Real Part of the $p-p$, $p-d$, and $p-n$ Forward Scattering Amplitudes from 50 to 400 GeV

Proton-proton and proton-deuteron elastic scattering has been measured for incident laboratory energy from 50 to 400 GeV; minimum $\mathrm{}\left|t\right|\mathrm{}$ values were, for $p-p$, 0.0005 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, and for $p-d$, 0.0008 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. From the differential cross sections we have determined the ratios of the real to imaginary parts of the forward scattering amplitude, ${\rho }_{\mathrm{pp}}$ and ${\rho }_{\mathrm{pd}}$, for $p-p$ and $p-d$ scattering. Using a Glauber approach and a sum-of-exponentials form factor we obtain ${\rho }_{\mathrm{pn}}$ for $p-n$ scattering.