Successes and Difficulties in Calculating Atomic Oscillator Strengths and Transition Rates

Alan Hibbert

doi:10.3390/galaxies6030077

Abstract

There is an on-going need for accurate oscillator strengths to be used in astrophysical applications, particularly in plasma diagnostics and in the modelling of stellar atmospheres and the interstellar medium. There are several databases in regular use which contain some of the required data, although often insufficiently complete, and sometimes not sufficiently accurate. In addition, several atomic structure packages are available through the literature, or from their individual authors, which would allow further calculations to be undertaken. Laboratory measurements provide an important check on the accuracy of calculated data, and the combined efforts of theorists and experimentalists have succeeded in providing data of an accuracy sufficient for some astrophysical applications. However, the insufficiency or inadequacy of atomic data is a continuing problem. We discuss in the context of appropriate examples some of the principal steps which researchers have taken to calculate accurate oscillator strengths, including both ab initio results and also various extrapolation processes which attempt to improve such results. We also present some examples of the main causes of difficulty in such calculations, particularly for complex (many-electron) ions, and indicate ways in which the difficulties might be overcome.

Highlights

For more than half a century, calculations of atomic oscillator strengths and transition rates have been undertaken with a level of accuracy and a range of atomic systems studied that have increased with increasing computer power
We have provided a few examples in which, by systematic inclusion of configuration state functions (CSFs), sometimes in conjunction with the fine-tuning process, it has been possible to reach levels of accuracy in the calculated oscillator strengths which are sufficient for the needs of those who use this data in their modelling of, for example, stellar atmospheres or the determination of elemental abundances in stars or the interstellar medium
Where possible—that is, where the calculations do not become prohibitively large—systematic ab initio calculations are the most reliable, and accuracy which is sufficient for astrophysical modelling has been achieved in a large number of cases

Summary

Introduction

For more than half a century, calculations of atomic oscillator strengths and transition rates have been undertaken with a level of accuracy and a range of atomic systems studied that have increased with increasing computer power. Should it not, be a straightforward matter to calculate the atomic data needed for any astrophysical application? The improvement of computer power has happened alongside the improvement of resolution of observational data, from space-based observations This has resulted in both increased accuracy of observational data, and the observation of transitions which were previously too weak to discern. Even so, could not the additional data required be calculated in a manner which would be quite straightforward by today’s standards?

Objectives

Methods

Conclusion