Critical charges of simple Coulomb molecular systems: One-two electron case

A. V. Turbiner; H. Medel Cobaxin

paper

Critical charges of simple Coulomb molecular systems: One-two electron case

arXiv:1102.4493

Abstract

Let us consider some Coulomb systems of several infinitely massive centers of charge Z and one-two electrons: $(Z, e)$ , $(2 Z, e)$ , $(3 Z, e)$ , $(4 Z, e)$ , $(2 Z, e, e)$ , $(3 Z, e, e)$ . It is shown that the physical, integer charges $Z = 1, 2, ...$ do not play a distinguished role in total energy and equilibrium distance of a system giving no indication to a charge quantization. By definition, a critical charge $Z_{cr}$ for a given Coulomb system $(n Z, e)$ or $(n Z, e, e)$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For all above-mentioned systems critical charges $Z_{c}$ as well as equilibrium geometrical configurations are found. For all studied systems there was obtained an indication to a square-root singularity at $Z = Z_{cr}$ .

arXiv comment28 pages, 9 figures, 5 tables