Pseudostate bases including an L2 description of the continuum for use in e--He collision calculations

Abstract

The possibility of constructing a distorted-wave second Born approximation model for electron-helium collisions at energies above 30 eV is examined. It is proposed to calculate the second Born term by analytic integration over the intermediate momentum of the colliding electron and by replacing the infinite sum over intermediate target states by a finite sum over a pseudostate expansion. A method is proposed for obtaining pseudostate bases which approximately reproduce known bound-state contributions to the oscillator strength sum rules for n3,1S to n3,1P transitions and polarizabilities of the 11S, 21S and 23S states. These bases are composed of 'exact' n3,1S, n3,1P and n3,1D states up to n=3 and of a restricted number of 3,1S, 3,1P and 3,1D L2-type pseudostates. Certain of the latter lie in the continuum and their energies are adjusted to correspond to quadrature points for Gauss-Laguerre integration, this in order to easily evaluate the continuum contributions to oscillator strength sums, polarizabilities and second Born terms.