Deformed Atoms and the Projected Hartree-Fock Method

Abstract

Atoms are usually considered as spherical systems. The selfconsistent field is commonly supposed to be a central field and the atomic orbitals are taken as eigenfunctions of the angular momentum i. It is well known that in the case on non-closed shell configurations these assumptions are inconsistent. The valence electrons will deform the core and give rise to a non-central field. These effects can be described in two equivalent ways: either by introducing deformation parameters in the selfconsistent potential and working with orbitals in a deformed field or by considering the orbitals as mixtures of eigenvalues of angular momentum with different ℓ-values. It is, of course to be expected that due to the preponderance of the nuclear field, this deformation and these admixtures will be small and hence will not influence the binding energies very much. Nevertheless certain operators which are particularly sensitive to special modes of deformation might show marked effects in their expectation values.