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The curvature correction term to the surface tension is used as a criterionfor the efficiency of the Skyrme interaction in describing surface properties.Based on the nuclear equation of state, the curvature correction term to thesurface tension coefficient is calculated for 97 standard Skyrme interactionparameter sets in the vicinity of nuclear saturation density at zerotemperature. The main idea is to find those parametrizations that give theTolman's $\delta$ correction close to the available theoretical predictionsfrom the statistical theory. Only 59 out of 97 models give satisfactoryresults. Comparison of the obtained results with the results of theimplementation of different macroscopic and microscopic constraints to Skyrmeparametrizations available in the literature allows us to select 4 models thatsatisfy all the constraints.

Curvature correction term as a constraint for the Skyrme interaction