On the Finite Volume Variational Method Based on the Logarithmic Derivative of the Wave Function

Abstract

One of the well known and widely used methods to study the collision problems is the R matrix developed in nuclear physics by Wigner and Eisenbud (1) and applied to atomic physics by Burke et al. (2) and to molecular physics by several authors (3–7). This method is based on the expansion of the continuum wave function on several known functions and the separation of the coordinate space into an internal (interaction) and external (asymptotic) regions. The technique of expanding the wave function is widely used in bound calculations and the R matrix borrows some computational techniques from this field. The separation of the coordinate space into two regions is common to all collision methods but in R matrix the size of the internal region is smaller than in other methods. The main advantage of the R matrix is that the functions used in the expansion are calculated only once. The disadvantage is that the R matrix, written as an expansion in terms of these functions at each continuum energy, converges slowly with the number of functions retained in the expansion. To speed this convergence different corrections can be added to the R matrix (7).