Implementation of the Variation-After-Projection Approach in Calculations with A Time-Odd Hartree-Fock Mean Field

We have implemented a new variation-after-projection (VAP) calculation based on a time-odd Hartree-Fock (HF) mean field. The exact Hessian matrix of the projected energy has been successively evaluated for the first time, which makes the VAP calculation much more stable. With the time-odd mean field, the present VAP can be applied to the yrast states not only in the even-even nuclei, but also in the odd-A and odd-odd ones. The VAP energies throughout all spins for some calculated sd-shell nuclei are very close to the corresponding shell model ones. Our calculations clearly show that the spin projection is very important in achieving a good approximation to the full shell model.