Some applications of excited-state-excited-state transition densities

We derive an approximation for transition moments between excited states consistent with the approximations and assumptions normally used to obtain transition moments betwen the ground and excited states in the random-phase approximation and its higher-order approximations. We apply the result to the calculation of the photoionization cross sections of the $2{}_{}{}^3{}_{}{}^{}S$ and $2{}_{}{}^1{}_{}{}^{}S$ metastable states of helium by a numerical analytical continuation of the frequency-dependent polarizability. The procedure completely avoids the need for continuum basis functions. The cross sections agree well with the results of other calculations. We also predict an accurate two-photon decay rate for the $2{}_{}{}^1{}_{}{}^{}S$ metastable state of helium. The entire procedure is immediately applicable to several problems involving photoionization of metastable states of molecules.