Study of electron—molecule collision via finite-element method and R-matrix propagation technique: Exact exchange
✍ Scribed by Farzan Abdolsalami; Mehran Abdolsalami; Lennard Perez; Pedro Gomez; Mark Silva
- Book ID
- 104147616
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 723 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
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 pub!ished e-N2 cross sections (M. A. Morrison and B. C. Saha, Phys. Rev. A 36, 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 finiteelement 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,