The well-known graphical representation called the Lu-Fano plot was originally developed for multichannel 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 with the traditional Lu-Fano plot, the modified representation developed here can be utilized for problems where there are more than two ionization thresholds. An example application to Rydberg series of the manganese atom illuminates its use in a practical problem.

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• Atomic & molecular structure
• Atomic spectra
• Electronic structure of atoms & molecules
• Fine & hyperfine structure