Two-electron atoms, ions and molecules

Hallstein Høgaasen∗ 

Department of Physics University of Oslo Box 1048 NO-0316 Oslo Norway

Jean-Marc Richard† 

Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Joseph Fourier, CNRS-IN2P3, INPG 53, avenue des Martyrs, F-38036 Grenoble cedex, France

Paul Sorba‡ 

Laboratoire d’Annecy-le-Vieux de Physique Th´eorique, UMR 5108, Universit´e de Savoie, CNRS 9, chemin de Bellevue, B.P. 110, F-74941 Annecy-le-Vieux cedex, France


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 ≥ 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.


To download the article click on the following link:

https://arxiv.org/pdf/0907.2614.pdf