Skyrme interaction to second order in nuclear matter

Abstract

Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin-orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between $s$-wave and $p$-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region $0<\rho <2{\rho }_0$. The reason for this feature is the too strong density-dependence ${\rho }^{8/3}$ of several second-order contributions. The inclusion of the density-dependent term $\frac{1}{6}{t}_3{\rho }^{1/6}$ is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.

19 pages, 6 figures

References in corpus (8)

• Chiral effective field theory and nuclear forces
• The Skyrme Interaction in finite nuclei and nuclear matter
• Particle-Number Projection and the Density Functional Theory
• Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms
• Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence
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• New density-independent interactions for nuclear structure calculations
• Semi-contact 3-body interaction for nuclear density functional theory

Cited by in corpus (7)

• Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory
• Effective density functionals beyond mean field
• From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter
• Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory