  We apply the dimensional regularization procedure to treat an ultraviolet
divergence occurring in the framework of the nuclear many-body problem. We
consider the second--order correction (beyond the mean-field approximation) to
the equation of state of nuclear matter with a zero-range effective
interaction. The unphysical ultraviolet divergence that is generated at second
order by the zero range of the interaction is removed by the regularization
technique and the regularized equation of state (mean-field + second-order
contributions) is adjusted to a reference equation of state. The main practical
advantage of this procedure, with respect to a cutoff regularization, is to
provide a unique set of parameters for the adjusted effective interaction. This
occurs because the regularized second-order correction does not contain any
cutoff dependence. The encouraging results found in this work indicate that
such an elegant technique to generate regularized effective interactions is
likely to be applied in future to finite nuclei in the framework of beyond
mean-field models.
