The angular momentum and parity projected multidimensionally constrained relativistic Hartree–Bogoliubov model

Abstract

Nuclear deformations are fundamentally important in nuclear physics. We recently developed a multidimensionally constrained relativistic Hartree–Bogoliubov (MDCRHB) model, in which all multipole deformations respecting the V 4 symmetry can be considered self-consistently. In this work we extend this model by incorporating the angular momentum projection and parity projection to restore the rotational and parity symmetries broken in the mean-field level. This projected MDCRHB (p-MDCRHB) model enables us to connect certain nuclear spectra to exotic intrinsic shapes such as triangles or tetrahedrons. We present the details of the method and an exemplary calculation for 12C. We develop a triangular moment constraint to generate the triangular configurations consisting of three α clusters arranged as an equilateral triangle. The resulting 12C spectra are consistent with that from a triangular rigid rotor for large separations between the α clusters. We also calculate the B(E2) and B(E3) values for low-lying states and find good agreement with the experiments.