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

TL;DR

This paper investigates the critical charges and equilibrium configurations of simple Coulomb systems with one or two electrons, revealing that integer charges do not uniquely determine system properties and identifying singularities at critical charges.

Contribution

It provides the first detailed analysis of critical charges and equilibrium geometries for various Coulomb systems with one or two electrons, highlighting the non-quantized nature of charge effects.

Findings

Critical charges are identified for all studied systems.

No special role for integer charges in energy and distance.

Indications of square-root singularities at critical charges.

Abstract

Let us consider some Coulomb systems of several infinitely massive centers of charge Z and one-two electrons: $(Z,e)$, $(2Z,e)$, $(3Z,e)$, $(4Z,e)$, $(2Z,e,e)$, $(3Z,e,e)$. 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 $(nZ,e)$ or $(nZ,e,e)$ 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 $Z=Z_{cr}$.