Analysis of Peierls-Yoccoz rotational energy of nuclei with semi-realistic interaction

TL;DR

This paper analyzes the Peierls-Yoccoz rotational energy of nuclei using angular-momentum projection with a semi-realistic Hamiltonian, revealing the contributions of various Hamiltonian terms and deriving a general formula.

Contribution

It provides a detailed decomposition of the PY rotational energy contributions and introduces a general formula highlighting higher-order effects in light or weakly-deformed nuclei.

Findings

Kinetic energy contributions are large and near rigid-rotor values.

Central force contributions are sizable and influence moment-of-inertia.

Noncentral forces significantly affect the rotational energy in certain nuclei.

Abstract

The Peierls-Yoccoz (PY) rotational energy of nuclei has been analyzed by the angular-momentum projection (AMP) on the axial Hartree-Fock solutions, by using the semi-realistic effective Hamiltonian M3Y-P6. The rotational energy is decomposed into contributions of the individual terms of the Hamiltonian, and their ratios to the total PY rotational energy are calculated. Except for light or weakly-deformed nuclei, the ratios of the individual terms of the Hamiltonian are insensitive to nuclides and deformation. The contributions of kinetic energies are large and close to the rigid-rotor values, although those of central forces are sizable. For light or weakly-deformed nuclei, the ratios significantly depend on nuclei and deformation. The contributions of noncentral forces are not negligible. Regardless of nuclides, the attractive forces decrease the moment-of-inertia, and the repulsive forces increase it. A general formula for the PY rotational energy is derived, which suggests that higher-order terms of the cumulant expansion play roles in the rotational energy and the moment-of-inertia for light or weakly-deformed nuclei.