Theory of direct scattering of neutral and charged atoms

Abstract

The theory for direct elastic and inelastic collisions between composite atomic systems (ions or neutral atoms) is formulated within the framework of the Glauber approximation. It is shown that the phase-shift function $\ensuremath{\chi}$, which depends on the coordinates of all electrons in the projectile and target as well as on the impact parameter, is the sum of a point Coulomb contribution and a contribution which may be expressed entirely in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase-shift functions. The scattering amplitude is reexpressed in terms of an optical profile function which depends on the initial and final states of the atoms. The pure Coulomb scattering in the case of elastic collisions between ions is explicitly isolated and the additional effects of the long-range point Coulomb interaction in both elastic and inelastic collisions are exhibited. The exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account certain multiple collisions. The approximate optical profile function consists of two types of terms, one corresponding to interactions involving only one electron, the other to interactions involving two electrons, one from each atom or ion. The former is obtained in closed form in terms of Meijer $G$ functions. The latter is obtained as a one-dimensional integral. The scattering amplitude is thereby reduced from a [$3(M+N)+2$]-dimensional integral, where $M+N$ is the total number of electrons in the projectile and target, to a two-dimensional integral. For collisions involving one or two neutral atoms, as in ion-atom or atom-atom collisions, the scattering amplitude is further reduced to a simple closed-form expression.