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

Abstract

The validity of the quantum-number-projected generator coordinate method ͑PGCM͒ 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 M 1/E2 transition probabilities concerning the Iϭ1 ϩ 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.

Configuration mixing of angular-momentum and particle-number projected triaxial Hartree-Fock-Bogoliubov states using the Skyrme energy density functional

“…Bohr). In the context of the GCM, however, this has so far only been done in highly schematic models, by using either a single-j shell [31] or a very small shell model space and a schematic interaction [32,33]. A first step toward the simultaneous treatment of these five degrees of freedom has been carried out recently with the GCM mixing of angular-momentum projected quadrupole-deformed axial mean-field states.…”

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

“…omitting the density-dependent part of the Gogny interaction and keeping exactly all exchange terms in the computation of MR kernels. In fact, MR calculations employing Hamiltonian operators are rather performed within a limited valence space, in the spirit of the interacting shell model, either of projected-GCM type [58,59,60,61] or using more elaborate schemes to select the set of reference states like in the MONSTER and VAMPIR approaches [62,63,64].…”

Shell Model Study of Nuclei around Mass 100

“…In order to interpret the shell model results, the generator coordinate method (GCM) is applied to even-even nuclei under the same interaction as used for the shell model calculations. The previous GCM studies [10][11][12][13] made it clear that, for a description of the nuclear collective and single-particle motions, angular momenta of the neutron and proton systems (I ν and I π ) should be projected out separately, and the total spin I is constructed by angular momentum coupling. Thus in the present GCM calculations, the angular momentum projection is performed separately for each proton or neutron space.…”