Nuclear liquid-drop model and surface-curvature effects

TLDR

The study revisits the nuclear liquid‑drop model by explicitly incorporating surface‑curvature terms. The authors extend the classical liquid‑drop energy formula with surface‑curvature terms and refit its parameters to contemporary nuclear binding energies and fission‑barrier data, then compare the resulting performance to traditional models. The extended model reduces the rms mass deviation to 0.698 MeV (≈6× improvement) and the fission‑barrier deviation to 0.88 MeV (≈3.5× improvement), aligns well with Thomas‑Fermi and fission‑lifetime systematics, remains stable when extrapolated to exotic nuclei, and predicts lower, flatter, stiffer barriers that could stabilize hyperdeformed minima.

Abstract

Nuclear liquid-drop model is revisited and an explicit introduction of the surface-curvature terms is presented. The corresponding parameters of the extended classical energy formula are adjusted to the contemporarily known nuclear binding energies and fission-barrier heights. Using 2766 binding energies of nuclei with $Z>~8$ and $N>~8$ it is shown that the performance of the new approach is improved by a factor of about 6, compared to the previously published liquid-drop model results, in terms of the masses (new rms deviation $〈\ensuremath{\delta}M〉=0.698\mathrm{MeV})$ and the fission barriers by a factor of about 3.5 (new rms deviation of the fission barriers of isotopes with $Z>70$ is $〈\ensuremath{\delta}{V}_{B}〉=0.88\mathrm{MeV}).$ The role of the nuclear surface-curvature terms and their effects on the description of the experimental quantities are discussed in detail. For comparison, the parameters of the more ``traditional'' classical energy expressions are refitted, taking into account the nuclear masses known today and the performances of several variants of the model are compared. The isospin dependence in the new description of the barriers is in a good agreement with the extended Thomas-Fermi approach. It also demonstrates a good qualitative agreement with the fission lifetime systematics tested on the long chain of Fermium isotopes known experimentally. The new approach offers a very high stability in terms of the extrapolation from the narrower range of nuclides to a more extended one---a property of particular interest for the contemporary exotic beam projects: the corresponding properties are illustrated and discussed. The new description of the fission barriers being significantly improved, in particular, the new calculated barriers being lower, flatter, but stiffer against high-multipolarity deformations. The chances for ``extra'' stabilization of the hyperdeformed minima at high spin increase, thus calling for the new total energy Strutinsky-type calculations.