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Zero-range effective interactions are commonly used in nuclear physics todescribe a many-body system in the mean-field framework. If they are employedin beyond- mean-field models, an artificial ultraviolet divergence is generatedby the zero-range of the interaction. We analyze this problem in symmetricnuclear matter with the t0-t3 Skyrme model. In this case, the second-orderenergy correction diverges linearly with the momentum cutoff. After that, weextend the work to the case of nuclear matter with the full Skyrme interaction.A strong divergence related to the velocity-dependent terms of the interactionis obtained. Moreover, a global fit can be simultaneously performed for bothsymmetric and nuclear matter with different neutron-to-proton ratios. Theseresults pave the way for applications to finite nuclei in the framework ofbeyond mean-field theories.

A beyond-mean-field example with zero-range effective interactions in infinite nuclear matter