Nuclear energy density functional from chiral pion-nucleon dynamics

Abstract

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 ${\tilde{M}}^{\ast }(\rho )$ deviates by at most 15% from its free space value $M$, with $0.89M<{\tilde{M}}^{\ast }(\rho )<M$ for $\rho <0.11{\mathrm{fm}}^{-3}$ and ${\tilde{M}}^{\ast }(\rho )>M$ 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 ${\tilde{M}}^{\ast }(\rho )$ 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).

16 pages, 5 figures

References in corpus (5)

• Chiral Dynamics and Nuclear Matter
• Nuclear mean field from chiral pion-nucleon dynamics
• Single-particle potential in a chiral approach to nuclear matter including short range NN-terms
• Nuclear spin-orbit interaction from chiral pion-nucleon dynamics
• Isovector nuclear spin-orbit interaction from chiral pion-nucleon dynamics

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