Effect of high-order empirical parameters on the nuclear equation of state
Abstract
A quantitative knowledge of the nuclear equation of state (EoS) requires an accurate estimation of the uncertainties on the EoS parameters and their mutual correlations. Such correlations are empirically observed in a large set of EoS models by different authors, but they are not always fully understood. We show that some of these correlations can be interpreted from basic physical constraints imposed on a simple Taylor expansion of the binding energy around saturation density. In particular, we investigate the correlations among the following empirical parameters: the symmetry energy Esym, the slope and curvature of the symmetry energy Lsym and Ksym, and the curvature and skewness of the binding energy in symmetric matter Ksat and Qsat. The uncertainties on these correlations is estimated through analytical modeling as well as a metamodeling analysis of the EoS subject to physical constraints. We show that a huge dispersion of the correlations among low-order empirical parameters is induced by the unknown higher-order empirical parameters, such as Ksym (second order) and Qsat and Qsym (third order). We also propose an explanation of the reason why Qsat is weakly constrained by present experimental data. We conclude that selective observables on high-order parameters, such as Ksym and Qsat, should be better determined before the present uncertainties on the EoS can be further reduced.
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