Sergey I. Vinitsky

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupledchannel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrodinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summary

Cosmological production of vector bosons and cosmic microwave background radiation

An intensive cosmological production of vector W and Z bosons is considered within a cosmological model that involves a relative scale of measurement. Field-theory models are studied in which cosmic microwave background radiation and baryon matter may appear as products of the decay of such primordial bosons.

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem ✩

article i nfo abstract A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm- Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for

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.

Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions

Symbolic-numerical algorithms for solving a boundary value problem (BVP) for the 2D Schrodinger equation with homogeneous third type boundary conditions to study the quantum tunneling model of a coupled pair of nonidentical ions are described. The Kantorovich reduction of the above problem with non-symmetric long-range potentials to the BVPs for sets of the second order ordinary differential equations (ODEs) is given by expanding solution over the one-parametric set of basis functions. Symbolic algorithms for evaluation of asymptotics of the basis functions, effective potentials, and linear independent solutions of the ODEs in the form of inverse power series of independent variable at large values are given by using appropriate etalon equations. Benchmark calculation of quantum tunneling problem of coupled pair of identical ions through Coulomb-like barrier is presented.

KANTBP 3.0: New version of a program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel adiabatic approach

A FORTRAN program for calculating energy values, reflection and transmission matrices, and corresponding wave functions in a coupled-channel approximation of the adiabatic approach is presented. In this approach, a multidimensional Schrodinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with the homogeneous boundary conditions of the third type at the left- and right-boundary points for continuous spectrum problem. The resulting system of these equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reflection and transmission matrices and corresponding wave functions for the two-dimensional problem with different barrier potentials.

Symbolic-Numerical Algorithms for Solving Parabolic Quantum Well Problem with Hydrogen-Like Impurity

For parabolic quantum well problem with hydrogen-like impurity a two-dimensional boundary-value problem is formulated in spherical coordinates at fixed magnetic quantum number. Calculational scheme using modified angular prolate spheroidal functions is presented. Symbolic-numerical algorithms for solving the problem are elaborated. The efficiency of the algorithms and their implementation is demonstrated by solving typical test examples and proving the compatibility conditions for asymptotic solutions of scattering problems in spherical and cylindrical coordinates.

A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in the magnetic field: cylindrical coordinates

The boundary problem in cylindrical coordinates for the Schrodinger equation describing a hydrogen-like atom in a strong homogeneous magnetic field is reduced to the problem for a set of the longitudinal equations in the framework of the Kantorovich method. The effective potentials of these equations are given by integrals over transversal variable of a product of transverse basis functions depending on the longitudinal variable as a parameter and their first derivatives with respect to the parameter. A symbolic-numerical algorithm for evaluating the transverse basis functions and corresponding eigenvalues which depend on the parameter, their derivatives with respect to the parameter and corresponded effective potentials is presented. The efficiency and accuracy of the algorithm and of the numerical scheme derived are confirmed by computations of eigenenergies and eigenfunctions for the low-excited states of a hydrogen atom in the strong homogeneous magnetic field.

A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in magnetic field

The boundary-value problem in spherical coordinates for the Shrodinger equation describing a hydrogen-like atom in a strong magnetic field is reduced to the problem for a set of radial equations in the framework of the Kantorovich method. The effective potentials of these equations are given by integrals over the angular variable between the oblate angular spheroidal functions depending on the radial variable as a parameter and their derivatives with respect to the parameter. A symbolic-numerical algorithm for evaluating the oblate spheroidal functions and corresponding eigenvalues which depend on the parameter, their derivatives with respect to the parameter and matrix elements is presented. The efficiency and accuracy of the algorithm and of the numerical scheme derived are confirmed by computations of eigenenergies and eigenfunctions for the low-excited states of a hydrogen atom in the uniform magnetic field.

Effective Adiabatic Approximation in the Problem of Three Bodies Coupled via Short-Range Potentials

The effective adiabatic approximation is constructed for the problem of three bodies on a straight line that are coupled via short-range attractive delta-function potentials. It is shown that, in this system, there arise a nonlocal momentum-dependent long-range effective potential and a polarization potential. A lower bound on the binding energy of the system is obtained to a relative precision of about 10−6. It is shown that, to within 0.03%, this approximation yields a correct asymptotic behavior of solutions and a correct behavior of the phase shift for elastic scattering at relative momenta below the three-body-breakup threshold. A local convergence of the adiabatic expansion in a finite interval of the radial variable is demonstrated.