Nucleon-Nucleon Scattering from One-Boson-Exchange Potentials

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Nucleon-nucleon scattering is studied for laboratory scattering energies over the 0 to 320-MeV range for states with angular momentum $l\ensuremath{\ge}1$. 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 $\ensuremath{\rho}$, $\ensuremath{\omega}$, $\ensuremath{\pi}$, and $\ensuremath{\eta}$, 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 $N\ensuremath{-}N$ data by several groups. We achieve reasonable fits to the $P$, $D$, and $F$ states with the following searched parameters: ${{g}_{\ensuremath{\eta}}}^{2}=7.0$, ${{g}_{\ensuremath{\pi}}}^{2}=11.7$, ${{g}_{\ensuremath{\omega}}}^{2}=21.5$, ${{g}_{\ensuremath{\rho}}}^{2}=0.68$, $\frac{{f}_{\ensuremath{\rho}}}{{g}_{\ensuremath{\rho}}}=1.8$, ${m}_{0}=560$ MeV, ${{g}_{0}}^{2}=9.4$, ${m}_{1}=770$ MeV, and ${{g}_{1}}^{2}=6.5$; the parameters of the $T=0$ and $T=1$ scalar mesons are identified by the subscripts 0 and 1, respectively, and ${{\mathcal{L}}_{\mathrm{int}}}^{(\ensuremath{\rho})}={(4\ensuremath{\pi})}^{\frac{1}{2}}{g}_{\ensuremath{\rho}}\overline{\ensuremath{\psi}}\ensuremath{\tau}{\ensuremath{\gamma}}^{\ensuremath{\mu}}\ensuremath{\psi}{\ensuremath{\rho}}_{\ensuremath{\mu}}+{(4\ensuremath{\pi})}^{\frac{1}{2}}(\frac{{f}_{\ensuremath{\rho}}}{2{m}_{\ensuremath{\rho}}})\overline{\ensuremath{\psi}}\ensuremath{\tau}{\ensuremath{\sigma}}^{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{\psi}[{\ensuremath{\partial}}_{\ensuremath{\nu}}{\ensuremath{\rho}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\rho}}_{\ensuremath{\nu}}].$ Predetermined parameters are ${m}_{\ensuremath{\rho}}=760$ MeV, ${m}_{\ensuremath{\omega}}=782$ MeV, ${m}_{\ensuremath{\pi}}=138.2$ MeV, ${m}_{\ensuremath{\eta}}=548$ MeV, and $\frac{{f}_{\ensuremath{\omega}}}{{g}_{\ensuremath{\omega}}}=0$. Because of the ${r}^{\ensuremath{-}3}$ 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 $^{3}P_{2}$ and $^{3}F_{4}$ states. The effect of including the $\ensuremath{\varphi}$ and the relation to other experiments is discussed.