Calculation of the electric potential around two identical atoms or ions.

Abstract

Problems of diatomic molecules and atom-atom collisions, in which two identical atoms take part, or nearest-neighbor interactions in hot plasmas require the computations of the electric potential and the electron charge distribution around such a two-centered object. The electric potential around two such identical atoms or ions fulfills special symmetry conditions. These symmetries include a cylindrical symmetry around the line connecting the centers of the two atoms and a reflection symmetry around the plane perpendicular to this line halfway between the two atoms. When the two atoms are far apart, the asymptotic behavior of the charge-state distribution and the potential are those of two separated isolated atoms each of which can be expanded into multipole components around its nucleus. We define a set of new functions ${\mathit{T}}_{\mathit{m}\mathit{k}}$(y,${\mathit{y}}_{\mathit{n}}$) Eq. (2.25), which connect the various multipole components of the electric potential to those of the electron charge distribution in such a two-identical-atom problem, and which take into account all the above symmetry conditions. The great advantage of these transformation functions is the fact that by accounting for the above symmetry conditions, the three-dimensional integration required for the computation of the local electric microfield directly from the Poisson equation is practically reduced to a one-dimensional one. It is shown that the use of these functions greatly reduces the complexity and computation times of problems in which two identical atoms are involved, particularly for high-Z atoms. Explicit exact formulas are given for the computation of the ${\mathit{T}}_{\mathit{m}\mathit{k}}$ functions. An example is given which illustrates the use of these functions in first-order perturbation theory. For this special class of problems the procedure presented here results in a closed recursive equation, in which the interatomic distance is the only free parameter.