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Searching for isovector signatures in the neutron-rich oxygen and calcium isotopes

We search for potential isovector signatures in the neutron-rich oxygen and calcium isotopes within the framework of a relativistic mean-field theory with an exact treatment of pairing correlations. To probe the isovector sector we calibrate a few relativistic density functionals using the same isoscalar constraints but with one differing isovector assumption. It is found that under certain conditions, the isotopic chain in oxygen can be made to terminate at the experimentally observed ${}^{24}$O isotope and in the case of the calcium isotopes at ${}^{60}$Ca. To produce such behavior, the resulting symmetry energy must be soft, with predicted values for the symmetry energy and its slope at saturation density being $J\!=\!(30.92\pm0.47)$ MeV and $L\!=\!(51.0\pm1.5)$ MeV, respectively. As a consequence, the neutron-skin thickness of ${}^{208}$Pb is rather small: $R_{\rm skin}^{208}\!=\!(0.161\pm0.011)$ fm. This same model - labelled "FSUGarnet" - predicts $R_{1.4}\!=\!(13.1\pm0.1)$ km for the radius of a "canonical" 1.4$M_{\odot}$ neutron star, yet is also able to support a two-solar-mass neutron star.