Analytic properties of three-body continuum Coulomb wave functions

Abstract

We study the analytic properties of the functions known as C3 and ${\ensuremath{\Phi}}_{2},$ used in atomic collision theory for the description of the three-body continuum state. We analyze the bound states for both models obtained by analytic continuation in the case of ion-atom collision. The C3 wave function is an uncorrelated model represented by the product of two-body Coulomb functions and the bound states are found for negative relative energies of electron-target or electron-projectile pairs. On the other hand, the ${\ensuremath{\Phi}}_{2}$ model is based on a two-variable hypergeometric function that correlates the electron motion relative to both the target and projectile. We found that only decaying bound states are allowed and the atomic spectra becomes continuous. The bound states of the ${\ensuremath{\Phi}}_{2}$ model have a complex energy due to the action of the projectile. Expressions for the wave functions in the different thresholds are given and studied.