Generalized local frame transformation theory for excited species in external fields

TL;DR

This paper introduces a rigorous generalized local frame transformation (GLFT) theory for excited species in external fields, significantly improving the accuracy of spectral predictions for Rydberg atoms and negative ions.

Contribution

The paper develops a comprehensive GLFT framework that includes the full on-shell Hilbert space, enhancing the accuracy of spectral calculations compared to previous models.

Findings

Errors in Stark spectra are reduced to a few tens of MHz.

The GLFT outperforms the original Fano-Harmin theory by a factor of 10-100 in accuracy.

The method provides a systematic way to match modern experimental precision.

Abstract

A rigorous theoretical framework is developed for a generalized local frame transformation theory (GLFT). The GLFT is applicable to the following systems: to Rydberg atoms or molecules in an electric field, or to negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local frame transformation theory developed initially by Fano and Harmin. This revised GLFT theory yields non-trivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semi-analytical GLFT Stark spectra with {\it ab initio} numerical simulations yields errors in the range of a few tens of MHz, an improvement over the original Fano-Harmin theory whose errors are 10-100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.