Moment-theory investigations of photoabsorption and dispersion profiles in atoms and ions

An improved (Tchebycheff) moment approach is introduced which gives profiles that are continuous in the photoionization region and exhibit the delta-function-like behavior associated with discrete transitions at the appropriate frequencies. The methods are applied in illustrative calculations of absorption and dispersion profiles in one- and two-electron atoms and ions. In the case of one-electron atomic systems the necessary polynomial recurrence coefficients are obtained in closed form from the known spectral moments. Variational calculations using large basis sets of square-integrable functions provide accurate spectra moments for atomic helium and the negative hydrogen ion.