Positron scattering by singly charged helium ions in the ground state

A coupled channel approximation has been employed to calculate cross sections for positron collisions with He⁺(1s) in the energy ranges 0-40.8, 40.8-47 and 50-250 eV. In the lowest energy interval only elastic scattering is possible whereas in the intermediate energy interval both elastic and inelastic cross sections are calculated. Above the capture threshold total cross sections have been calculated for the excitation of He⁺, for the formation of positronium and for ionization. The target basis set includes the n = 1 and 2 eigenstates on the He⁺ and Ps centres together with up to 23 pseudostates centred on the He⁺. The coupled equations were solved using a new minimum-norm extension of the least-squares method. The new approach provides accurate solutions to even large coupled sets of scattering equations. Where possible the results of the present calculations have been compared with previous investigations.