Hyperspherical close-coupling calculation of positronium formation cross sections in positron-hydrogen scattering at low energies

The hyperspherical close-coupling method is applied to calculate both the elastic and positronium formation cross sections for positron collisions with atomic hydrogen at low energies. By treating the hyperradius as a slow variable, the Schrodinger equation in the body frame at each fixed hyperradius is solved using the higher-order finite-element method and the resulting hyperradial equations are solved using the diabatic-by-sector method. The coupled hyperradial equations are integrated to a large hyperradius where the wavefunctions are matched to the known asymptotic solutions to extract the scattering matrix. Both the elastic and the positronium formation cross sections are calculated at energies below the H(n=2) excitation threshold for J=0, 1, 2 and 3. It is shown that the present hyperspherical close coupling method gives results comparable to those obtained by elaborate variational methods.