An alternative representation of multichannel Rydberg spectra: a modified Lu-Fano plot, applied to manganese spectroscopy

TL;DR

This paper introduces a modified Lu-Fano plot for multichannel Rydberg spectra that overcomes limitations of the traditional method, especially with multiple ionization thresholds and closely split thresholds, demonstrated through manganese spectroscopy.

Contribution

The study presents a new graphical representation that improves analysis of multichannel Rydberg spectra with multiple thresholds, applicable to complex atomic systems.

Findings

The modified plot handles more than two ionization thresholds.

It simplifies analysis near closely split thresholds.

Applied to manganese, it effectively visualizes Rydberg series.

Abstract

The well-known graphical representation called the Lu-Fano plot was originally developed for multi-channel Rydberg spectroscopy, especially in quantum defect theory. The present study shows some of the limitations of this traditional Lu-Fano plot that are desirable to improve on, when there are closely split ionization thresholds as in many current generation quantum information applications involving hyperfine-split thresholds, or when there are more than two ionization threshold energies. The modified representation introduced here is especially simplifying in the situation where one is exploring the bound states lying very far below those closely split thresholds. Moreover, it overcomes one limitation, namely that in contrast to the traditional Lu-Fano plot, the modified representation developed here can be utilized for problems where there more than two ionization thresholds. An example application to Rydberg series of the manganese atom illuminates its use in a practical problem.