Symmetry conserving configuration mixing method with cranked states

We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus $^{32}$Mg is chosen to show the performance and reliability of the calculations. Additionally, $0^{+}_{1}$, $2^{+}_{1}$ and $4^{+}_{1}$ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data.