Curvature correction term as a constraint for the Skyrme interaction

The curvature correction term to the surface tension is used as a criterion for the efficiency of the Skyrme interaction in describing surface properties. Based on the nuclear equation of state, the curvature correction term to the surface tension coefficient is calculated for 97 standard Skyrme interaction parameter sets in the vicinity of nuclear saturation density at zero temperature. The main idea is to find those parametrizations that give the Tolman's $\delta$ correction close to the available theoretical predictions from the statistical theory. Only 59 out of 97 models give satisfactory results. Comparison of the obtained results with the results of the implementation of different macroscopic and microscopic constraints to Skyrme parametrizations available in the literature allows us to select 4 models that satisfy all the constraints.