Second approximation of the generalized WKBJ method IV. Calculation of phase shifts for elastic scattering of electrons

The generalized WKBJ method is used to calculate the phase shifts for the elastic scattering of electrons by a central Hartree-Fock field described by means of a Gaspar potential, with an accuracy to terms of the order of ² inclusively. A calculation is made in this approximation for s-wave elastic scattering of electrons by mercury atoms.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 7, pp. 86–96, July, 1969.The author thanks L. A. Kronrod for carrying out the computer calculations.     

Second approximation of the generalized wkb method. I

Solutions are obtained for the one-dimensional Schrödinger equation corresponding to the second approximation of the generalized Wentzel-Kramers-Brillouin method (Petrashen-Miller-Good method). In the same approximation, the energy quantization conditions are found for bound particle states in a potential well.     

Elastic scattering of slow particles by some long-range potentials

We investigate the elastic s-scattering of slow particles by some model long-range potentials, obtained by joining the Coulomb potential to a polarization potential in the form-A · (r + a)^–4.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–79, August, 1972.     

The probability of potential barrier penetration in the generalized wkB approximation

The approximation method, discussed in [1], of calculating the coefficients of penetration through one-dimensional potential barriers is unsuitable at small values of the energy. In the present work this insufficiency is removed by applying some additional conditions to the basic potential W(S). A new solution is given for the problem of particle penetration through a symmetric barrier.     

Status of PERST-5 package

The methods and algorithms used in the PERST-5 package are described. This package is part of the MCU-5 code and is intended for neutron-physical calculation of the cells and parts of nuclear reactors using a generalized method of first collision probabilities.     

Towards a theory of the field emission of electrons

Application of a generalized WKB method to the investigation of the field emission of electrons from conductors and semiconductors is considered. Formulas are obtained for estimating the coefficients of transmission of electrons through a potential barrier created by an external electric field and the image force.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 7–13, November, 1972.     

Barrier-transmission probability in the extended petrashenfok method

The transmission coefficient of a one-dimensional barrier with a single peak of arbitrary shape is considered via Miller and Good 's [1] approximation, which is found to be very poor in the general case. A method of improving the approximation is presented.