The technique of calculating the matrix elements of spectroscopic quantities for complex atomic configurations

Abstract

The technique of calculating the matrix elements of spectroscopic quantities for complex atomic configurations

Kasprzhitskii A.S., Lazorenko G.I.,Yavna V.A.

Incoming article date: 30.12.2018

The paper presents an overview of the existing calculation schemes and the technique for obtaining the angular parts of the matrix elements of the spectroscopic quantities operators with the discussion of cases of complex electron configurations containing nonequivalent electrons. Using the example of a configuration with four unfilled electronic shells, the high efficiency of the technique for constructing wave functions of arbitrary electronic configurations is shown, based on a combination of Slater's determinant approach and the procedure for sequential coupling of orbital and spin moments on the basis of the Clebsch-Gordan coefficients in the LS coupling approximation.

Keywords: Slater determinant, Clebsch-Gordan coefficient, orbital angular momentum, spin moment, 3j-symbol, coefficients of fractional parentage, LS-coupling