Direct Approach to Electron-Impact Excitation/Ionization of Hydrogen


Principal Investigator

Andris Stelbovics


Murdoch University


Steve Jones


Murdoch University


h15 - VPP

When an electron collides with an atom, the
electrons in the atom can be excited to higher
energy levels or even knocked out of the atom. There are an infinite number of possible outcomes of such a scattering event and all must be taken into account to obtain accurate results. We are developing a stable, high-order finite-difference scheme to directly solve the partial-differential equation that governs the scattering. Our approach uses far less time and storage than methods which do not even work for the case where an electron is knocked out.


What are the results to date and the future of this work?

We have greatly reduced the amount of storage and time needed to solve this basic, important three-body problem of atomic physics. Moreover, our improvements automatically reduce round-off error simply by reducing the number of operations. Round-off error plays an essential, limiting role in solving very-large-scale systems of linear equations. By significantly reducing round-off error, we will be able to obtain more accurate results. This will become even more important in the future when we include more degrees of freedom for the system. The inclusion of more degrees of freedom greatly increases the size of the calculation, however, so having the VPP as a computational resource becomes more and more important as our work progresses.

What computational techniques are used?

We use a high-order (Numerov) finite-difference propagation scheme. The partial-differential equation is integrated outward from the origin. The number of difference equations is reduced each step outward, resulting in a propagating solution. The use of a propagation scheme greatly reduces the size of the matrices to be inverted and also makes it much easier to impose correct boundary conditions. Earlier researchers all imposed a grid with fixed spacing. We use variable spacing for the first time, which is orders of magnitude faster.


S. Jones and A. T. Stelbovics, Towards a Direct Numerical Solution of Schroedinger's Equation for (e,2e) Reactions, Australian Journal of Physics (in press).

- Appendix B