  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.
