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

Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0-t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.