Two-electron atoms, ions and molecules

TL;DR

This paper reviews the quantum mechanics of two-electron systems, exploring stability, wave functions, and symmetry breaking in atoms, ions, and molecules, including the positronium molecule, with emphasis on correlation effects and stability conditions.

Contribution

It introduces a unified approach to studying two-electron systems, revisiting Chandrasekhar's wave function and analyzing stability across various systems with symmetry considerations.

Findings

Negative hydrogen ion stability requires electron correlation.

Positronium molecule is stable against dissociation.

Symmetry breaking influences system stability.

Abstract

The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$, cannot be achieved using a mere product of individual electron wave functions, and requires instead an explicit account for the anticorrelation among the two electrons. The wave function proposed by Chandrasekhar is revisited, where the permutation symmetry is first broken and then restored by a counter-term. More delicate problems can be studied using the same strategy: the stability of hydrogen-like ions $(M^+,m^-,m^-)$ for any value of the proton-to-electron mass ratio $M/m$; the energy of the lowest spin-triplet state of helium and helium-like ions; the stability of the doubly-excited hydrogen ion with unnatural parity. The positronium molecule $(e^+,e^+,e^-,e^-)$, which has been predicted years ago and discovered recently, can also be shown to be stable against spontaneous dissociation, though the calculation is a little more involved. Emphasis is put on symmetry breaking which can either spoil or improve the stability of systems.