Angular momentum projection in the deformed relativistic Hartree-Bogoliubov theory in continuum

The angular momentum projection (AMP) method is implemented in the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the point-coupling density functional. The wave functions of angular momentum projected states are expanded in terms of the Dirac Woods-Saxon (WS) basis, providing a proper description of the asymptotic behavior of the wave functions for weakly bound nuclei. The contribution of continuum induced by the pairing is considered by treating the pairing correlation with the Bogoliubov transformation. We present the formulae and numerical checks for the DRHBc+AMP approach and use it to study low-lying excited states of weakly bound deformed nuclei. Our calculations show that neutron-rich magnesium isotopes $^{36,38,40}$Mg are all well deformed nuclei. The low-lying excited states of these three nuclei are obtained by performing the AMP on the mean-field ground-states. The ground-state rotational bands of $^{36,38,40}$Mg are reproduced reasonably well by using this new DRHBc+AMP approach with the density functional PC-F1.