Incompressibility in finite nuclei and nuclear matter

Abstract

The incompressibility (compression modulus) $K_0$ of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions. We present a comprehensive re-analysis of recent data on GMR energies in even-even ${}^{112-124}$Sn and ${}^{106,100-116}$Cd and earlier data on 58 $\le$ A $\le$ 208 nuclei. The incompressibility of finite nuclei $K_{\mathrm{A}}$ is expressed as a leptodermous expansion with volume, surface, isospin and Coulomb coefficients $K_{\mathrm{vol}}$, $K_{\mathrm{surf}}$, $K_{\tau }$ and $K_{\mathrm{coul}}$. \textit{Assuming} that the volume coefficient $K_{\mathrm{vol}}$ is identified with $K_0$, the $K_{\mathrm{coul}}$ = -(5.2 $\pm$ 0.7) MeV and the contribution from the curvature term K${}_{\mathrm{curv}}$A${}^{-2/3}$ in the expansion is neglected, compelling evidence is found for $K_0$ to be in the range 250 $<K_0<$ 315 MeV, the ratio of the surface and volume coefficients $c=K_{\mathrm{surf}}/K_{\mathrm{vol}}$ to be between -2.4 and -1.6 and $K_{\tau }$ between -840 and -350 MeV. We show that the generally accepted value of $K_0$ = (240 $\pm$ 20) MeV can be obtained from the fits provided $c\sim$ -1, as predicted by the majority of mean-field models. However, the fits are significantly improved if $c$ is allowed to vary, leading to a range of $K_0$, extended to higher values. A self-consistent simple (toy) model has been developed, which shows that the density dependence of the surface diffuseness of a vibrating nucleus plays a major role in determination of the ratio K${}_{\mathrm{surf}}/K_{\mathrm{vol}}$ and yields predictions consistent with our findings.

arXiv comment26 pages, 13 figures; corrected minor typos in line with the proof in Phys. Rev. C

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