Dimensional regularization applied to nuclear matter with a zero--range interaction

Abstract

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.

11 figures. Revised version

References in corpus (3)

• Resummation of fermionic in-medium ladder diagrams to all orders
• Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence
• Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models

Cited by in corpus (8)

• Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions
• Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon
• Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation
• Regularization of zero-range effective interactions in finite nuclei
• Newton's gravitation-force's classical average proof of a Verlinde's conjecture
• Skyrme interaction to second order in nuclear matter