Extension of the sum rule for the transition rates between multiplets to the multiphoton case

TL;DR

This paper extends the sum rule for transition rates between multiplets from one-photon to multiphoton processes in hydrogen-like ions, providing numerical comparisons with previous calculations for specific transitions.

Contribution

The paper introduces a generalized sum rule applicable to multiphoton transitions, expanding the theoretical framework for atomic transition rate calculations.

Findings

Extended sum rule to multiphoton transitions

Numerical results align with previous calculations

Analyzed specific transitions in hydrogen-like ions

Abstract

The sum rule for the transition rates between the components of two multiplets, known for the one-photon transitions, is extended to the multiphoton transitions in hydrogen and hydrogen-like ions. As an example the transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are compared with previous calculations.