Nuclear energy density functional from chiral pion-nucleon dynamics

Details Nuclear energy density functional from chiral pion-nucleon dynamics Nuclear energy density functional from chiral pion-nucleon dynamics

2002-12-11

arxiv.org/abs/nucl-th/0212049v1

Nucl.Phys. A724 (2003) 47-68

Physics

Nuclear Physics

Nuclear Theory

16 pages, 5 figures

Scientific paper

10.1016/S0375-9474(03)01475-1

We calculate the nuclear energy density functional relevant for N=Z even-even nuclei in the systematic framework of chiral perturbation theory. 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 very good equation of state of isospin symmetric nuclear matter. We find that in the region below nuclear matter saturation density the effective nucleon mass $\widetilde M^*(\rho)$ deviates by at most 15% from its free space value $M$, with $0.89M<\widetilde M^*(\rho)M$ for higher densities. The parameterfree strength of the $(\vec\nabla \rho)^2$-term, $F_\nabla(k_f)$, is at saturation density comparable to that of phenomenological Skyrme forces. The magnitude of $F_J(k_f)$ accompanying the squared spin-orbit density $\vec J ^2$ comes out somewhat larger. The strength of the nuclear spin-orbit interaction, $F_{so}(k_f)$, as given by iterated one-pion exchange is about half as large as the corresponding empirical value, however, with the wrong negative sign. The novel density dependencies of $\widetilde M^*(\rho)$ and $F_{\nabla,so,J}(k_f)$ as predicted by our parameterfree calculation should be examined in nuclear structure calculations (after introducing an additional short range spin-orbit contribution constant in density).

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