PHASE-AMPLITUDE ALGORITHMS FOR ATOMIC CONTINUUM ORBITALS AND RADIAL INTEGRALS

We present a new, fast and accurate phase-amplitude algorithm for the calculation of atomic continuum orbitals needed for cross sections com putations of various atomic processes in plasmas. A coarse, energy ind ependent, mesh is sufficient to achieve high accuracy. A straightforwa rd application of a predictor-corrector procedure to the non-linear di fferential equations would fail, in particular for high energy free el ectrons in any atomic potential. The present algorithm overcomes this problem. In addition, we describe a novel method for calculating the r adial integrals by integration over the phases instead of r. With the use of Gaussian trigonometric formulas over half periods, the integral s are expressed as alternating series. Levin's transform for convergen ce acceleration then provides the sum of the series with a few terms o nly. These methods are applicable in a relativistic framework as well as non-relativistic.