CONVERGENCE OF AN L2 APPROACH IN THE COUPLED-CHANNEL OPTICAL-POTENTIAL METHOD FOR E-H SCATTERING

An L2 approach to the coupled-channel 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 approximations 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 ten Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements, and 2% in the differential cross sections for nonlarge angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow.