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 $l\ge 1$. 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 $\rho$, $\omega$, $\pi$, and $\eta$, 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 $N-N$ data by several groups. We achieve reasonable fits to the $P$, $D$, and $F$ states with the following searched parameters: ${g_{\eta }}^2=7.0\mathrm{}$, ${g_{\pi }}^2=11.7\mathrm{}$, ${g_{\omega }}^2=21.5\mathrm{}$, ${g_{\rho }}^2=0.68\mathrm{}$, $\frac{f_{\rho }}{g_{\rho }}=1.8\mathrm{}$, $m_0=560\mathrm{}$ MeV, ${g_0}^2=9.4\mathrm{}$, $m_1=770\mathrm{}$ MeV, and ${g_1}^2=6.5\mathrm{}$; the parameters of the $T=0\mathrm{}$ and $T=1\mathrm{}$ scalar mesons are identified by the subscripts 0 and 1, respectively, and ${{\mathcal{L}}_{\mathrm{int}}}^{\left(\rho \right)}={\left(4\mathrm{}\pi \right)}^{\frac{1}{2}}{g}_{\rho }\overline{\psi }\tau {\gamma }^{\mu }\psi {\rho }_{\mu }+{\left(4\mathrm{}\pi \right)}^{\frac{1}{2}}\left(\frac{f_{\rho }}{2m_{\rho }}\right)\overline{\psi }\tau {\sigma }^{\mu \nu }\psi [{\partial }_{\nu }{\rho }_{\mu }-{\partial }_{\mu }{\rho }_{\nu }].\mathrm{}$ Predetermined parameters are $m_{\rho }=760\mathrm{}$ MeV, $m_{\omega }=782\mathrm{}$ MeV, $m_{\pi }=138.2\mathrm{}$ MeV, $m_{\eta }=548\mathrm{}$ MeV, and $\frac{f_{\omega }}{g_{\omega }}=0\mathrm{}$. Because of the $r^{-3\mathrm{}}$ 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 $\phi$ and the relation to other experiments is discussed.