Ground-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni in the unitary-model-operator approach

TL;DR

This paper uses the unitary-model-operator approach with a charge-dependent nucleon-nucleon interaction to calculate ground-state energies and charge radii of selected nuclei, successfully reproducing experimental saturation trends.

Contribution

It introduces the particle-basis formalism into the UMOA, enabling charge-dependent interactions to be used in nuclear structure calculations.

Findings

Ground-state energies are mainly influenced by one- and two-body cluster contributions.

Charge radii are more affected by one-particle-one-hole excitations.

Results align with experimental saturation properties of finite nuclei.

Abstract

We study the nuclear ground-state properties by using the unitary-model-operator approach (UMOA). Recently, the particle-basis formalism has been introduced in the UMOA and enables us to employ the charge-dependent nucleon-nucleon interaction. We evaluate the ground-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni with the charge-dependent Bonn potential. The ground-state energy is dominated by the contributions from the one- and two-body cluster terms, while, for the radius, the one-particle-one-hole excitations are more important than the two-particle-two-hole excitations. The calculated results reproduce the trend of experimental data of the saturation property for finite nuclei.