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

Abstract

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 $A=({A}_{0}, \mathrm{A})=(\frac{i\ensuremath{\eta}{e}^{\ensuremath{-}\ensuremath{\Lambda}r}}{r, 0, 0, 0})$ inserted into the Klein-Gordon equation $[{({\mathrm{p}}_{\mathrm{o}p}\ensuremath{-}\mathrm{A})}^{2}+{m}^{2}]\ensuremath{\psi}={(E\ensuremath{-}{A}_{0})}^{2}\ensuremath{\psi}$. 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.