Convergence of an L2-approach in the coupled-channels optical potential method for e-H scattering

An L2 approach to the coupled-channels optical method is studied. The investigation is done for electron-hydrogen elastic scattering at projectile energies of 30, 50, 100 and 200 eV. Weak coupling, free-particle Green's function and no exchange in Q-space are appoximations used to calculate the polarization potential. This model problem is solved exactly using actual hydrogen discrete and continuum functions. The convergence of an L2 approach with the Laguerre basis to the exact result is investigated. It is found that a basis of 10 Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements and 2% in the differential cross sections for non-large angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow. 12 refs., 2 tabs., 2 figs