Analyzing power in nucleon-deuteron scattering and three-nucleon forces

Three-nucleon forces have been considered to be one possibility to resolve the well known discrepancy between experimental values and theoretical calculations of the nucleon analyzing power in low energy nucleondeuteron scattering. In this paper, we investigate possible effects of twopion exchange three-nucleon forces on the analyzing power and the differential cross section. We found that the reason for different effects on the analyzing power by different three-nucleon forces found in previous calculations is related to the existence of the contact term. Effects of some variations of two-pion exchange three-nucleon forces are investigated. Also, an expression for the measure of the nucleon analyzing power with quartet P-wave phase shifts is presented. Differential cross sections for nucleon-deuteron elastic scattering have peaks at forward and backward scattering angles and a minimum at a c.m. scattering angle of, e.g., θ ∼ 105 at E Lab = 3 MeV. Around the cross section minimum angle, some observables calculated with realistic nucleon-nucleon (NN) potentials are known to deviate systematically from experimental values [1]. The nucleon analyzing power Ay(θ) for energies below ≈ 30 MeV has exhibited a notable discrepancy [2, 3], which is referred to as the Ay(θ) puzzle. E.g., in the neutron-deuteron (n-d) elastic scattering at E Lab = 3 MeV, experimental Ay(θ) has a maximum value at θ ∼ 105 [4], while theoretical calculations with modern realistic NN potentials [5, 6, 7] undershoot the value by about 30 %. The three-nucleon (3N) system has been considered as a good testing ground for the NN interaction. The discrepancy between the experimental and calculated