Close-coupling Formalism for Electron/Positron–Atom Systems and Underlying Scattering Theory

Abstract

The close-coupling method for electron/positron–atom scattering promises to give a complete description of the scattering process provided the space of target states is properly spanned. This paper will discuss the structure of the equations, emphasising questions of stability associated with the expansions over sets of target states. For electron–atom scattering, the character of the solution is discussed and a simple example is given to illustrate the non-convergence of the half-shell T-matrix. This lack of convergence can be fixed by application of the symmetrisation boundary condition, leading to new forms of the equations. For positron–atom scattering, the standard equations yield convergent half-shell T-matrices for all but the largest calculations.