Reexamination of nuclear oscillator parameters: Toward precise calculations of isospin-symmetry-breaking correction

The oscillator parameters in nuclei are reevaluated using three different methods. The first employs a conventional approach, utilizing updated experimental charge-radius data and neutron skin thicknesses obtained from self-consistent mean-field calculations as constraints. The occupations of unique-parity intruder states, induced by the spin-orbit coupling, are properly accounted for using the level ordering generated with a realistic potential. However, the results from this method show no significant difference from those obtained in the prior work [Nucl. Phys. A 781, 350 (2007)]. In the second method, we explicitly introduce Coulomb and symmetry terms to the oscillator Hamiltonian. Within a specific form of these additional terms, their contributions can be absorbed, leading to a formal definition of an isospin-invariant and an isospin-dependent oscillator parameter. The oscillator parameter for protons corresponds exactly to those extracted from the charge-radius systematics in the first method, while the one for neutrons differs considerably from that obtained via neutron skin thickness. The isospin-invariant parameter does not have a traditional correspondence because its evaluation requires subtraction of Coulomb and symmetry contributions. This distinction could be impactful to the shell model where the configuration space is extremely limited, especially if isospin-nonconserving forces are incorporated. The final method involves direct adjustment of the oscillator functions to maximize the overlap with Hartree-Fock eigenfunctions using the effective Skyrme interaction. Despite larger uncertainties, reflecting substantial orbital- and Skyrme-parametrization dependences, the results of this approach agree fairly well with those extracted from the charge-radius systematics.