A semi-analytic approximation for a single-particle continuum wavefunction

Abstract

A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.