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

Abstract

Using chiral perturbation theory, we calculate the density-dependent spin-orbit coupling generated by the two-pion exchange three-nucleon interaction involving virtual $\Delta$-isobar excitation. From the corresponding three-loop Hartree and Fock diagrams we obtain an isoscalar spin-orbit strength $F_{\mathrm{so}}(k_f)$ which amounts at nuclear matter saturation density to about half of the empirical value of $90$MeVfm${}^5$. The associated isovector spin-orbit strength $G_{\mathrm{so}}(k_f)$ 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 $\pi \pi NN$-contact interaction. We find similar (numerical) results for the isoscalar and isovector spin-orbit strengths $F_{\mathrm{so}}(k_f)$ and $G_{\mathrm{so}}(k_f)$ with a strong dominance of the p-wave part of the $\pi \pi NN$-contact interaction and the Hartree contribution.

8 pages, 4figure, published in : Physical Review C68, 054001 (2003)

References in corpus (1)

• Nuclear energy density functional from chiral pion-nucleon dynamics

Cited by in corpus (14)

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• Chiral SU(3) dynamics and $\Lambda$-hyperons in the nuclear medium
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• Nuclear energy density functional from chiral pion-nucleon dynamics revisited
• Strength of reduced two-body spin-orbit interaction from chiral three-nucleon force
• In-medium chiral SU(3) dynamics and hypernuclear structure
• Note on spin-orbit interactions in nuclei and hypernuclei
• Uncovering the mechanism of chiral three-nucleon force in driving spin-orbit splitting
• From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure
• Hypernuclei and in-medium chiral dynamics
• Standard Model Masses and Models of Nuclei