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 Weise^1,2 — ¹Physik 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 k_f²/5]/(2 M^*(ρ))+ (∇^→ρ)²  F_∇(ρ)+ ∇^→ρ ·J^→  F_so(ρ)+ J^→ 2   F_J(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 F_J(ρ) (accompanying the squared spin-orbit density J^{→  2}) comes out somewhat larger. The strength of the nuclear spin-orbit interaction, F_so(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).