Hyperspherical Coordinate Description of Single- and Multiphoton Processes in Two-Electron Systems

The purpose of this chapter is to review the use of the adiabatic hyperspherical approximation for the quantitative calculation of single- and multiphoton cross sections of two-electron systems. In Section 2 we provide a brief general orientation to the hyperspherical coordinate representation, the adiabatic approximation, and a diabatic approximation for treating strongly avoided crossings between adiabatic potential curves. In Section 3 we review applications to photoionization and photodetachment processes in He, Be, H–, and Ps–. In Section 4 we review applications to multiphoton processes in H–. Finally, in Section 5 we assess the adiabatic hyperspherical approximation and discuss future prospects for going beyond this approximation