Deformation and shell effects in nuclear mass formulas

TL;DR

This study evaluates various liquid drop mass formulas and microscopic models in predicting nuclear masses, revealing better accuracy for prolate deformed nuclei and highlighting the importance of shell effects and deformation dependence.

Contribution

It compares the performance of different mass models across deformation regions and demonstrates the significance of shell effects and deformation in nuclear mass predictions.

Findings

Prolate deformed nuclei are fitted with RMS < 750 keV.

Spherical and semi-magic nuclei have RMS > 2000 keV.

Adding shell effects improves mass predictions, especially for deformed nuclei.

Abstract

We analyze the ability of the three different Liquid Drop Mass (LDM) formulas to describe nuclear masses for nuclei in various deformation regions. Separating the 2149 measured nuclear species in eight sets with similar quadrupole deformations, we show that the masses of prolate deformed nuclei are better described than those of spherical ones. In fact, the prolate deformed nuclei are fitted with an RMS smaller than 750 keV, while for spherical and semi-magic species the RMS is always larger than 2000 keV. These results are found to be independent of pairing. The macroscopic sector of the Duflo-Zuker (DZ) mass model reproduces shell effects, while most of the deformation dependence is lost and the RMS is larger than in any LDM. Adding to the LDM the microscopically motivated DZ master terms introduces the shell effects, allowing for a significant reduction in the RMS of the fit but still exhibiting a better description of prolate deformed nuclei. The inclusion of shell effects following the Interacting Boson Model's ideas produces similar results.