Spin-dependent three-nucleon force effects on nucleon-deuteron scattering

Abstract

We construct a phenomenological three-nucleon force (3NF) model that gives a good description of polarization observables in elastic nucleon-deuteron (N -d) scattering at a low energy together with a realistic nucleon-nucleon force and a 3NF arising from the exchange of two pions. Parameters of the model, which consists of spinindependent, spin-orbit, and tensor components, are determined to reproduce the three-nucleon binding energy and polarization observables in N -d scattering at 3 MeV. Predictions of the 3NF model on N -d polarization observables at higher energies are examined, and the effects of each component on the observables are investigated. As is well known, modern two-nucleon force (2NF) models have a deficiency in explaining the binding energies of three-nucleon (3N) systems, and this problem is successfully solved by introducing a 3NF arising from the exchange process of two pions among three nucleons, which is called the two-pion-exchange (2π E) 3NF [1,2]. However, such combinations of the 2NFs and the 2π E-3NF that reproduce the 3N binding energy do not necessarily explain polarization observables in 3N scattering systems such as vector or tensor analyzing powers in elastic N -d scattering. See, e.g., Table III of Ref. [3], where calculations of observables with and without a 2π E-3NF are compared in terms of χ 2 with experimental data below 30 MeV of incident nucleon energy in the laboratory system. In spite of recent progress in constructing realistic 3NFs from chiral effective field theory or from heavier-boson-exchange mechanisms, no consensus has been obtained for possible mechanisms of 3NFs consistent with all of the experimental data. On the other hand, model 3NFs with artificial functional forms have been proposed to explain the polarization observables quite well [4][5][6]. These 3NFs have a form that typical components in 2NFs, e.g., central spin-independent, tensor, or spin-orbit components, are modified in the presence of third nucleon. [See Eq. (1) below.]In this paper, we introduce such a phenomenological 3NF to resolve the discrepancies of a 2NF and the 2π E-3NF at a low energy, and we examine whether it is still valid for N -d observables at higher energies up to 30 MeV. Since it may not be so difficult to understand what physical process is simulated by the spin dependence of each component, we expect that the present study will provide some hint of which characteristics of more realistic 3NFs should be studied.Our 3N calculations are based on a formalism to solve the Faddeev equations in coordinate space as integral equations [7,8]. For scattering states below the 3N breakup threshold energy, effects of the long-range Coulomb force between two * ishikawa@hosei.ac.jp protons are exactly treated [9]. Calculations for energies above the 3N breakup threshold are formulated in Ref. [10]. 3N partial wave states for which 2NFs and 3NFs act, are restricted to those with total two-nucleon angular momenta j 6 for bound state calculations, and j 3 for scattering state calculations. The ...

Coordinate space proton-deuteron scattering calculations including Coulomb force effects

“…In Ref. [12], it is shown that the use of the phenomenological 3NF together with the AV18+BR 800 , which is tuned to reproduce the 3N binding energy; A y (θ) and T 21 (θ) at E p = 3.0 MeV, is also successful in describing the neutron vector analyzing power A y (θ) of the nd scattering at higher energies. In Fig.…”

“…7, suggest that the 2πE-3NF is insufficient to comprise a Nuclear Hamiltonian in addition to the realistic 2NF. Since no possible mechanism to produce additional 3NF to remedy above defects is established, at the moment, a phenomenological 3NF model is introduced [12], which has a form that typical components in 2NP: central, tensor, and spinorbit components, are modified in the presence of third nucleon. The explicit form of the 3NF is…”

“…[8,9], and for the nd scattering at energies above the TBT in Refs. [10,11,12]. A direct application of the Faddeev equation to Coulombnic 3N systems, namely the 3 He bound state and the pd scattering, is known to bring a severe singularity to the integral kernel due to the long-range character of the proton-proton (pp) Coulomb force.…”

Momentum-space calculation of proton-deuteron scattering including Coulomb and irreducible three-nucleon forces

“…Nucleon-deuteron scattering has been extensively studied in the past with the aim of testing various nuclear interaction models, i.e., nucleon-nucleon (N N ) potentials and also three-nucleon (3N ) forces. While the theoretical description of neutron-deuteron (nd) scattering is considerably simpler and a number of highly sophisticated calculations [1][2][3][4][5] exists with realistic N N potentials and 3N forces, the experimental data are much more abundant and precise for proton-deuteron (pd) reactions. In that case there are only few realistic calculations above the deuteron breakup threshold.…”

Model study of short-range three-nucleon forces

“…Here we consider a phenomenological 3NF, V phe , of the following form [4,6,18], ¢ . Here we consider a phenomenological 3NF, V phe , of the following form [4,6,18], ¢ .…”