of the impact parameter plane onto the transferred momenta plane is conformal, providing the scatterer is harmonic (the potential energy satisfies the Laplace equation). A consequence is that complex variables can be employed in both planes and the calculations are thus simplified considerably. The rainbow lines (singularities of the differential cross section) in this case degenerate into focal points. A result is that even after averaging over the directions of the scatterer, singularities of the step type are retained in the cross section (halo effect) and can be observed on scattering of protons by molecules or by the crystal surface. Rigorous inequalities for the effective scattering cross section of a system of coulomb centers follow, in the case of small or relatively large transferred momenta, from the extremal properties of the conformal mapping onto a circle. The approximation is also applicable to the problem of scattering of a charged particle by a magnetic scatterer and hence may be used not only in atomic and nuclear problems but also in electron optics.

**Author****Demkov****YuN**.**Institution**- A.A. Zhdanov State Univ., Leningrad, USSR.
**Title**- Long-focal-length, all-wavelength telescopes with ultrahigh angular resolution.
**Source**- Pis'Ma V Zhurnal Tekhnicheskoi Fizika, vol.6, no.11-12, June 1980, pp.756-60. USSR.
**Abstract**- Telescopes with a large entrance-aperture radius R and a very large focal length F are impracticable for ground-based installations. However, systems with a very large focal length-comparable to the diffraction limit R/sup 2// lambda -offer a way to greatly relax the requirements on the accuracy of the fabrication of the objective, and in principle they offer a way to raise the angular resolution by several orders of magnitude. As an example, the author considers a Fresnel zone plate of radius R=10 m with n=100 zones (50 transparent and 50 opaque). The outer zone has a width Delta =R/2n=5 cm, and an absolute fabrication accuracy of 5 mm is quite adequate and easily arranged. Such a plate focuses electromagnetic radiation with a wavelength lambda =1 mu m at a distance F=R/sup 2//n lambda =1000 km; the diffraction spot for a point source is 5 cm in size. The width of the last Fresnel zone Delta is the same, and the angular resolution is 10/sup 7/. Such a telescope can be realized by mounting the focusing and detection systems independently on different astronomical bodies.

**Author****Demkov****YuN**.**Institution**- A.A. Zhdanov State Univ., Leningrad, USSR.
**Title**- Method of complex impact parameters for problems concerning small-angle scattering.
**Source**- Pis'Ma V Zhurnal Tekhnicheskoi Fizika, vol.6, no.13-14, July 1980, pp.833-7. USSR.
**Abstract**- The classical or quantum (eikonal method) small-angle scattering problem for a wide class of scatterers can in principle be simplified by introducing into the theory a new representation-a complex momentum transfer and a complex impact parameter. This becomes possible because scattering at small angles is an effectively two-dimensional problem, which allows one to use the powerful apparatus of the theory of functions of a complex variable.

**Author**- Abramov DI.
**Demkov****YuN**. Shcherbakov AP. **Title**- Scattering of charged particles by a system of Coulomb centers and factorization of the eikonal amplitude.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.80, no.4, 1981, pp.1334-47. USSR.
**Abstract**- Small angle scattering of fast particles (short waves) is considered in the eikonal approximation for a harmonic target when the interaction potential satisfies the Laplace equation; in particular, the scattering of charged particles by electric and magnetic fields is considered. The variables in the eikonal integral can be separated by introducing the complex plane of the impact parameter b and complex plane of transferred momentum p. The scattering amplitude can then be represented as the sum of the product of contour integrals which depend on p and p* respectively and can be expressed in terms of generalized hypergeometric functions. The particular cases of scattering by a system of charges, by two different, identical or opposite charges are considered. The limiting transition to a point dipole or to a coinciding charge and dipole is also studied. In all cases the scattering amplitude can be expressed in terms of generalized hypergeometric or confluent hypergeometric functions and various types of Bessel functions. The scattering amplitude in the vicinity of the focal points is also investigated.

**Author****Demkov****YuN**. Kondratovich VD. Ostrovski VN.**Title**- Electron interference during the photoionisation of atoms in an electric field.
**Source**- Pis'Ma V Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, vol.34, no.8, 20 Oct. 1981, pp.425-7. USSR.
**Abstract**- During photoionisation in homogeneous electric fields, the trajectories of electrons, emitted by atoms in various directions may cross at large distances from the atoms, which leads to the formation of an interference picture. In certain conditions this may be experimentally observed.

**Author****Demkov****YuN**. Drukarev GF.**Title**- Loosely bound particle with a nonzero orbital moment in an electric or magnetic field.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.81, no.4, 1981, pp.1218-31. USSR.
**Abstract**- A consistent analysis of the Schroedinger equation within a potential well is replaced by a boundary condition for the wave function at the surface of a sphere. The radius of the sphere and the binding energy of the particle in absence of a field are regarded as phenomenological parameters. Outside the boundary sphere the wave function is set up by differentiating the Green function for the particle in the electric or magnetic field. The energy shifts in weak and strong magnetic fields are calculated for the p-state. The condition for appearance of a bound state induced by a magnetic field is determined for the case when such states are absent in the absence of the field. The binding energy of the state is calculated. The energy shift and level width in an electric field are calculated. The dependence of the polarizability on binding energy is considered for various orbital moments.

**Author****Demkov****YuN**. Komarov IV. Shcherbakov AP.**Title**- Quasiclassical peculiarities of the scattering amplitude on small angles by non-spherical potentials.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.4, Nov. 1981, pp.18-23. USSR.
**Abstract**- The behaviour of the quasiclassical scattering amplitude on small angles is considered, when the differential cross section in classical mechanics has singularities. If a potential is a harmonic, i.e. it obeys the Laplace equation, the singularities lie at separate points in the impact parameter plane. The interference patterns of the scattering amplitude are discussed in detail, when two or more singularities coincide.

**Author**- Bogdanov IV.
**Demkov****YuN**. **Title**- New classical inversion formulae for centrally-symmetric electric and magnetic fields and the focusing potentials.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.82, no.6, June 1982, pp.1798-806. USSR.
**Abstract**- Some new inversion formulae for the classical scattering of charged particles by spherically- or axially symmetric electric and magnetic fields are derived for fixed values of the impact parameter or angular momentum. Focusing fields are found for various cases; they are similar to those considered earlier for scattering by an electric field at a fixed energy (of the backscattering, Maxwell 'fish-eye' or Luneberg lens type). A magneto-electric analogy is formulated: the existence of equivalent axially symmetric electric and magnetic fields which scatter charged particles in an identical manner.

**Author**- Bogdanov IV.
**Demkov****YuN**. **Title**- Firsov formula and spherically symmetrical scattering potentials for relativistic particles.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.4, Nov. 1982, pp.5-10. USSR.
**Abstract**- On the basis of the generalized optical-mechanical analogy the classical Firsov formula which reconstructs a spherically symmetrical scattering potential, using the scattering angle as a function of impact parameter at fixed energy, is extended to the relativistic case. Different kinds of focusing potentials including Maxwell's 'fish-eye' and Lenz's potentials are considered for the relativistic case. The wave-mechanical generalization of relativistic problems is also considered.

**Author**- Bydin YuF.
**Demkov****YuN**. **Institution**- V.I. Ul'yanov Leningrad Electrotech. Inst., A.A. Zhdanov Leningrad State Univ., Leningrad, USSR.
**Title**- Electron energy spectrum in low-energy collisions of negative ions and atoms.
**Source**- Uspekhi Fizicheskikh Nauk, vol.137, no.3, July 1982, pp.377-414. USSR.
**Abstract**- The theory for electron detachment in low-energy collisions of negative ions and atoms and experimental methods for studying this detachment are reviewed. Theory and experiment are compared, particularly with regard to the energy spectra of the emitted electrons. The relationship between electron detachment and nonequilibrium processes in plasmas is discussed, as is the relationship between detachment and the occupation of highly excited states of the colliding particles. The typical parameters of the process, the possibility of extracting them from theory and experiment, and the various theoretical methods and models for detachment and ionization are all discussed. The excitation and decay of approximately stationary states (autoionization and autodetachment states) of quasimolecules and also of isolated atoms and negative ions are discussed. Isotopic effects and the corresponding theory are discussed. Information on the behavior of unstable terms of the colliding atomic particles and of the widths of these terms cannot be obtained by other methods, so that this branch of the physics of atomic collisions may be singled out for separate discussion as the 'electron spectroscopy of unstable quasimolecular states'.

**Author****Demkov****YuN**. Ostrovskii VN. Shevchenko SI.**Institution**- Leningrad State Univ., Leningrad, USSR.
**Title**- Asymptotic theory of charge exchange for relativistic velocities and binding energies.
**Source**- Yadernaya Fizika, vol.37, no.1, Jan. 1983, pp.94-104. USSR.
**Abstract**- The asymptotic theory of charge exchange (for large impact parameters) is extended to the case of relativistic velocities and binding energies. The leading term in the asymptotic behaviour of the charge-exchange amplitude is calculated for 1S/sub 1/2/ to 1S/sub 1/2/ transitions.

**Author**- Adamov MN.
**Demkov****YuN**. Filinskii AV. **Title**- Variational calculation of the ground state energy of three-particle systems on the exponential basis.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.4, Nov. 1983, pp.73-6. USSR.
**Abstract**- The ground state energy of three-particle mesomolecules and exotic atoms is calculated on the purely exponential basis. The results obtained are lower than the results of much more accurate variational calculations.

**Author**- Bogdanov IV.
**Demkov****YuN**. **Institution**- Inst. of Phys., Leningrad State Univ., Leningrad, USSR.
**Title**- Inverse problems in classical scattering theory for centrosymmetric electric and magnetic fields.
**Source**- Journal of Physics A-Mathematical & General, vol.17, no.4, 11 March 1984, pp.L155-7. UK.
**Abstract**- New results are obtained in general scattering theory. The inverse scattering problem is solved in quadratures at a fixed impact parameter in classical mechanics. The inverse problem is analysed for a magnetic field at a fixed angular momentum and the magnetoelectric analogy is formulated. Focusing force electric and magnetic fields are constructed for charged particles with a specified angular momentum. The generalised optical-mechanical analogy is established. This analogy allows one to investigate some previously considered problems in the relativistic case.

**Author****Demkov****YuN**. Ostrovskii VN. Tel'nov DA.**Institution**- A.A. Zhdanov State Univ., Leningrad, USSR.
**Title**- New type of cross section singularity in backward scattering: the Coulomb glory.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.86, no.2, Feb. 1984, pp.442-50. USSR.
**Abstract**- For classical scattering by a central potential that exhibits Coulomb behavior (i.e., that is attractive) at small distances, the scattering angle theta tends to pi as the orbital angular momentum L decreases. The differential cross section for scattering through angles close to pi can be characterized by the power series expansion of the difference theta (L)- pi in small L, only odd powers of L being present in this expansion. Expressions are found for the coefficients in the linear (c/sub 1/) and cubic (c/sub 3/)-in L-terms. It is shown that, for a broad class of screened Coulomb potentials, the coefficient c/sub 1/ vanishes at some value of the collision energy E/sub 0/. At the energy E=E/sub 0/ the classical cross section diverges in the case of backward scattering (the Coulomb glory); in wave mechanics the cross section possesses a maximum. The behavior of the cross section for energies close to E/sub 0/ is computed. The application of the theory to electron scattering by atoms, in which the Coulomb interaction at small distances is determined by the interaction with the nucleus (charge Z) and E/sub 0/=0.0103Z/sup 4/3/ keV, is discussed.

**Author****Demkov****YuN**. Adamov MN. Ustimov VI.**Title**- Variational calculations of simplest atomic and molecular systems with trial binomial functions.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.4, Nov. 1986, pp.3-8. USSR.
**Abstract**- Variational calculations of ground state energies of H/sub 2//sup +/-ion and one- and two-electron atoms are made using trial binomial functions. Exponential functions are shown to be extremals in the subspace of binomial functions.

**Author****Demkov****YuN**.**Title**- Harmonic scattering.
**Source**- Vestnik Leningradskogo Universiteta, Fizika i Khimiya, no.2, June 1987, pp.31-40. USSR.
**Abstract**- An entirely new application of the plane conformal mapping method is found in the theory of classical small angle scattering of a charged particle by a static electro-magnetic field. Unlike usual applications the transition from three-dimensional problem to the plane one occurs automatically because each classical scattering problem is actually a mapping one from the impact parameter (target) plane onto the scattering sphere, and the small-angle scattering is a mapping from the target plane onto the transverse momentum plane. It is remarkable that for conditions mentioned above such a mapping is conformal, that allows to introduce complex variables on both planes, and this drastically simplifies all calculations, when this method is applied.

**Author****Demkov****YuN**. Ovchinnikov SYu.**Institution**- A.F. Ioffe Physicotech. Inst., Acad. of Sci., Leningrad, USSR.
**Title**- Nature of the narrow energy peak of positions produced in heavy-ion collisions.
**Source**- Zhurnal Eksperimental'Noi i Teoreticheskoi Fiziki, Pis'Ma V Redaktsiyu, vol.46, no.1, 10 July 1987, pp.14-16. USSR.
**Abstract**- Some of the positrons may be temporarily captured by an open resonator formed between two repulsive Coulomb center and undergo an adiabatic cooling as the nuclei fly apart. This suggestion agrees qualitatively with experiment.

**Author**- Bogdanov IV.
**Demkov**YN. **Institution**- A.A. Zhdanov State Univ., Leningrad, USSR.
**Title**- Determination of the internal structure of relativistic astrophysical objects in the wave approximation.
**Source**- Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol.93, no.1, July 1987, pp.3-16. USSR.
**Abstract**- Spherically symmetric inverse problems for the scattering of quantum particles by a static gravitational field are considered in the framework of the general theory of relativity. Methods are developed for recovering the metric tensor from scattering data at fixed energy or zero angular momentum for the Klein-Fock-Gordon equation in the Schwarzschild metric. The connection between the S matrix and the operator of the square of the 4-momentum in curved space is investigated. The main links of the developed algorithm are two definite nonlinear ordinary differential equations of third and fourth order constructed from the scattering data. On the one hand, the investigated inverse problems generalize the previously solved classical inverse problems for the gravitational field to the quantum case; on the other hand, they generalize the Marchenko and Regge-Newton methods known in quantum scattering theory to include the case of gravitational fields. A certain analogy is established between the motion of a scalar particle in a strong gravitational field and motion in a field with a potential that depends on the angular momentum or the energy in nonrelativistic quantum mechanics. This analogy makes it possible to model relativistic problems in the general theory of relativity by nonrelativistic problems. The results are also valid for electromagnetic waves and may be topical for direct determination of the internal structure of neutron stars by probing in the range of radio waves.

**Author****Demkov**YN. Karpeshin FF.**Institution**- Inst. of Phys., Leningrad State Univ., USSR.
**Title**- Thomas peculiarities in atomic and nuclear processes.
**Source**- Journal of Physics B-Atomic Molecular & Optical Physics, vol.22, no.4, 28 Feb. 1989, pp.L83-7. UK.
**Abstract**- The velocity-diagram method is used for determination of critical angles corresponding to three possible mechanisms of Thomas exchange scattering. Formulae for angles and relative velocities before and after collision, as well as kinematically allowed regions, are considered. Generalisation to relativistic collisions is considered using the Lobachevsky geometry. The singularities of the scattering amplitude for the Hulthen interactions (which give as limiting cases both the Coulomb and short-range forces) are studied. These singularities are simple poles in the Coulomb case but have logarithmic terms in the general case. Possible experiments are discussed to search for these peculiarities in atomic and nuclear collisions.

**Author****Demkov****YuN**. Karpeshin FF.**Institution**- Leningrad State Univ., USSR.
**Title**- Thomas scattering in nuclear reactions.
**Source**- Izvestiya Akademii Nauk SSSR Seriya Fizicheskaya, vol.54, no.1, 1990, pp.109-13. USSR.
**Conference Information**- 39th All-Union Conference on Nuclear Spectroscopy and the Structure of the Atomic Nucleus. Tashkent, USSR. April 1989.
**Abstract**- Thomas exchange processes for short-range nuclear forces are discussed. Expressions for the critical angles and relative velocities of the particles before and after scattering are obtained by the velocity-diagram method for colliding particles. The prospects for studying Thomas scattering in nuclear reactions are discussed.

**Author**- Clark CW.
**Demkov**YN. **Institution**- Center for Atomic, Molecular, & Opt. Phys., Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA.
**Title**- Making zone plates with a laser printer.
**Source**- American Journal of Physics, vol.59, no.2, Feb. 1991, pp.158-62. USA.
**Abstract**- A simple program is presented for producing zone plates on laser printers, and some of its results and possible applications are discussed.

**Author****Demkov****YuN**. Rebane TK.**Institution**- State Univ., Leningrad, Russia.
**Title**- Atomic and molecular magnetic moments related to the anomalous electron magnetic moment.
**Source**- Optika i Spektroskopiya, vol.71, no.5, Nov. 1991, pp.714-16. Russia.
**Abstract**- A theoretical study is made of the effect of the anomalous spin magnetic moment on the magnetic properties of atoms and molecules.

**Author****Demkov****YuN**. Karpeshin FF.**Institution**- St. Petersburg State Univ., Russia.
**Title**- Harmonic scattering of electrons and quadrupole moment of nucleus.
**Source**- Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, vol.56, no.1, 1992, Russia.
**Conference Information**- Forty-First All-Union Conference on Nuclear Spectroscopy and the Structure of the Atomic Nucleus. Minsk, USSR. April 1991.
**Abstract**- Small-angle scattering of fast electrons on deformed nuclei is considered in terms of the theory of harmonic scattering. The contribution of the quadrupole component to differential scattering caused by nuclear deformation is calculated. It is proportional to Q/sub 0//sup 2/ and for light and medium nuclei makes up approximately 1% of the contribution of Rutherford scattering.

**Author****Demkov****YuN**.**Institution**- St. Petersburg State Univ., Russia.
**Title**- Glory effect for the backscattering of negatively charged particles by multicharged ions.
**Source**- American Institute of Physics Conference Proceedings, no.274, 1993, pp.512. USA.
**Conference Information**- 6th International Conference on the Physics of Highly Charged Ions. Manhattan, KS, USA. 28 Sept.-2 Oct. 1992.
**Abstract**- The classical elastic backscattering of a charged particle by an attractive screened Coulomb potential has a singularity for an energy comparable with the potential energy of the screening potential at the origin. This result can be applied to the elastic and inelastic backscattering of electrons, mu-mesons and antiprotons by multiply charged ions.

**Author**- Bitensky IS.
**Demkov****YuN**. **Institution**- Dept. of Radiat. Sci., Uppsala Univ., Sweden.
**Title**- Thomas scattering of an ion from a solid surface.
**Source**- Surface Science, vol.319, no.1-2, 1 Nov. 1994, pp.199-206. Netherlands.
**Abstract**- The capture of an atom from a solid surface by a fast ion via double elastic collision (Thomas scattering) is considered. The rigid geometry of such a process, in which the scattering angles depend only on the masses of the colliding particles, gives the possibility to use this scattering for the determination of adatom location. The conditions for the experimental observation of Thomas scattering of an ion from a solid surface are discussed.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Inst. of Phys., St. Petersburg Univ., Russia.
**Title**- Crossing of two bands of potential curves.
**Source**- Journal of Physics B-Atomic Molecular & Optical Physics, vol.28, no.3, 14 Feb. 1995, pp.403-14. UK.
**Abstract**- Various problems in atomic physics can be formulated in terms of two bands of potential curves which cross each other. Each band consists of parallel (non-interacting) diabatic potential curves equally spaced on the energy axis. The bands with infinite number of states are considered under the assumption of 'translational' symmetry along the energy axis. The adiabatic potential curves are constructed explicitly. The system of avoided crossings appears not only in the weak coupling case (which is obvious), but also in the strong coupling limit. This feature also holds in the generalized model where the bands are finite and non-equidistant. In the case of an infinite number of states in each band the dynamic description (i.e. evolution in time) is reduced to the two-state problem which contains an additional continuous parameter (analogue of the quasimomentum). Some peculiarities of the time propagation are discussed. The present model generalizes the famous Landau-Zener two-state case and
**Demkov**-Osherov model (one level interacting with a band of levels).

**Author****Demkov****YuN**. Kurasov PB. Ostrovsky VN.**Institution**- Inst. of Phys., St. Petersburg Univ., Russia.
**Title**- Doubly periodical in time and energy exactly soluble system with two interacting systems of states.
**Source**- Journal of Physics A-Mathematical & General, vol.28, no.15, 7 Aug. 1995, pp.4361-80. UK.
**Abstract**- The time-dependent matrix Schrodinger equation 1/ic( delta Psi / delta t)=H(t) Psi describing two bands of an infinite number of equidistant states with different energy spacings omega /sub +or-/ in each band is studied. Both bands are linearly dependent on time t. The interaction upsilon =( square root ( omega - omega +)/ pi )tan pi s between the bands is considered to be equal for any pair of states from each band. Using the Fourier series transformation the instant eigenvalues E(t, s) are calculated which reveal the double periodicity in the energy-time plane. The corresponding eigenvalue surface in the (E, t, s)-space, apart from the triple periodicity, shows quite unexpected symmetry properties relative to the exchange of t and s, and relative to some inversions in the (E, t) plane. The latter one leads to a new equivalence between weak and strong coupling, a new kind of pseudocrossing and a new concept of antidiabatic states. The Fourier transformation reduces the problem to a 2*2 first-order differential operator. The diagonalization of H(r) for fixed t produces explicit expressions for the eigenvalues (adiabatic potential curves) and eigenstates (adiabatic basis). The time evolution operator is calculated both in the diabatic and adiabatic representations. The results are simplified for the special value of the interaction parameter.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Inst. of Phys., St. Petersburg Univ., Russia.
**Title**- Multipath interference in a multistate Landau-Zener-type model.
**Source**- Physical Review A, vol.61, no.3, March 2000, pp.032705/1-14. Publisher: APS through AIP, USA.
**Abstract**- The bow-tie model is a particular generalization of the famous two-state Landau-Zener model to an arbitrary number of states. Recently, solution of the bow-tie model was found by the contour integral method V.N. Ostrovsky and H. Nakamura, J. Phys. A 30, 6939 (1997). However, its physical interpretation remained unclear, because the model implies simultaneous strong interaction of all the states apparently irreducible to any simpler pattern. We introduce here a generalized bow-tie model that contains an additional parameter epsilon and an additional state. It includes the conventional bow-tie model as a particular limiting case when epsilon to 0. In the generalized model all the state-to-state transitions are reduced to the sequence of pairwise transitions and the two-state Landau-Zener model is applied to each of them. Such a reduction is well justified at least in the opposite limit of large parameter epsilon . Several paths connect initial and final states; the contributions of different paths are summed up coherently to obtain the overall transition probability. The special ET (energy and time) symmetry intrinsic for the generalized bow-tie model results in a particular property of interference phases: only purely constructive or purely destructive interference is operative. The complete set of transition probabilities is obtained in a closed form. Importantly, the results do not depend on the parameter epsilon . In the limit of conventional bow-tie model all previously derived results are reproduced. This amounts to rationalization of the bow-tie model by its interpretation in terms of multipath successive two-state transitions.

**Author****Demkov****YuN**. Puchkov AM.**Institution**- Inst. of Phys., St. Petersburg State Univ., Russia.
**Title**- Gravitational focusing of cosmic neutrinos by the solar interior.
**Source**- Physical Review D, vol.61, no.8, 15 April 2000, pp.083001/1-4. Publisher: APS through AIP, USA.
**Abstract**- The Sun is transparent for cosmic neutrinos with an energy less than 80 GeV. The interior part of the Sun forms for this radiation a high-quality gravitational lens with the focal distance F=24 AU (astronomical units)-the distance between the Uranus and Neptune orbit radii. The factors distorting the focusing are estimated. Among them are the spherical aberration, astigmatism caused by the rotation of the Sun, fluctuations of density connected with convection, and sunspots, etc. The lens has the unprecedented angular resolution about 1.4*10/sup -11/ rad. In focus the increase in intensity for the neutrinos flux from the center of Sirius is about a million times and even larger for more distant objects. This is only two orders of magnitude less than the flux of solar neutrinos on the Earth. Information about the solar interior can also be obtained by such observations. The resulting increase in intensity of the neutrino flux from the Sirius seems to open great possibilities in their detection even at the present virtual level of registration technique.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Inst. of Phys., St. Petersburg Univ., Russia.
**Title**- The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model.
**Source**- Journal of Physics B-Atomic Molecular & Optical Physics, vol.34, no.12, 28 June 2001, pp.2419-35. Publisher: IOP Publishing, UK.
**Abstract**- The generalized bow-tie model is a particular generalization of the famous two-state Landau-Zener model widely used in atomic physics and beyond. It comprises an arbitrary number of states; the diabatic-potential curves are linear functions of time whereas the coupling matrix elements are constant. We derive a rigorous solution of the model by the contour integral method. The complete set of transition amplitudes is obtained by considering solution asymptotes for t to +or- infinity . It agrees with the transition probabilities evaluated earlier by heuristically appealing but non-rigorous reduction of the model to the sequence of two-state transitions. An unusual quasi-factorization property of the transition amplitude matrix is established. The entire matrix is expressed via a single complex-valued vector.

**Author****Demkov****YuN**. Ostrovsky VN.**Institution**- Inst. of Phys., St. Petersburg Univ., Russia.
**Title**- Enhanced backscattering in antiproton-atom collision: Coulomb glory.
**Source**- Journal of Physics B-Atomic Molecular & Optical Physics, vol.34, no.18, 28 Sept. 2001, pp.L595-9. Publisher: IOP Publishing, UK.
**Abstract**- The head-on collisions of an antiproton with an atom result in backscattering due to the attractive Coulomb p-nucleus interaction. Accounting for the screening of the Coulomb potential by atomic electrons leads to amplification of the backscattering. The effect is manifested at collision energies of about 2 keV, when the extended range of impact parameters contributes to the differential cross section at scattering angles close to 180 degrees . Our calculations for the representative case of p-Xe collision characterize quantitatively the main features of such a Coulomb glory phenomenon.

Information about Yu. N. Demkov (reproduced by A. Sergeev)