## Abstract

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density-dependent isovector nuclear spin-orbit strength V_{ls}(p,k_{f}). This quantity is derived from the spin-dependent part of the interaction energy Σ_{spin}=i/2σ→· (q→×p→)[U_{ls}(p,k_{f})- V_{ls}(p,k_{f})τ_{3}δ] of a nucleon scattering off weakly inhomogeneous isospin-asymmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, k_{f0}=272.7 MeV, an isovector nuclear spin-orbit strength at p=0 of V_{ls}(0,k_{f0})≃50 MeV fm^{2}. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength U_{ls}(0,k_{f0})≃35 MeV fm^{2} generated by the same two-pion exchange diagrams. We also calculate several relativistic 1/M-corrections to the isoscalar nuclear spin-orbit strength. In particular, we evaluate the contributions from irreducible two-pion exchange to U_{ls}(p,k_{f}). The effects of the three-body diagrams constructed from the Weinberg-Tomozawa ππNN-contact vertex on the isoscalar nuclear spin-orbit strength are computed. We find that such relativistic 1/M-corrections are less than 20% of the isoscalar nuclear spin-orbit strength generated by iterated one-pion-exchange, in accordance with the expectation from chiral power counting.

Original language | English |
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Pages (from-to) | 157-173 |

Number of pages | 17 |

Journal | Nuclear Physics, Section A |

Volume | 720 |

Issue number | 1-2 |

DOIs | |

State | Published - 2 Jun 2003 |

## Keywords

- Effective field theory at finite density
- Isoscalar and isovector nuclear spin-orbit interaction