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How well known is the compressibility of nuclear matter?

J. Margueron, E. Khan

Abstract

The most accurate approach to determine the compressibility of nuclear matter remains the one based on microscopic Energy Density Functionals (EDFs). Recent analyses yield a value for nuclear incompressibility modulus $K_\sat=240\pm 20$~MeV, defined in nuclear matter as the second derivative of the energy per particle at saturation density. However, we demonstrate that the compressibility modulus can be reduced to values shifted by four times the suggested uncertainty, i.e., $K_\sat\approx 160$~MeV, by providing examples based on models where the second derivative ($K_\sat$) and third derivative ($Q_\sat$) of the energy per particle at saturation density can be independently varied, while the experimental binding energies, charge radii, and ISGMR data in $^{120}$Sn and $^{208}$Pb are enforced. The present work suggests a new methodology to access the compressibility of nuclear matter from nuclear experiments, still based on microscopic models, but using EDFs containing more flexibility than the ones employed up to now. Consequences of our results for nuclear matter at supra-saturation density are also discussed by exploring the quarkyonic cross-over. We predict that, for our models with low values for $K_\sat$, the quark onset density has to be low for neutron stars to exist.

How well known is the compressibility of nuclear matter?

Abstract

The most accurate approach to determine the compressibility of nuclear matter remains the one based on microscopic Energy Density Functionals (EDFs). Recent analyses yield a value for nuclear incompressibility modulus ~MeV, defined in nuclear matter as the second derivative of the energy per particle at saturation density. However, we demonstrate that the compressibility modulus can be reduced to values shifted by four times the suggested uncertainty, i.e., ~MeV, by providing examples based on models where the second derivative () and third derivative () of the energy per particle at saturation density can be independently varied, while the experimental binding energies, charge radii, and ISGMR data in Sn and Pb are enforced. The present work suggests a new methodology to access the compressibility of nuclear matter from nuclear experiments, still based on microscopic models, but using EDFs containing more flexibility than the ones employed up to now. Consequences of our results for nuclear matter at supra-saturation density are also discussed by exploring the quarkyonic cross-over. We predict that, for our models with low values for , the quark onset density has to be low for neutron stars to exist.
Paper Structure (7 sections, 6 equations, 2 figures, 2 tables)

This paper contains 7 sections, 6 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The nuclear empirical parameters $K_\mathrm{sat}$ and $Q_\mathrm{sat}$
  3. Theoretical predictions for the iso-scalar giant monopole resonance (ISGMR) strength distribution
  4. Comparison between theoretical predictions and experimental measurements
  5. Prediction for the equation of state above saturation density
  6. Conclusions and outlooks
  7. Selected parameter sets

Figures (2)

  • Figure 1: Domain in ($K_{\mathrm{sat}}$, $Q_{\mathrm{sat}}$) parameter space for the EDFs (squares and lines): Skyrme, Generalized Skyrme, RMF (NLRHF and DDRH), DDRHF, Gogny, MBPT 2016 and Fayans EDFs Reinhard:2017Miller:2019Wang:2024 (see text for details). The parameter space explored in the present study is shown in blue surface, while the 95% C.I. associated with the ground-state energy ($E_{gs}$), the charge radius ($R_{ch}$) and the ISGMR ($E_{GMR}$) are shown in dashed lines. The correlation suggested by Pearson Pearson:1991 is shown in yellow.
  • Figure 2: Binding energy $E/A$ for the nuclear equation of state based on the EDFs shown in Fig. \ref{['fig:KQ:global']}. left: nucleonic models, right: quarkyonic models.