Variational equations for the solution of the Hartree-Fock problem with angular momentum projection before the variation
A variational principle is used to determine the optimal angular momentum projected one determinant approach to theN-nucleon yrast-wave function for a given total spin value. The solution is given in terms of a set of coupled nonlinear equations. Besides an orthonormality constraint for the occupied orbits and a normalization condition for the total wave function, this set consists out of a matrix equation taking care of the fact that the spin-projected wave function does not depend on the orientation of the intrinsic determinant it is based on, and a second subset of equations, which can be considered as a Thouless theorem for the spin-projectedN-nucleon state, and describes the diagonalization of the total Hamiltonian in the subspace of linear independentN-nucleon shell model configurations contained in the test-determinant. Furthermore, a numerical method for the solution of these equations is proposed and an extension of the theory for the description of excited bands is given. Finally, the consistency of the equations is checked by solving them for a simple example analytically.