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Tübingen 2003 – scientific programme

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HK: Physik der Hadronen und Kerne

HK 19: Theorie II

HK 19.10: Talk

Tuesday, March 18, 2003, 18:30–18:45, D

Nuclear energy density functional from chiral pion-nucleon dynamics — •Norbert Kaiser1, Stefan Fritsch1 und Wolfram Weise1,21Physik Department T39, Technische Universität München, D-85747 Garching — 2ECT*, Villa Tambosi, I-Villazzano (Trento)

We calculate the nuclear energy density functional E[ρ,τ,J  ] =ρĒ(ρ)+[τ−3ρ kf2/5]/(2 M*(ρ))+ (∇ρ)2  F(ρ)+ ∇ρ ·J  Fso(ρ)+ J 2   FJ(ρ) in the systematic framework of chiral perturbation theory. The calculation includes the two-loop Fock diagram of one-pion exchange and the three-loop Hartree and Fock diagrams of iterated one-pion exchange. These leading order contributions in the small momentum expansion lead already to a good equation of state of isospin symmetric nuclear matter (with a saturation density of ρ0 =0.174  fm−3 and a nuclear matter compressibility of K = 253 MeV) after adjusting one single momentum cut-off Λ= 612  MeV to the binding energy per particle Ē(ρ0)= −15.3 MeV. We find that the effective nucleon mass M*(ρ) deviates by about ± 14% from its free space value with M*(ρ)<M for ρ < 0.12   fm−3 and M*(ρ)>M for higher densities. The (parameterfree) strength of the (∇ρ)2-term, F(ρ), is comparable to that of Skyrme parameterizations. The magnitude of FJ(ρ) (accompanying the squared spin-orbit density J  2) comes out somewhat larger. The strength of the nuclear spin-orbit interaction, Fso(ρ), as given by iterated one-pion exchange is about half as large as the corresponding empirical value, however, with the wrong negative sign. The specific density dependencies of F∇,so,J(ρ) should be explored in nuclear structure calculations (after introducing an additional short range spin-orbit contribution).

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