Nuclear incompressibility and sound speed in uniform matter and finite nuclei

TL;DR

This paper extends the compressible liquid-drop model to unify descriptions of nuclear ground states and incompressibility, using Bayesian methods to fit experimental data and explore implications for nuclear matter properties and sound speed.

Contribution

It introduces a density-dependent surface term in the CLDM, employs Bayesian analysis with MCMC to constrain nuclear parameters, and investigates finite size effects on sound speed in nuclei.

Findings

Q_sat ≈ -950 ± 200 MeV fits experimental K_A data.

Finite size effects significantly reduce sound speed in finite nuclei.

A hypothetical measurement of GMR energy in 132Sn could better constrain K_sym and K_tau.

Abstract

We have extended the compressible liquid-drop model (CLDM) with a density-dependent surface term (eCLDM), which allows for a unified description of both the nuclear ground state energies and the incompressibility modulus in finite nuclei $K_A$. We analyse the role of the nuclear empirical parameters, e.g., $K_{sat}$, $Q_{sat}$, $L_{sym}$ and $K_{sym}$, which contribute to the bulk properties, as well as the role of the finite size contributions. For the bulk properties, the density and isospin dependencies of the nuclear incompressibility in infinite matter are characterized by introducing new empirical parameters, and two new constraints for the value of $K_{sym}$ are suggested. For finite nuclei, we employ a Bayesian approach coupled to a Markov-Chain Monte-Carlo (MCMC) exploration of the parameter space to confront the model predictions of $K_A$ in Zr, Sn and Pb isotopes to the experimental data. We show that $Q_{sat}\approx -950\pm 200$~MeV describes the experimental measurements of $K_A$ in these isotopes. This value is different from the ones deduced from phenomenological nuclear energy density functionals, suggesting a possible explanation of their difficulty to accurately describe Zr, Sn and Pb data all together. In addition we explore the impact of a fictitious measurement of the Giant Monopole Resonance energy in $^{132}$Sn. We show that this measurement, provided it is accurate enough, will allow to better determine $K_{sym}$ and $K_{\tau}$. Finally we explore the properties of the sound speed around saturation density and show the important role of finite size terms in finite nuclei since they reduce the sound speed to approximately half compared to nuclear matter.