Isovector nuclear spin–orbit interaction from chiral pion–nucleon dynamics

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 2 σ · ( q × p )[U ls (p, k f ) − V ls (p, k f )τ 3 δ] of a nucleon scattering off weakly inhomogeneous isospinasymmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, k f 0 = 272.7 MeV, an isovector nuclear spin-orbit strength at p = 0 of V ls (0, k f 0 ) ≃ 50 MeVfm 2 . This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength U ls (0, k f 0 ) ≃ 35 MeVfm 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 ππN N -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. : 12.38.Bx, 21.65.+f, 24.10.Cn Keywords: Effective field theory at finite density, Isoscalar and isovector nuclear spin-orbit interaction. PACSwhich include additional non-linear couplings of the scalar and vector fields or explicitly densitydependent point couplings of nucleons are nowadays widely and successfully used for nuclear structure calculations [3,4,5].The nuclear spin-orbit potential arises generally as a many-body effect from the underlying spin-orbit term in the (free) nucleon-nucleon scattering amplitude. The calculation of the tree level diagrams with one scalar-meson or one vector-meson exchange between nucleons gives indeed a spin-orbit term in the NN T-matrix proportional to 1/M 2 , with M denoting the nucleon mass. The nuclear spin-orbit potential corresponding to scalar and vector meson exchange is therefore obviously a truly relativistic effect. However, the quadratic reciprocal scaling of the spin-orbit NN-amplitude with the nucleon mass M is not universal, and it changes if one considers the exchange of two mesons between nucleons, i.e. loop diagrams. For example, irreducible two-pion exchange gives rise to a spin-orbit term in the NN T-matrix proportional to 1/M (see eqs. (22,23) in ref. [6]) and iterated one-pion exchange produces a spin-orbit term in the NN T-matrix which even scales linearly with the nucleon mass M (see eq.(33) in ref. [6]).In a recent work [7] we have used the systematic framework of chiral perturbation theory to calculate the nuclear spin-orbit interaction generated by one-and two-pion exchange. The momentum and density dependent nuclear spin-orbit strength U ls (p, k f ) is derived from the spindependent part of the interaction energy Σ spin = i 2 σ · ( q × p ) U ls (p, k f ) of a nucleon ...

Nuclear energy density functional from chiral pion–nucleon dynamics

“…Their effect on the nuclear spin-orbit interaction has been calculated in ref. [18]. Inserting the expression U (2π) ls (p, k f ) in eq.…”

“…( 18) of ref. [18] into the "master formula" eq. (32) one derives the following contribution from irreducible 2π-exchange to the spin-orbit strength function:…”

Hypernuclear single particle spectra based on in-medium chiral dynamics

“…Three-nucleon interactions are systematically incorporated. Spin-orbit forces follow consistently from the evaluation of spin-dependent terms in inhomogeneous nuclear matter [23][24][25][26][27].…”