Finite-size scaling method for the stability of atomic and molecular ions

Phase transitions at absolute: zero temperature can take place as some para meter in the Hamiltonian of the system is varied. For the Hamiltonian of N- electron atoms, this parameter is taken to be the nuclear charge. As the nu clear 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 the large-dimension approximation and the finite-size scaling method to calculate the critical nuclear charge for which an atom can bind an extra electron to form a stable negative ion. Results show that, aa mos t, only one electron can be added to a free atom in the gas phase. The exis tence of doubly charged atomic negative ions in a strong magnetic field wil l be discussed. (C) 2000 Elsevier Science B.V. All rights reserved.