Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

N. Kaiser

doi:10.1140/epja/i2010-10980-4

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Hadrons and Nuclei

Eur. Phys. J. A (2010) 45: 61-68
https://doi.org/10.1140/epja/i2010-10980-4

Regular Article - Theoretical Physics

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

N. Kaiser^*

Physik Department T39, Technische Universität München, D-85747, Garching, Germany

^* e-mail: nkaiser@ph.tum.de

Received: 26 February 2010
Revised: 27 April 2010
Accepted: 29 April 2010
Published online: 28 May 2010

Abstract

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: ( $\vec \nabla \rho _p - \vec \nabla \rho _n$ )² G _d( $\rho$ ) + ( $\vec \nabla \rho _p - \vec \nabla \rho _n$ ·( $\vec J_p - \vec J_n$ )G _so( $\rho$ ) + ( $\vec J_p - \vec J_n$ )² G _J( $\rho$ ) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from 1 $\pi$ -exchange, iterated 1 $\pi$ -exchange, and irreducible 2 $\pi$ -exchange with intermediate $\Delta$ -isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions G _d( $\rho$ ) , G _so( $\rho$ ) and G _J( $\rho$ ) which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.