Phase transitions and the stability of atomic and molecular ions

Abstract

Quantum phase transitions at absolute zero temperature can take place as some parameter in the Hamiltonian of the system is varied. For such transitions, crossing the phase boundary means that the quantum ground state changes in some fundamental way. For the Hamiltonian of N-electron atoms, this parameter is taken to be the nuclear charge. As the nuclear charge reaches a critical point, the quantum ground state changes its characters from being bound to being degenerate or absorbed by a continuum. We describe here a method to calculate the critical nuclear charge for which an atom can bind an extra electron to form a stable negative ion. The estimate of the critical nuclear charge will be used to explain and predict the stability of atomic negative ions. The method can be generalized to predict the stability of molecular negative ions. A detailed calculation for the critical parameters for two center molecular ions is also included.