Two-electron exchange interaction of an atom with an ion

Abstract

In the earlier examined symmetrical [3, 2] and almost symmetrical [3] cases two-electron exchange splitting of terms of the internuclear region of electron coordinates was determined, when both electrons are removed from the atom by a distance of the order of the internuclear distance. The method used in [1-3] makes it possible to obtain a value of this splitting asymptotically accurate at R § =. The result of the Heitler--London approximation, in which unperturbed wave functions of the initial states of atoms are used, is also nearly accurate. For example, for the interaction of two hydrogen atoms in the ground state [3], exchange splittings obtained by these two methods coincide with each other with an accuracy of... 5% in a broad region of internuclear distances (R = 5-30 a.u.). In the region of large R~.~30 a.u., where these two results begin to differ significantly, the size of the interaction itself is so small that it becomes less than the magnetic spin--spin interaction [4]. The cross section of exchange by electrons during collision of alkali metal atoms, calculated on the basis of asymptotically accurage splitting of terms [3] and using uperturbed wave functions [5], also practically do not differ from each other. This paper examines the asymmetric cases of two-electron exchange interaction at large internuclear distances, differing from the case examined in [6] in that the energy of the weakly bonded electron is not small, so that the parameters of the desired interaction cannot be associated with the parameters of elastic scattering of the electron on the atom. Interaction of the atom (ion) with the ion is examined in addition. In the examined case the region in the vicinity of the move strongly bonded electron, where the quasi-classical method of constructing an accurate wave function [1-3] is not effective, is the main region. In this region, however, the effect of interelectronic interaction on the wave function is small in comparison with the effect in the internuclear region, since here interaction of the electron with the nucleus is not small. The circumstance makes it possible to use the generalized Heitler-London method in which perturbation of wave functions of the unshielded part of the Coulomb field of the nucleus (in the case of interaction with the ion) is considered. Consideration of perturbation shows up significantly on the value of the asymptotic interaction sought. Let us construct the complete wave function of two electrons in a Coulomb field of two stationary nuclei A and B with charges Z A and Z B. To the two possible spin states of the electrons [singlet (+) and triplet (--)] correspond two types of wave functions