Applications of the dynamical generator coordinate method to quadrupole excitations

Abstract

We apply the dynamical generator coordinate method (DGCM) with a conjugate momentum to a nuclear collective excitation. To this end, we first discuss how to construct a numerically workable scheme of the DGCM for a general one-body operator. We then apply the DGCM to the quadrupole vibration of 16 O using the Gogny D1S interaction. We show that both the ground state energy and the excitation energies are lowered as compared to the conventional GCM with the same number of basis functions. We also compute the sum rule values for the quadrupole and monopole operators, and show that the DGCM yields more consistent results than the conventional GCM to the values from the double commutator. These results imply that the conjugate momentum is an important and relevant degree of freedom in collective motions.

Structural analysis of a collective subspace in the dynamical generator coordinate method

“…For example, several groups have performed it as the double projection method for the rotational motion [24][25][26][27][28], and the results reproduce experimental values well. In the study for the quadrupole oscillation based on this approach [36], the sum rule result suggests the separable structure of the collective subspace. In addition, one can extract information on P from the numerical results if Eqs.…”

“…However, note that the degree of freedom in the SCC is the path itself, and it has a different theoretical framework from the DGCM (GCM), which deals with the mixture of the path. In recent years, an application of the DGCM based on the GOA [34] and direct applications for a particle number [35] and a quadrupole oscillation [36] have been performed.…”