Variations on a theme by Skyrme: A systematic study of adjustments of model parameters

TLDR

The study surveys how Skyrme‑Hartree‑Fock model parameters are phenomenologically adjusted to describe nuclear structure and low‑energy excitations, and examines the predictive value of these adjustments by varying key nuclear‑matter properties. The authors use least‑squares fitting of bulk nuclear data, augmented by giant‑resonance constraints, to generate families of Skyrme‑Hartree‑Fock parametrizations that are then applied to observables such as neutron skins, isotope shifts, and super‑heavy elements, enabling systematic variation of forces to assess predictive power. Ground‑state data alone allow a wide range of Skyrme parameters, but least‑squares fitting yields reliable uncertainty estimates for extrapolations, though the resulting predictions vary strongly with the observable considered.

Abstract

We present a survey of the phenomenological adjustment of the parameters of the Skyrme-Hartree-Fock (SHF) model for a self-consistent description of nuclear structure and low-energy excitations. A large sample of reliable input data from nuclear bulk properties (energy, radii, surface thickness) is selected guided by the criterion that ground-state correlations should remain small. Least-squares fitting techniques are used to determine the SHF parameters that accommodate best the given input data. The question of the predictive value of the adjustment is scrutinized by performing systematic variations with respect to chosen nuclear matter properties (incompressibility, effective mass, symmetry energy, and sum-rule enhancement factor). We find that the ground-state data, although representing a large sample, leave a broad range of choices, i.e., a broad range of nuclear matter properties. Information from giant resonances is added to pin down more precisely the open features. We then apply the set of newly adjusted parametrizations to several more detailed observables such as neutron skin, isotope shifts, and super-heavy elements. The techniques of least-squares fitting provide safe estimates for the uncertainties of such extrapolations. The systematic variation of forces allows to disentangle the various influences on a given observable and to estimate the predictive value of the SHF model. The results depend very much on the observable under consideration.