Description of odd-nuclei based on the Higher Tamm-Dancoff approximation
In beyond mean-field approaches the description of odd-mass nuclei requires one to break time-reversal invariance of the underlying one-body Hamiltonian, inducing a polarization of the even-even core to which the odd nucleon is added. We study the effect of this core polarization on the resulting splitting of the Kramers degenerate single-particle states, the magnetic dipole moment and the isospin mixing in the ground state. This study id performed first in the Hartree-Fock approximation using the Skyrme energy density functional (SIII and SLy4 parametrizations), then within the Higher Tamm-Dancoff approximation in whoch one includes pairing correlations (in T=1 and T=0 channels) using a residual delta interaction without breaking the particle-number symmetry. Regarding the magnetic properties, we find a correction to the unified-model description due to the core polarization involving mostly spin degrees of freedom. This correction is able to reproduce the phenomenologically observed quenching (amounting to about 30%) of the effective spin gyromagnetic factors from the free values. As for the isospin-mixing parameter in the ground state, we estimate it assuming negligible contributions from T-values above |T_z|+1 and find reasonable values below 1%. We study its sensitivity to the relative strenghts in T=0 and T=1 channels of the delta residual interaction.