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 nuclear spin-orbit strength U 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 ) of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, k f 0 = 272.7 MeV, a spinorbit strength at p = 0 of U ls (0, k f 0 ) ≃ 35 MeVfm 2 in perfect agreement with the empirical value used in the shell model. This novel spin-orbit strength is neither of relativistic nor of short range origin. The potential V ls underlying the empirical spin-orbit strength U ls = V ls r 2 ls becomes a rather weak one, V ls ≃ 17 MeV, after the identification r ls = m −1 π as suggested by the present calculation. We observe however a strong p-dependence of U ls (p, k f 0 ) leading even to a sign change above p = 200 MeV. This and other features of the emerging spin-orbit Hamiltonian which go beyond the usual shell model parametrization leave questions about the ultimate relevance of the spin-orbit interaction generated by 2π-exchange for a finite nucleus. We also calculate the complex-valued isovector singleparticle potential U I (p, k f )+i W I (p, k f ) in isospin asymmetric nuclear matter proportional to τ 3 (N − Z)/(N + Z). For the real part we find reasonable agreement with empirical values and the imaginary part vanishes at the Fermi-surface p = k f . : 12.38.Bx, 21.65.+f, 24.10.Cn Keywords: Effective field theory at finite density, Nuclear spin-orbit interaction, Complex single-particle potential in isospin asymmetric nuclear matter. PACS

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].…”

Relativistic models for nuclear structure and low-energy QCD phenomenology

“…The low-energy constants (contact terms or subtraction constants) are adjusted to reproduce basic properties of symmetric and asymmetric nuclear matter at the saturation point. The same framework has also been used for other purposes: deriving a (non-relativistic) energy density functional [7], extracting the nuclear spin-orbit interaction [8] and the description of hyperons in a nuclear medium [9]. Concerning the spin-orbit interaction, and in particular its microscopic origin, it is worthy mentioning the new remarkable interpretation presented in Ref.…”

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

“…A strong p-dependence of the nuclear spin-orbit strength U ls (p, k f 0 ) arising from iterated 1π-exchange has however been observed in ref. [7]. A further property of the spin-orbit Hamiltonian emerging from that diagrammatic calculation was that it has (in coordinate space) terms proportional to ∇f (r) as well as terms proportional to f (r) ∇f (r) (with f (r) = ρ(r)/ρ(0) the normalized radial density profile) which get weighted differently at the surface of a finite nucleus.…”

“…[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 scattering off weakly inhomogeneous isospin-symmetric nuclear matter.…”

“…Nuclear structure calculation which use the results of ref. [7] as input are necessary in order to clarify the role of the nuclear spin-orbit interaction generated by 2π-exchange.The purpose of the present work is to calculate using the same framework as in ref.[7] the isovector spin-orbit strength V ls (p, k f ) generated by iterated 1π-exchange in order to reveal the underlying isospin dependence. Furthermore, we calculate here several relativistic 1/Mcorrections to the isoscalar nuclear spin-orbit strength U ls (p, k f ).…”