The nuclear symmetry energy and the neutron skin thickness in nuclei

We investigate possible correlations between the stiffness of the symmetry energy at saturation density, the so-called $L$ parameter, and the neutron skin thickness of ${^{48}}$Ca and ${^{208}}$Pb, for which the recent measurements from the CREX and PREX I+II experiments at the Thomas Jefferson Laboratory became available. We choose an ensemble of nucleonic equations of state (EoS) derived within microscopic (BHF, Variational, AFDMC) and phenomenological (Skyrme, RMF, DD-RMF) approaches. They are all compatible with the laboratory nuclear collisions data and with current observations of neutron stars (NS) mass and the tidal polarizability of a 1.4 $M_{\odot}$ NS, as deduced from the GW170817 event. We find some degree of correlation between the $L$ parameter and the neutron skin thickness whereas a much weaker correlation does exist with the tidal polarizability and the symmetry energy at saturation density. However, some EoS which are able to explain the CREX experimental data, are not compatible with the PREX I+II data, and viceversa. We confirm the results previously obtained with a different set of EoS models, and find a possible tension between the experimental data and the current understanding of the nuclear EoS.