A symmetry-conserving description of odd nuclei with the Gogny force. Particle number and angular-momentum projection with self-consistent blocking

We present an approach for the calculation of odd nuclei with exact self-consistent blocking and particle number and angular-momentum projection with the finite-range density-dependent Gogny force. As an application we calculate the nucleus ³¹Mg at the border of the N = 20 inversion island. We evaluate the ground-state properties, the excited states and the transition probabilities. In general we obtain a good description of the measured observables. (orig.)