1202.3257 (Kassem Moghrabi et al.)

Dimensional regularization applied to nuclear systems    [PDF]

Kassem Moghrabi, Marcella Grasso

We apply for the first time 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 symmetric nuclear matter with a
zero-range effective interaction. The unphysical ultraviolet divergence
generated at second order by the zero range of the interaction is properly
removed by the regularization technique and the regularized equation of state
(mean-field + second-order contributions) is adjusted to a reference equation
of state. One of the main practical advantages 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 and rigorous technique
to remove the divergent terms and to generate regularized effective
interactions is likely to be applied in future in the framework of beyond
mean-field models for finite nuclei.

View original: http://arxiv.org/abs/1202.3257