FitAik: a package to calculate least-square fitted atomic transitions probabilities. Application to the Er+ lanthanide ion

TL;DR

The paper introduces FitAik, a new software package that performs least-squares fitting of atomic transition probabilities, demonstrated on Er+ ion, improving agreement with experimental data and enabling further calculations like polarizability.

Contribution

We developed FitAik, a novel package interfaced with Cowan codes, for accurate least-squares fitting of atomic transition probabilities using transition integrals.

Findings

Excellent agreement between fitted and experimental Einstein coefficients for Er+

FitAik automates input/output with Cowan codes, streamlining calculations

The package is publicly available on GitLab and enhances atomic data accuracy.

Abstract

We present a new method implemented in our new package \textit{FitAik}, to perform least-squares fitting of calculated and experimental atomic transition probabilities, by using the mono-electronic transition integrals $\langle n\ell |r| n'\ell' \rangle$ (with $r$ the electronic radial coordinate) as adjustable quantities. \textit{FitAik} is interfaced to the Cowan suite of codes, for which it automatically writes input files and reads output files. We illustrate our procedure with the example of Er$^{+}$ ion, for which the agreement between calculated and experimental Einstein coefficients is found to be very good. The source code of \emph{FitAik} can be found on GitLab, and the calculated Einstein coefficients are stored in our new database CaDDiACs. They are also used to calculate the dynamic dipole polarizability of Er$^+$.