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

Abstract

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 to 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.

29 figures, 9 tables

References in corpus (3)

• Linear response of homogeneous nuclear matter with energy density functionals
• Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence
• Regularization of zero-range effective interactions in finite nuclei

Cited by in corpus (13)

• Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions
• Energy-density functionals inspired by effective-field theories: Applications to neutron drops
• Towards a self-consistent dynamical nuclear model
• A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length
• From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter
• Beyond-mean-field effects on the symmetry energy and its slope from the low-lying dipole response of ${}^{68}$Ni
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Dimensionally regularized Boltzmann-Gibbs Statistical Mechanics and two-body Newton's gravitation
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Lee-Yang-inspired energy-density functional including contributions from $p$-wave scattering
• Newton's gravitation-force's classical average proof of a Verlinde's conjecture
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory