Study of electron—molecule collision via finite-element method and R-matrix propagation technique: Exact exchange

Abstract

We have applied the finite-element method to electron-molecule collision with the exchange effect implemented rigorously. All the calculations are done in the body-frame within the fixed-nuclei approximation, where the exact treatment of exchange as a nonlocal effect results in a set of coupled integro-differential equations. The method is applied to e-H2 and e-N2 scatterings and the cross sections obtained are in very good agreement with the corresponding results we have generated from the linear-algebraic approach. This confirms the significant difference observed between our results generated by linear-algebraic method and the previously published e-N2 cross sections (M. A. Morrison and B. C. Saha, Phys. Rev. A36, 3682, 1987). Our studies show that the finite-element method is clearly superior to the linear-algebraic approach in both memory usage and CPU time especially for large systems such as e-N2. The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique. Moreover, the CPU time required to obtain stable results with the finite-element method is significantly smaller than the linear-algebraic approach for one incident electron energy. The usage of computer resources in the finite-element method can even be reduced much further when (1) scattering calculations involving multiple electron energies are preformed in one computer run and (2) exchange, which is a short range effect, is approximated by a sparse matrix.