Second-order equation of state with the Skyrme interaction : Cutoff and dimensional regularization with the inclusion of rearrangement terms

We evaluate the second-order (beyond-mean-field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero-range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond-mean-field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated with the density-dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second-order calculations in nuclear matter.