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Three-body spin-orbit forces from chiral two-pion exchange

N. Kaiser
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Abstract

Using chiral perturbation theory, we calculate the density-dependent spin-orbit coupling generated by the two-pion exchange three-nucleon interaction involving virtual $Δ$-isobar excitation. From the corresponding three-loop Hartree and Fock diagrams we obtain an isoscalar spin-orbit strength $F_{\rm so}(k_f)$ which amounts at nuclear matter saturation density to about half of the empirical value of $90 $MeVfm$^5$. The associated isovector spin-orbit strength $G_{\rm so}(k_f)$ comes out about a factor of 20 smaller. Interestingly, this three-body spin-orbit coupling is not a relativistic effect but independent of the nucleon mass $M$. Furthermore, we calculate the three-body spin-orbit coupling generated by two-pion exchange on the basis of the most general chiral $ππNN$-contact interaction. We find similar (numerical) results for the isoscalar and isovector spin-orbit strengths $F_{\rm so}(k_f)$ and $G_{\rm so}(k_f)$ with a strong dominance of the p-wave part of the $ππNN$-contact interaction and the Hartree contribution.

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N. Kaiser. 2003-12-16. Three-body spin-orbit forces from chiral two-pion exchange. https://doi.org/10.1103/physrevc.68.054001

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