Validity of the two-determinantal deformed Hartree-Fock approximation

The two-fold degeneracy of the deformed Hartree-Fock (HF) solutions in thes-d shell suggests the use of a two-determinantal intrinsic state. The validity of this two-determinantal variational method is established in the case of the exactly solvable Lipkin Hamiltonian, for which the usual HF solution is known to be 2 fold degenerate. The approximation of using a two-determinantal intrinsic state turns out to be an exceedingly good one and in general as the particle number and the strength of the interaction increase, the exact solution is rapidly approached. The states of positive (negative) parity which are obtained by projection from the intrinsic two-determinantal state are found to reproduce the exact ground (first excited) state with a high accuracy.