Nuclear masses and the equation of state of nuclear matter

TL;DR

This paper links the liquid-drop model of nuclear masses to the nuclear matter equation of state using the Oyamatsu-Iida model, revealing how key parameters influence nuclear properties and fitting experimental data.

Contribution

It demonstrates the relationship between ILD energies and the nuclear matter equation of state within the OI model, and constrains the symmetry energy slope parameter L.

Findings

The ILD and OI models agree well for stable nuclei with A ≥ 40.

The OI model with L ≤ 100 MeV better predicts recent mass data.

Suggested L range is 20 to 90 MeV, with the lower bound less constrained.

Abstract

The incompressible liquid-drop (ILD) model reproduces masses of stable nuclei rather well. Here we show how the ILD volume, surface, symmetry, and Coulomb energies are related to the equation of state of nuclear matter using the Oyamatsu-Iida (OI) macroscopic nuclear model, which has reasonable many-body energy and isoscalar inhomogeneity gradient energy. We use 304 update interactions, covering wide ranges of the incompressibility $K_0$ of symmetric matter and the density slope of symmetry energy $L$, which fit almost equally empirical mass and radius data of stable nuclei. Thus, the $K_0$ and $L$ dependences are nearly frozen in stable nuclei as in the ILD model, leading to clear correlations among interaction and saturation parameters. Furthermore, we assume that the surface energy of the OI model is twice as large as the gradient energy using the size equilibrium conditions of the ILD and OI models. Then, the four energies of the ILD and OI models agree well for stable nuclei with $A \gtrsim 40$. Meanwhile, the OI model with $L \lesssim 100$ MeV predicts the latest mass data better than those of stable nuclei, and we suggest $20 \lesssim L \lesssim 90$ MeV, although the lower boundary is not constrained well.