Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

TL;DR

This paper develops a coupled tensorial form for two-electron operators in relativistic atomic systems using second quantization, providing a unified framework for different wave function symmetries.

Contribution

It introduces a general coupled tensorial formulation of two-electron operators in relativistic approximation, applicable to open-subshell atoms, using second quantization techniques.

Findings

Unified tensorial form for two-electron operators derived

Comparison of uncoupled, coupled, and antisymmetric wave functions provided

Framework applicable to relativistic atomic calculations

Abstract

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric two-electron wave functions in constructing coupled tensorial form of the operator are studied. The second quantization technique is used. The considered operator acts in the space of states of open-subshell atoms.