Quantum-number-projected generator coordinate method and the shell model

Abstract

The validity of the quantum-number-projected generator coordinate method (PGCM) is investigated within the proton-neutron single-j shell model. The results of the PGCM are compared with exact solutions in the shell model. It is concluded that the PGCM provides a good approximation of the shell model for low-lying collective states. In order to describe the proton-neutron relative motion such as a scissors mode, we also propose a truncation scheme in terms of the PGCM. Various classes of PGCM truncations are examined by changing sets of generator coordinates. Flexibility with respect to the choice of generator coordinates is advantageous to illuminate the underlying physics. As an application of the PGCM truncation, the $M1/E2$ transition probabilities concerning the ${I=1}^{+}$ scissors state are analyzed for nuclei exhibiting stable triaxiality. The electromagnetic properties are identified. Those are characteristic of the $O(6)$ dynamical symmetry limit of the proton-neutron interacting boson model.