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In the framework of nuclear energy density functional (EDF) methods, manynuclear phenomena are related to the deformation of intrinsic states. Theiraccurate modeling relies on the correct description of the change of nuclearbinding energy with deformation. The two most important contributions to thedeformation energy have their origin in shell effects that are correlated tothe spectrum of single-particle states, and the deformability of nuclearmatter, that can be characterized by a model-dependent surface energycoefficient a_{surf}.  With the goal of improving the global performance of nuclear EDFs throughfine-tuning of their deformation properties, the purpose of this study isthreefold. First, to analyze the impact of systematic variations of a_{surf} onproperties of nuclei; second, to identify observables that can be safely usedto narrow down the range of appropriate values of a_{surf} to be targeted infuture parameter fits; third, to analyze the interdependence of a_{surf} withother properties of a nuclear EDF.  Results for a large variety of relevant observables of deformed nucleiobtained from self-consistent mean-field calculations with a set ofpurpose-built SLy5sX parameterizations of the Skyrme EDF are correlated withthe value of a_{surf}.  The three main conclusions are that there is an evident preference for acomparatively low value of a_{surf}, as expected from the performance ofexisting parameterizations; that the isospin dependence of the surface energyalso needs further finetuning in order to describe trends across the chart ofnuclei; and that a satisfying simultaneous description of fission barriers andsuperdeformed states requires a better description of the single-particlespectra.  [Note: The abstract has been abbreviated because of length restrictionsimposed by the arXiv. See the paper for the full abstract.]

The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals