Proton-Proton Elastic Scattering Involving Large Momentum Transfers

Twenty-nine proton-proton differential elastic cross sections for lab momenta ${p}_{0}$ from 11 to 31.8 BeV/c, at four-momentum transfers squared, $\ensuremath{-}t$, from 2.3 to 24.4 ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, have been measured at the Brookhaven alternating gradient synchrotron. The circulating proton beam impinged upon a thin C${\mathrm{H}}_{2}$ internal target. Both scattered protons from $p\ensuremath{-}p$ elastic events were detected by scintillation-counter telescopes which were placed downstream from deflection magnets set at the appropriate angles to the incident beam. The angular correlation of the protons, their momenta, and the coplanarity of the events were determined by the detection system. The results show that at high momentum transfers the differential cross section, $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$, depends strongly upon the energy; for $\ensuremath{-}t=10$ ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, the value of $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ at ${p}_{0}=30$ BeV/c is smaller by a factor\ensuremath{\sim}1000 than at ${p}_{0}=10$ BeV/c. At all energies, $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}$ falls rapidly with increasing $|t|$ for scattering angles up to about 65\ifmmode^\circ\else\textdegree\fi{} (c.m.), while in the range from 65 to 90\ifmmode^\circ\else\textdegree\fi{} the cross section falls only by a factor of about 2. The smallest cross section measured was 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}37}$ ${\mathrm{cm}}^{2}$ ${\mathrm{sr}}^{\ensuremath{-}1}$ (c.m.), at ${p}_{0}=31.8$ BeV/c and $\ensuremath{-}t=20.4$ ${(\mathrm{B}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$; this is about 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ of the zero-degree cross section at the same energy.