Evaluation of the Use of Finite Element Methods in Time Dependent Atomic Physics

Abstract

In this article we evaluate the use of finite elements methods in solving the time dependent Schrödinger equation (TDSE) for ion-atom collisions. While finite difference methods have been used for that for a while, finite elements have not been much used in atomic physics. There are mathematical reasons for that choice, but the impressive development that finite elements based codes and packages have had in recent years as well as the improvement in hardware mean that the implementation of finite elements code for realistic atomic systems are now straightforward. Adaptive mesh methods usually implemented in finite elements packages are particularly suitable for the study of atomic collisions. The accurate evaluation of collision process cross sections is probably still better archieved by the use of traditional methods, but the possibility of time evolution visualization of the collision process enhances the comprehension of the physics behind the quatum dynamics of electrons during atomic collisions.