Ground-state properties of even-even N=Z nuclei within the Hartree-Fock-BCS and Higher Tamm-Dancoff approaches

We calculate the ground-state properties of well deformed, even-even N=Z nuclei in the region between Ni-56 and Sn-100 within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parameterization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a n-particle-n-hole expansion using up to n=4 particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.