Vladislav V. Serov

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field☆

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented.

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.

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.

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.

Wave-packet evolution approach to ionization of the hydrogen molecular ion by fast electrons

The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schrodinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.

Laser-induced radiative recombination of antihydrogen in a magnetic field through a quasi-stationary state

To increase the efficiency of laser-induced recombination of antihydrogen from cold antihydrogen—positron plasma in a trap, it is proposed to use a new resonance mechanism with the participation of positron quasi-stationary states, arising under the joint action of an antiproton Coulomb field and a strong magnetic field of the trap. The recombination rate is expressed through the atomic laser ionization cross section whose frequency dependence is nonmonotonic due to the presence of quasi-stationary states against the background of the continuum. The estimates with the use of the ionization cross sections calculated earlier demonstrate the possibility of improving the efficiency of the laser-induced recombination at an optimally selected laser frequency.

On an effective approximation of the Kantorovich method for calculations of a hydrogen atom in a strong magnetic field

A new effective method of calculating the wave functions of discrete and continuous spectra of a hydrogen atom in a strong magnetic field is developed based on the Kantorovich approach to the parametric eigenvalue problems in spherical coordinates. The two-dimensional spectral problem for the Schrodinger equation with fixed magnetic quantum number and parity is reduced to a spectral parametric problem for a one-dimensional equation for the angular variable and a finite set of ordinary second-order differential equations for the radial variable. A canonical transformation is applied to approximate the finite set of radial equations by means of a new radial equation describing an open channel. The rate of convergence is examined numerically and illustrated with a set of typical examples. The results are in good agreement with calculations by other authors.

Adaptive numerical methods for time-dependent Schrodinger equation in atomic and laser physics

Stable adaptive methods for solving the time-dependent Schrodinger equation (TDSE)) are considered in the framework of conventional finite-element representation of smooth solutions over coordinate spaces of a projective type with long derivatives. Generalization of Cranck-Nicholson scheme of forth order in time step is implemented. Projective “hidden variable” representation of strongly oscillating solutions is realized to extract explicitly the strongly variable gauge phase factor and to evaluate only the “pilot solution” which is reduced to a smooth envelope of the solution under consideration. Such an approach corresponds to the known transformation from Euler space variables to Lagrangian ones and the inducing characteristic representation of self-similar solutions widely used in the flow propagation problems. We study both smooth and strongly oscillating solutions of TDSE describing conventional atomic models in the laser pulse field. It is shown that for short-range potentials the “pilot solution” can be naturally interpreted as the spectrum of the outgoing wave. The examples considered show the efficiency and stability of the elaborated methods.

Application of Kantorovich method for calculations of a hydrogen atom photoionization in a strong magnetic field

A new efficient method of calculating the photoionization of a hydrogen atom in a strong magnetic field is developed basing on the Kantorovich approach to the parametric boundary problems in spherical coordinates. The progress as compared with our previous paper [SPIE Proc. 6165, p. 66−82, (2006)] consists in computation of the wave functions of continuous spectrum, including the quasi-stationary states imbedded in the continuum. The photoionization cross sections for the ground and excited states are in good agreement with the calculations by other authors.