Applications of the dynamical generator coordinate method to quadrupole excitations

TL;DR

This paper introduces an improved dynamical generator coordinate method (DGCM) incorporating conjugate momentum, demonstrating enhanced accuracy in modeling quadrupole excitations in nuclei, specifically for $^{16}$O, compared to traditional methods.

Contribution

The paper develops a numerically feasible DGCM scheme with conjugate momentum and applies it to nuclear quadrupole vibrations, showing improved results over conventional GCM.

Findings

Lowered ground state and excitation energies with DGCM

More accurate sum rule values for quadrupole and monopole operators

Conjugate momentum enhances modeling of collective nuclear motions

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.