Analysis of the Elastic Scattering of Protons at High Energy and Momentum Transfer Using the Serber Model

Serber's model for describing proton-proton scattering is investigated in detail at two laboratory momenta, 11.26 and 30.0 GeV/c, by carrying out a partial-wave computation with the potential $A=(A_0, \mathrm{A})=\left(\frac{i\eta e^{-\Lambda r}}{r, 0, 0, 0}\right)$ inserted into the Klein-Gordon equation $[{({\mathrm{p}}_{\mathrm{o}p}-\mathrm{A})}^2+m^2]\psi ={(E-A_0)}^2\psi$. The two resulting momentum-transfer distributions obtained differ from those obtained by Serber, who used an optical approximation. Both curves are raised above Serber's in the high-momentum-transfer region. This causes the 11.26-GeV/c curve to be in better agreement with the data and the 30.0-GeV/c curve to overshoot the data, yielding worse agreement. The raising of these momentum-transfer curves in the high-momentumtransfer region is due to the appearance of a real part in the low-angular-momentum contributions to the scattering amplitude.