Analysis of Triply Excited States of Atoms in Hyperspherical Coordinates

A new method for obtaining accurate adiabatic potential curves of a three-electron atom in hyperspherical coordinates has been developed. These potential curves are used to study singly, doubly, and triply excited states all at the same time. The group of potential curves that supports triply excited states of atoms is analyzed. For the Li atom, these curves are used to interpret and identify the triply excited states observed recently in the measurements using synchrotron radiation. For the ${\mathrm{H}}^{2-}$ ion, all the potential curves are repulsive, which clearly implies that there are no resonances of any type for this system.