Vladimir L. Derbov

Calculation of a hydrogen atom photoionization in a strong magnetic field by using the angular oblate spheroidal functions

A new efficient method for calculating the photoionization of a hydrogen atom in a strong magnetic field is developed based on the Kantorovich approach to the parametric boundary problems in spherical coordinates using the orthogonal basis set of angular oblate spheroidal functions. The progress as compared with our previous paper (Dimova M G, Kaschiev M S and Vinitsky S I 2005 J. Phys. B: At. Mol. Opt. Phys. 38 2337–52) consists of the development of the Kantorovich method for calculating the wavefunctions of a continuous spectrum, including the quasi-stationary states imbedded in the continuum. Resonance transmission and total reflection effects for scattering processes of electrons on protons in a homogenous magnetic field are manifested. The photoionization cross sections found for the ground and excited states are in good agreement with the calculations by other authors and demonstrate correct threshold behavior. The estimates using the calculated photoionization cross section show that due to the quasi-stationary states the laser-stimulated recombination may be enhanced by choosing the optimal laser frequency.

Channeling problem for charged particles produced by confining environment

Channeling problem produced by confining environment that leads to resonance scattering of charged particles via quasistationary states imbedded in the continuum is examined. Nonmonotonic dependence of physical parameters on collision energy and/or confining environment due to resonance transmission and total reflection effects is confirmed that can increase the rate of recombination processes. The reduction of the model for two identical charged ions to a boundary problem is considered together with the asymptotic behavior of the solution in the vicinity of pair-collision point and the results of R-matrix calculations. Tentative estimations of the enhancement factor and the total reflection effect are discussed.

Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate representation and studied within the s-wave approximation. The symbolic-numerical algorithms for calculating the effective potentials of the close-coupling equations in terms of the cluster wave functions and the energy of the barrier quasistationary states are formulated and implemented using the Maple computer algebra system. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, the number of the particles A = 2,3,4, and their symmetry type, is analyzed. It is shown that the resonance behavior of the total transmission coefficient is due to the existence of barrier quasistationary states imbedded in the continuum.

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size, making use of the complete sets of exact and adiabatic quantum numbers in appropriate analytic approximations.

Symbolic-numeric algorithms for computer analysis of spheroidal quantum dot models

A computational scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications.

Resonant tunneling of a few-body cluster through repulsive barriers

A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s-wave approximation. A constructive method for symmetrizing or antisymmetrizing the (A − 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.

Interpretation of the time delay in the ionization of Coulomb and two-center systems

We consider the time delay of electron detachment from a Coulomb center and two-center systems in the process of ionization. It is shown that the attosecond streaking, most usual method of time delay measure, can be formally described by placing a virtual detector of the arrival time delay at a certain distance from the center of the system. This approach allows derivation of a simple formula for Coulomb-laser coupling that perfectly agrees with the results of numerical solution of ���� ���� ��� � �� ��� ��� ��� � �� �� �� �� �� �� �� � ��

Ionization excitation of diatomic systems having two active electrons by fast electron impact: a probe to electron correlation

(e, 2e) ionization excitation of diatomic hydrogen to the first dissociative state of H + by fast electrons is studied theoretically using the prolate spheroidal twocentre continuum numerical solutions to construct the partial-wave description of the slow ejected electron in a variety of situations. Our results confirm the fundamental role of the initial bound state ‘left–right’ correlation and show the breakdown of dynamical behaviours observed in the case of simple (e, 2e) ionization. Actually realizable complete experiments detecting the scattered and ejected electrons in coincidence with the bare detached nucleus are expected to verify our theoretical predictions.

Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions

The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

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