Application of the Close Coupling Method to Electron-Molecule Scattering
The close coupling method has been applied to the scattering of electrons by atomic and molecular systems for a long time now and the basic idea is very well known. The total wave function for an (N+1)-electron system consisting of an N-electron atom, ion, or molecule plus an additional electron is expanded in antisymmetrized products of N-electron target eignefunctions and a set of unknown functions representing the added electron. The unknown functions are calculated by solving a set of coupled integro-differential (ID) equations which are derived from a variational principle: the asymptotic forms of these functions give the reactance and scattering matrices and thence the cross sections. If it were possible to retain an infinite number of terms in the expansion (including an integral over the continuum states of the system) the close coupling method would yield an exact solution to the problem. In practice, of course, a finite number of terms must be retained. The accuracy of the method should improve as this number is increased and in fortunate cases some kind of convergence may be obtained. However, in many cases the convergence is very slow and so many equations have to be solved that the method becomes intractable. If the method is to be extended, we need to develop techniques for dealing, in a fast and efficient manner, with large sets of coupled integro-differential equations. If this cannot be done then we must conclude that the method has been carried to its limits, and should seek alternative formulations of the problem.
KeywordsDiatomic Molecule Mesh Point Close Coupling Total Wave Function Nuclear Part
Unable to display preview. Download preview PDF.
- 2.C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford, California, 1957 ).Google Scholar