Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence

Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy that display an ultraviolet divergence are found. We propose a general strategy to regularize this divergence and we illustrate it in the case of the second-order corrections to the equation of state (EOF) of uniform symmetric matter. By setting a momentum cutoff $\Lambda$, we show that for every (physically meaningful) value of $\Lambda$ it is possible to determine a new interaction such that the EOS with the second-order corrections reproduces the empirical EOS, with a fit of the same quality as that obtained at the mean-field level.