Hyperspherical analysis of doubly and triply excited states of Li

Abstract

A computational method for calculating the hyperspherical adiabatic potential curves for three-electron atomic systems is presented. This method allows us to obtain accurate potential curves for any symmetries more efficiently. The potential curves for the $\mathrm{Li}{(}^{2}{S}^{e})$ symmetry are analyzed. For the ground state, the energy calculated using the single channel adiabatic approximation is in good agreement with experiment. For doubly excited states, in the region of small and medium hyperradius the potential curves are similar to those for the doubly excited states of two-electron atoms and these curves can be classified using the same set of $K$, $T$, and $A$ quantum numbers. For triply excited states, the potential curves are used to show the different Rydberg series that converge to the doubly excited states of ${\mathrm{Li}}^{+}$. We also illustrate the rotor structure in the energies of triply excited states of Li.