# Bonn 2010 – wissenschaftliches Programm

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# HK: Fachverband Physik der Hadronen und Kerne

## HK 24: Struktur und Dynamik von Kernen V

### HK 24.9: Vortrag

### Dienstag, 16. März 2010, 18:45–19:00, HG II

**Nuclear energy density functional from chiral pion-nucleon dynamics** — •Norbert Kaiser and Wolfram Weise — Physik-Department, Technische Universität München, Garching

We use a recently improved density-matrix expansion (B. Gebremariam, T. Duguet, S.K. Bogner, nucl-th:0910.4979) to calculate the nuclear energy density functional in chiral perturbation theory. Our calculation treats systematically the effects from 1π-exchange, iterated 1π-exchange, and irreducible 2π-exchange with intermediate Δ-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass *M*^{*}(ρ) is identical to the one of Fermi-liquid theory. The strength *F*_{∇}(ρ) of the (∇^{→}ρ)^{2} surface-term as provided by
the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region ρ_{0}/2 <ρ < ρ_{0}. The spin-orbit coupling strength *F*_{so}(ρ) receives contributions from iterated 1π-exchange (of the “wrong sign”) and from three-nucleon interactions mediated by 2π-exchange with virtual Δ-excitation (of the “correct sign”). In the region around ρ_{0}/2 ≃ 0.08 fm^{−3} where the spin-orbit interaction in nuclei gains most of its weight these two components
tend to cancel, thus leaving all room for the short-range spin-orbit interaction. The strength function *F*_{J}(ρ) multiplying the squared spin-orbit density *J*^{→}^{ 2} is also studied.

Work supported in part by BMBF, GSI and the DFG cluster of excellence: Origin and Structure of the Universe.