Showing papers by "Peter J. Rossky published in 1977"

Model perturbation theoretic calculations with finite continuum basis sets

Abstract: To examine various aspects of the methods employed in diagrammatic perturbation theory applications the model problem of a hydrogenic atom of nuclear charge Z perturbed by the potential −Z′/r is analyzed. The use of a discrete quadrature for the continuous energy spectrum and a finite coordinate space integration cutoff are tested by comparison with analytic methods. It is found that accurate results are obtained if a physically reasonable choice for the spatial cutoff is used, namely, the maximum significant extent of the zero order wavefunction. For larger values the use of the discrete continuum basis results in a spurious logarithmically divergent contribution to the energy which can be of practical significance. A detailed examination is made of the summation techniques commonly employed in diagrammatic perturbation theory. For the physical choice of cutoff the geometric summation of higher order terms involving excited states in the continuum, as well as bound states, is shown to yield meaningful and accurate results. To illustrate the analysis numerical results are given for Z=1, Z′=1 and Z=4, Z′=1.