Papers by Evgeni Solov'ev
Journal of Physics B: Atomic, Molecular and Optical Physics, 2001
A classification of hidden crossings in the three-body Coulomb problem is developed on the basis ... more A classification of hidden crossings in the three-body Coulomb problem is developed on the basis of hyperspherical adiabatic approach and approximate separability of the hyperspherical adiabatic eigenvalue problem in hyperspherical elliptic coordinates. For the case when two of three particles are identical we found two main types of hidden crossings which generalize the well-known S and T series of hidden
Journal of Experimental and Theoretical Physics
A general theory is considered of the scattering of electrons by a long linear chain in three-dim... more A general theory is considered of the scattering of electrons by a long linear chain in three-dimensional space; the chain consists of a large number of identical cells. Such a system has a translational symmetry, which is unusual in scattering problems. However, the symmetry is only approximate, because of the finiteness 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 (the analog of powder diagrams in x-ray structure analysis). As N ~ao, the averaged differential cross section changes discontinously at the angles 8 m = 2 arcsin('IT m I k d) (k is the momentum, d is the cell length, and m is an integer). The magnitude of the discontinuity is of the same order as the cross section itself at 8m , For long but finite chains, the singularities become less pronounced and the discontinuity is replaced by a shaTfl increase, the derivative of the differential cross section with respect to angle increasing linearly with increase in N A model calculation is carried out for chains consisting of wells of zero radius, and the results are compared with the general theory.
Physical Review A
The properties of the two-state approximation are considered from the p'oint of view of atomic co... more The properties of the two-state approximation are considered from the p'oint of view of atomic collision theory in the hmit 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 X-II 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-peturbation limit) the evolution operator to zeroth and first order in T is calculated. We introduce a general and unambiguous definition of an adiabatic basis as a basis of eigenvectors of the evolution matrix to zeroth order in T.
Journal of Experimental and Theoretical Physics - J EXP THEOR PHYS, 1974
We calculate the differential cross section for elastic scattering for the collision of a charged... more We calculate the differential cross section for elastic scattering for the collision of a charged particle and an excited hydrogen atom, a collision accompanied by transition between degenerate states of the atoms having the same principal quantum number n. The Schrodinger equation is solved in a basis of n 2 degenerate states of the atom; the dipole approximation is used for the interaction with the incident particle. The problem is solved in the quasiclassical approximation in the motion of the colliding particles; this approximation is constructed here in a somewhat modified form. This gives rise to dynamic wave functions of the quasimolecule, analogous to those obtained earlier in the nonstationary problem [11 and making it possible in this case to describe in a self-consistent manner the state of the atom and the motion of the colliding particles. Since the effective interaction depends strongly on the dynamic term, it follows that scattering through a given angle corresponds to several different quasiclassical trajectories, and this leads to interference oscillations in the cross sections. The mixing of 2s and 2p states is considered in detail.
Theoretical and Mathematical Physics, 1976
Physics Letters A - PHYS LETT A, 1998
The hidden crossings of rotational energy levels of a H2O molecule embedded in an electric field ... more The hidden crossings of rotational energy levels of a H2O molecule embedded in an electric field are studied. It is found that non-adiabatic transitions associated with the hidden crossings become significant if the product F0ω≥10−8, where F0 is the amplitude of the periodic field and ω is its frequency (both in atomic units).
The terms of the two-Coulomb-center problem are calculated in the complex plane of the internucle... more The terms of the two-Coulomb-center problem are calculated in the complex plane of the internuclear distance R. The calculations reveal term intersection (branch) points of a new type: the adiabatic terms ENLM(R) and EN+,,,,(R) successively intersect in pairs for all values of N (N, L , and M are the spherical quantum numbers of the united atom). At small values of M, the branch points are close to the real axis of R. This leads to the formation of infinite series of quasi-intersections than can be considered to be the result of the interaction of the diabatic term that goes over into the continuous spectrum with the Rydberg states of the quasimolecule. The cross section for ionization due to the evolution of the system along this diabatic term is obtained. The discovered branch points also play an important role in the united-atom approximation: the distance to them is the radius of convergence of the asymptotic expansions for R 4.
The equivalent second-order perturbation theory correction operators for the hydrogen atom in cro... more The equivalent second-order perturbation theory correction operators for the hydrogen atom in crossed electric and magnetic fields are computed with the aid of the Sturm basis. The corrections themselves are computed, and the question of the lifting the residual degeneracy in this order in the case of perpendicular fields is also investigated.
A method for calculating spectra of complicated systems in the quasiclassical approximation is pr... more A method for calculating spectra of complicated systems in the quasiclassical approximation is proposed, which is based on. the adiabatic invariance of quantum numbers; this enables one to avoid the basic calculational dificulties involved in finding caustics and fixing initial data for the quantized classical trajectories. The validity of this method is verified with the example of a two-dimensional anharmonic oscillator. The results of the adiabatic calculation are identical with those obtained previously by an exact direct quasiclassical calculation for this case. Some general questions connected with the application of the method are discussed.
Рассмотрен процесс выхода терма в сплошной спектр при сближе нии отталкивающего кулоновского цент... more Рассмотрен процесс выхода терма в сплошной спектр при сближе нии отталкивающего кулоновского центра и короткодействующего по тенциала. Получено поведение терма и ширины в окрестности границы сплошного спектра, а также соотношение, связывающее значение точки выхода терма в "сплошной спектр с параметрами, характеризующими потенциал.
A quasiclassical perturbation theory in the interelectron interaction is developed for equivalent... more A quasiclassical perturbation theory in the interelectron interaction is developed for equivalent electrons (n, = n,, where ni is the quantum number of the ith electron) with zero total angular momentum. The application of this theory to other states of a heliumlike system is considered.
Journal of Experimental and Theoretical Physics
Selective cross sections for (n,l) + (n',l') transitions between subshells of a Rydberg atom and ... more Selective cross sections for (n,l) + (n',l') transitions between subshells of a Rydberg atom and for ionization in a collision with a fast charged particle are derived in the binary approximation.
Mathematics, 2015
The relation between analyticity in mathematics and the concept of a global information field in ... more The relation between analyticity in mathematics and the concept of a global information field in physics is reviewed. Mathematics is complete in the complex plane only. In the complex plane, a very powerful tool appears-analyticity. According to this property, if an analytic function is known on the countable set of points having an accumulation point, then it is known everywhere. This mysterious property has profound consequences in quantum physics. Analyticity allows one to obtain asymptotic (approximate) results in terms of some singular points in the complex plane which accumulate all necessary data on a given process. As an example, slow atomic collisions are presented, where the cross-sections of inelastic transitions are determined by branch-points of the adiabatic energy surface at a complex internuclear distance. Common aspects of the non-local nature of analyticity and a recently introduced interpretation of classical electrodynamics and quantum physics as theories of a global information field are discussed.
Solid State Phenomena, 1998
Physical Review A, 2013
ABSTRACT The hyperspherical adiabatic curves (adiabatic eigenenergies as functions of the hyperra... more ABSTRACT The hyperspherical adiabatic curves (adiabatic eigenenergies as functions of the hyperradius R) of helium for zero total angular momentum are analyzed by studying the underlying classical dynamics which in the adiabatic treatment reduces to constrained two-electron motion on a hypersphere. This dynamics supports five characteristic classical configurations which can be represented by five types of short periodic orbits: the frozen planet (FP), the inverted frozen planet (IFP), the asymmetric stretch (AS), the asynchronous (ASC), and the Langmuir periodic orbit (PO). These POs are considered as fundamental modes of the two-electron motion on a hypersphere which, after quantization, give five families of so-called adiabatic lines (adiabatic energies related to these POs as functions of R). It is found that multiplets, each of them consisting of adiabatic curves which converge to the same ionization threshold, are at large values of R delimited from the bottom and from the top by the adiabatic lines which are related to the IFP and stable AS POs and to the FP PO, respectively. At smaller values of R, where the AS PO becomes unstable, the curves move to the area between the ASC (bottom) and AS (top) lines by crossing the latter. Therefore, at different values of R the lower limiting line of the multiplet is related to the three types of PO (IFP, AS, and ASC), which are all stable in the negative-energy part of this line. As a consequence, the quantum states of helium in principle are not related individually to a single classical configuration on the hypersphere. In addition, it is demonstrated that “unstable parts” of adiabatic lines (the so-called diabatic curves) determine the positions and type of avoided and hidden crossings between hyperspherical adiabatic curves. Two clearly visible classes of avoided crossings are related to the AS and ASC POs. In addition, a number of avoided crossings of the adiabatic curves is observed at the positions where the adiabatic lines that are related to different types of PO cross mutually. Finally, a class of hidden crossings which is located near the saddle point of the potential is related to the Langmuir orbit. The large spacing between adiabatic curves at the positions of these hidden crossings is explained by high instability of the Langmuir PO compared to the AS and ASC POs.
Theoretical and Mathematical Physics, 1977
Рассмотрен процесс выхода терма в сплошной спектр при сближе нии отталкивающего кулоновского цент... more Рассмотрен процесс выхода терма в сплошной спектр при сближе нии отталкивающего кулоновского центра и короткодействующего по тенциала. Получено поведение терма и ширины в окрестности границы сплошного спектра, а также соотношение, связывающее значение точки выхода терма в "сплошной спектр с параметрами, характеризующими потенциал.
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Papers by Evgeni Solov'ev