Constraining equation of state of nuclear matter by charge-changing cross section measurements of mirror nuclei

Abstract

The nuclear symmetry energy plays a key role in determining the equation of state (EoS) of dense, neutron-rich matter, which connects the atomic nuclei with the hot and dense matter in universe, thus has been the subject of intense investigations in laboratory experiments, astronomy observations and theories. Various probes have been proposed to constrain the symmetry energy and its density dependence. Currently, the extensive data yield already a good and consistent constraint to the symmetry energy ($E_{\text{sym}}(\rho )$) at saturation density, but do not yet give a consistent result of one critical EoS parameter, $L$, the density dependence of the symmetry energy. In this work, we report a new probe of $L$ at saturation density. A good linear correlation is found between $L$ and the charge changing cross section difference ($\Delta {\sigma }_{\text{cc}}$) of mirror nuclei ${}^{30}$Si-${}^{30}$S for both the Skyrme-Hartree-Fock theory (SHF) and covariant (relativistic) density functionals (CDF). We found that the pairing effect for this mirror pair is essential to get a consistent correlation between $L$ and $\Delta {\sigma }_{\text{cc}}$ in both the SHF and CDF. Here, the cross sections are calculated on the same target and at the same energy using the zero-range optical-limit Glauber model. The linearity is found to be in the same precision as those found between $L$ and neutron skin thickness or proton radius difference.

8 pages; 4 figures

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• Improved description of nuclear charge radii: Global trends beyond $N=28$ shell closure
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• Charge-changing cross section measurements of 300 MeV/nucleon ${}^{28}$Si on carbon and data analysis
• Correlation between the charge radii difference in mirror partner nuclei and the symmetry energy slope
• Bayesian inference of nuclear incompressibility from collective flow in mid-central Au+Au collisions at 400--1500 MeV/nucleon
• Implication of shell quenching in scandium isotopes around N=20
• Role of nuclear and electromagnetic fragmentation in the charge-changing reactions of 18O on carbon and lead targets at around 370 MeV/nucleon
• Implication of odd-even staggering in the charge radii of calcium isotopes