Hierarchy of Sum Rules for Oscillator Strengths

TL;DR

This paper generalizes sum rules for oscillator strengths in hydrogen, introduces a numerical approach for their calculation, and discusses extensions to other potentials, Kramers relations, and the Virial theorem.

Contribution

It presents a new class of generalized sum rules for oscillator strengths and discusses their numerical evaluation and extensions to general potentials.

Findings

Sum rules include contributions from discrete and continuum spectra.

Numerical methods validate the generalized sum rules.

Extensions to Kramers relations and the Virial theorem are discussed.

Abstract

It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be calculated numerically. The numerical calculations are carried out to check the validity of the sum rules. The procedure for constructing sum rules for general potentials is discussed. Generalisations of Kramers relations and the Virial theorem are discussed.