A complete set of total cross sections for imaginary parts of nd forward scattering amplitudes and three-nucleon force effects

In the neutron-deuteron scattering, four total cross sections are shown to form a complete set for the determination of the imaginary parts of the forward amplitudes because of the optical theorem. The amplitudes are decomposed into scalar and tensor ones in the spin space. Contributions of threenucleon forces (3NF) to these amplitudes are studied, by the Faddeev calculation, which predicts significant tensor effects of the 3NF. In recent years, three-nucleon systems have attracted a considerable attention as important sources of information on nuclear interactions, because of possible participation of three-nucleon forces (3NF) in addition to two-nucleon ones. Various versions of the two-nucleon force (2NF) have been examined as the input of three-nucleon (3N) calculations and have been found to be deficient in reproducing some empirical observables [1]. Improvements of the calculations have been achieved by introducing the 2π exchange 3NF on the three-nucleon binding energy [2] and the minimum of the proton-deuteron (pd) elastic scattering cross section between 50 and 200 MeV [3]. However, the prescription is not always effective for observables in polarization phenomena. In fact, the 3NF cannot explain the proton vector analyzing power between 65 and 200 MeV[4] of ~ pd scattering, and the deuteron tensor analyzing powers at 270 MeV of ~ dp scattering [5]. Also, discrepancies of the nucleon and deuteron vector analyzing powers between the calculated and the measured in low energy neutron-deuteron (nd) scattering still remain to be unsolved even with the 3NF [6, 7]. These indicate that the comprehensive understanding about a role of the nuclear interactions, particularly that of their spin dependence, on the 3N spin observables has not yet been obtained. In general, the spin dependence of the nuclear interactions should be reflected in the spin observables through the spin structure of scattering amplitudes. Paying attention to the spin structure, we will consider imaginary parts of forward amplitudes of the nd elastic scattering, which are described in terms of total cross sections by the optical theorem, to criticize the nuclear interactions in a different aspect. Total cross sections have varieties due to the combination of the spin orientation of projectiles and that of targets. Denoting spin density matrices of the neutron and the deuteron in the initial state by ρ and ρ [8], respectively, and the scattering matrix at the forward angle by Mθ=0, the corresponding total cross section σ is given by the optical theorem as σ = αIm { Tr(ρρMθ=0) } , (1) where α = 4π k , (2) with k being the magnitude of the nd relative momentum k. When such kinds of total cross sections are measured sufficiently, the determination is unambiguous and the imaginary parts obtained will become