Scaled Spectroscopy of 1Se and 1Po Highly Excited States of Helium

Abstract

In this paper, we examine the properties of the 1Se and 1Po states of helium, combining perimetric coordinates and complex rotation methods. We compute Fourier transforms of quantities of physical interest, among them the average of the operator cos(theta_12), which measures the correlation between the two electrons. Graphs obtained for both 1Se and 1Po states show peaks at action of classical periodic orbits, either "frozen planet" orbit or asymmetric stretch orbits. This observation legitimates the semiclassical quantization of helium with those orbits only, not just for S states but also for P states, which is a new result. To emphasize the similarity between the S and P states we show wavefunctions of 1Po states, presenting the same structure as 1Se states, namely the "frozen planet" and asymmetric stretch configurations.