Convergence of the multipole expansion for the doubly differential ionization cross section.

Abstract

We analyze the convergence of the Legendre polynomials expansion of the doubly differential cross section (DDCS) for soft electron emission (SEE) in ion-atom collisions. This expansion has been recently employed in the analysis of the angular shape of theoretical as well as experimental data on SEE. Numerical calculations using the continuum-distorted-wave--eikonal-initial-state (CDW-EIS) approximation show that for sufficient low electron velocity, the DDCS for ionization is well described with a few terms of the expansion. Besides, we show analytically that the expansion reduces to the first three terms in the zero-emission-velocity limit, within CDW or CDW-EIS approaches.