The spherically symmetric model of e–H scattering

The spherically symmetric model (SSM) for electron--hydrogen scattering is one in which the Coulomb repulsion between the electrons, 2/r12, is replaced by 2/r>, where r> is the greater of r1 or r2. The partial wave decomposition of the wave function for this model is carried out with emphasis on L > 0 partial waves, in which case it is shown that singlet and triplet results are identical. The model, nevertheless, retains all inelastic and ionization channels, and therefore provides a nontrivial testing ground for methods of calculation. The decomposition results in two-dimensional partial differential equations (PDEs). Here numerical calculations are carried out in two ways using (i) a propagation method, and (ii) a noniterative PDE method. The latter is augmented by an integral formula, which greatly enhances the practicality of the method. Elastic phase shifts for L = 1,2,3 partial waves in the elastic region are presented. PACS No. 34.80