Calculation of the two-photon decay rates of hydrogen-like ions by using B-polynomials

TL;DR

This paper introduces a novel method using Bernstein Polynomial basis sets for calculating two-photon decay rates in hydrogen-like ions, enabling analytical matrix element evaluation and improving computational efficiency.

Contribution

It presents a new approach employing B-polynomials for relativistic two-photon transition calculations, offering analytical solutions and validation against existing B-spline methods.

Findings

Accurate calculation of 2s_{1/2}-1s_{1/2} transition rates in hydrogen-like ions.

Method shows promising results comparable to established B-spline approaches.

Potential for extension to higher-order relativistic atomic calculations.

Abstract

A new approach is laid out to investigate the two photon atomic transitions. It is based on application of the finite basis solutions constructed from the Bernstein Polynomial (B-Polynomial) sets. We show that such an approach provides a very promising route for the relativistic second- (and even higher-order) calculations since it allows for analytical evaluation of the involved matrices elements. In order to illustrate possible applications of the method and to verify its accuracy, detailed calculations are performed for the 2s_{1/2}-1s_{1/2} transition in neutral hydrogen and hydrogen-like ions, and are compared with the theoretical predictions based on the well-established B-spline-basis-set approach.