Analytical expressions for special cases of LS-jj transformation matrices for a shell of equivalent electrons

TL;DR

This paper derives analytical formulas for specific LS-jj transformation matrices in atomic physics, facilitating faster calculations of energy level classifications while preserving key relativistic effects.

Contribution

It introduces analytical expressions for LS-jj transformation matrices for special electron configurations, improving computational efficiency over traditional recurrent methods.

Findings

Analytical formulas for transformation matrices are derived for specific cases.

The approach reduces computational time in atomic energy level analysis.

Preserves main relativistic effects in atomic state classification.

Abstract

Transformation matrices of the weights of the atomic wave functions in jj coupling to the relevant weights of LS coupling are considered for a shell of equivalent electrons. Their use allows one to preserve main part of relativistic effects but to classify the energy levels of an atom or an ion considered with the help of a set of quantum numbers of LS coupling scheme. Having in mind that the numerical values of the abovementioned transformation matrix (LS-jj) may be generally obtained in a very time consuming recurrent way, the analytical expressions of these matrices for a number of special cases of electronic configurations are presented.