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

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.