Nucleon-Nucleon Scattering from One-Boson-Exchange Potentials

Nucleon-nucleon scattering is studied for laboratory scattering energies over the 0 to 320-MeV range for states with angular momentum l≥1. Our central hypothesis is that the interaction may be represented by a series of one-boson-exchange potentials. To this end, we attempt to fit the phenomenological models of Lassila et al. (Yale) and of Hamada and Johnston with the series of one-boson-exchange potentials due to the ρ, ω, π, and η, with the meson-nucleon coupling constants taken as adjustable parameters. We find that additional attraction is required in the central potentials, and we provide this by introducing two scalar mesons of isotopic spin 0 to 1, respectively. We next consider the nucleon-nucleon phase shifts that have been determined through phase-shift analysis of the N-N data by several groups. We achieve reasonable fits to the P, D, and F states with the following searched parameters: g_η²=7.0, g_π²=11.7, g_ω²=21.5, g_ρ²=0.68, f_ρg_ρ=1.8, m₀=560 MeV, g₀²=9.4, m₁=770 MeV, and g₁²=6.5; the parameters of the $T=0$ and $T=1$ scalar mesons are identified by the subscripts 0 and 1, respectively, and ${{L}ᵢₙₜ}^{({ρ})}={(4{π})}1/2{g}_{{ρ}}{{ψ}}{τ}{{γ}}^{{μ}}{ψ}{{ρ}}_{{μ}}+{(4{π})}1/2({{f}_{{ρ}}}{2{m}_{{ρ}}}){{ψ}}{τ}{{σ}}^{{μ}{ν}}{ψ}[{{∂}}_{{ν}}{{ρ}}_{{μ}}{-}{{∂}}_{{μ}}{{ρ}}_{{ν}}].$ Predetermined parameters are ${m}_{{ρ}}=760$ MeV, ${m}_{{ω}}=782$ MeV, ${m}_{{π}}=138.2$ MeV, ${m}_{{η}}=548$ MeV, and ${{f}_{{ω}}}{{g}_{{ω}}}=0$. Because of the ${r}^{{-}3}$ behavior of the potentials at the origin, all potentials are set to zero within 0.6 F. This has (surprisingly) little effect in most states but does eliminate bound $³P₂$ and $³F₄$ states. The effect of including the ${φ}$ and the relation to other experiments is discussed.