Hartree-Fock theory with constrained deformation

The variational Hartree-Fock problem with constrained deformation is studied. If the deformation is defined by prescribed expectation values of the conventional multipole moments, it is shown that a necessary condition for the problem to have physically meaningful solutions is that the multipole operators are negligible outside the nucleus, so that they must be state dependent. In this way, a further non-linearity is introduced into the problem. An alternative formulation is to impose a given shape to the nuclear surface by means of two inequality constraints. (Auth.)