Scaled-energy spectroscopy for alkali-earth rydberg atom in external fields

The alkali-earth Rydberg atom in external fields is theoretically investigated by scaled-energy spectroscopy incorporating energy-dependent quantum defects. Closed-orbit theory is successful in reproducing the experimental observations for hydrogen and hydrogen-like alkali atoms in external fields. However, for the alkali-earth atoms such as barium, even the highly excited Rydberg electron can not be taken as isolated from the spectator valence electron(s) for the electron correlations. Closed-orbit theory cannot give a satisfactory explanation since the electron correlations are angular momentum and energy-dependent. In this paper, we perform a quantum calculation incorporating implicitly the quantum defects varying with energy where the electron correlation information is subsumed. The results recover the experimental observations for barium in magnetic or electric fields very well.