Correlations among symmetry energy elements in Skyrme models

Motivated by the interrelationships found between the various symmetry energy elements of the energy density functionals (EDF) based on the Skyrme forces, possible correlations among them are explored. A total of 237 Skyrme EDFs are used for this purpose. As some of these EDFs yield values of a few nuclear observables far off from the present acceptable range, studies are done also with a subset of 162 EDFs that comply with a conservative set of constraints on the values of nuclear matter incompressibility coefficient, effective mass of the nucleon and the isovector splitting of effective nucleon masses to see the enhancement of the correlation strength, if any. The curvature parameter $K^0_{sym}$ and the skewness parameter $Q^0_{sym}$ of the symmetry energy are found to be very well correlated with the linear combination of the symmetry energy coefficient and its density derivative $L_0$ . The isovector splitting of the effective nucleon mass, however, displays a somewhat meaningful correlation with a linear combination of the symmetry energy, its slope and its curvature parameter.