Electric-dipole matrix-element formulas in hyperspherical coordinates with applications to H- and He.

Abstract

Theoretical formulas for the length, velocity, and acceleration forms of the electric-dipole matrix element within the adiabatic hyperspherical coordinate representation are presented. The length and acceleration formulas are used to calculate the photoionization cross section for He up to 1.0 a.u. above threshold and the photodetachment cross section for ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ up to 0.35 a.u. above threshold. Length- and acceleration-form results for the dipole oscillator strengths for the discrete He transitions, 1sns${(\mathrm{}}^{1}$${S}^{e}$)\ensuremath{\rightarrow}1smp${(\mathrm{}}^{1}$${P}^{o}$), where n=1, 2, and 3 and m=2, 3, and 4, are also presented. The accuracy of the length- and acceleration-form adiabatic hyperspherical coordinate approximation results is discussed.