Interpretation of inversions of single-particle levels in self-consistent field theories

An interpretation is offered for the level inversion that usually occurs in self-consistent field calculations when only one of a pair of symmetry-related levels is occupied: the single-particle energy of the level unoccupied in the A-particle system is its energy of removal from the (A + 1) -particle system. The correction of this energy to convert it to the corresponding energy in system A is simply given. When both symmetry-related levels are calculated in the same system there is no level inversion. The prescription to occupy the lowest levels should be amended to state that the energies should all correspond to removal energies from system A