Stieltjes-Tchebycheff moment-theory approach to photoeffect studies in Hilbert space

An outline is given of the so-called Stieltjes-Tchebycheff method for studies of photo cross sections in Hilbert space. This approach, based on recognition of the convergence of spectral moments of the cross section in an L2 basis, has proved particularly useful in studies of molecular photo-effect, in which case the potentials are noncentral and nonlocal, and electronic wavefunction antisymmetry under permutation must be maintained. Moreover, moment-theory strategy has been adopted recently in nuclear photoeffect studies, and so a description of the Stieltjes-Tchebycheff formalism and related techniques seems appropriate at this time. The general theoretical development is presented. Illustrative applications, including photodissociation of the deutron, photoabsorption in atomic hydrogen and helium, and photodetachment in the hydrogen anion, are given. Polynomial-expansion and continued-fraction summation techniques for obtaining photo cross sections from Hilbert-space calculations are described and are contrasted and compared with the Stieltjes-Tchebycheff approach