Direct calculation of the scattering amplitude without partial-wave analysis - art. no. 062714

Two developments in scattering theory are reported. We show, in a practical way, how one can calculate the scattering amplitude without invoking a par tial-wave expansion. First, the integral expression for the scattering ampl itude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wave function that appears in the integr al expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method. As an example, we calculate electron scatte ring from static hydrogen (the Hartree potential). With minimal computation al effort, we obtain accurate and stable results for the scattering amplitu de.