Irreducible tensor-form of the relativistic corrections to the M1 transition operator

TL;DR

This paper derives an irreducible tensor-operator form of relativistic corrections to the M1 transition operator, facilitating atomic structure calculations using Fano-Racah-Wigner algebra.

Contribution

It introduces a new tensor-operator formulation of relativistic M1 corrections for improved atomic structure computations.

Findings

Provides explicit tensor-operator form for relativistic M1 corrections

Enables more accurate matrix element calculations in atomic physics

Facilitates implementation in atomic structure codes

Abstract

The relativistic corrections to the magnetic dipole moment operator in the Pauli approximation were derived originally by Drake (Phys. Rev. A 3(1971)908). In the present paper, we derive their irreducible tensor-operator form to be used in atomic structure codes adopting the Fano-Racah-Wigner algebra for calculating its matrix elements.