K-matrix method with B-splines:: σ nl, βn and resonances in He photoionization below N=4 threshold

A B-spline based K-matrix method has been implemented to investigate the photoionization of atoms with simple valence shells. With a particular choice of knots, the present method is able to reproduce all the essential features of the continuum wavefunctions including up to 20-25 resonant multiplets below each ionization threshold. A detailed study of the interval between the N = 3 and N = 4 thresholds where the state labelled [031](5)(+) (parabolic quantum numbers: [N(1)N(2)m](n)(A)), the first of a series converging to the higher N = 5 threshold, is known to fall, is presented. According to propensity rules this state cannot decay directly in the underlying continuum, but interacts strongly with the [021](n)(+) series and appreciably with the [030](n)(-) series. As a result all parameters of the two series are strongly modulated and, between 75.5 eV and 75.57 eV, partial cross section and asymmetry parameter patterns change dramatically.