Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector spin-orbit terms

Abstract

We extend a recent calculation of the nuclear energy density functional in the systematic framework of chiral perturbation theory by computing the isovector spin-orbit terms: $(\vec{\nabla }{\rho }_p-\vec{\nabla }{\rho }_n)\cdot ({\vec{J}}_p-{\vec{J}}_n)G_{so}(k_f)+({\vec{J}}_p-{\vec{J}}_n{)}^2{G}_J(k_f)$. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a good equation of state of isospin-symmetric nuclear matter. We find that the parameterfree results for the (density-dependent) strength functions $G_{so}(k_f)$ and $G_J(k_f)$ agree fairly well with that of phenomenological Skyrme forces for densities $\rho >{\rho }_0/10$. At very low densities a strong variation of the strength functions $G_{so}(k_f)$ and $G_J(k_f)$ with density sets in. This has to do with chiral singularities $m_{\pi }^{-1}$ and the presence of two competing small mass scales $k_f$ and $m_{\pi }$. The novel density dependencies of $G_{so}(k_f)$ and $G_J(k_f)$ as predicted by our parameterfree (leading order) calculation should be examined in nuclear structure calculations.

Comments: 9 pages, 3 figure, published in: Physical Review C68, 014323 (2003)