Large-Angle Elastic Scattering at High Energies

Abstract

High-energy scattering under reproducible conditions has been investigated for primary proton energies of up to 30 GeV at Brookhaven and CERN. The process can be divided into three main types: 1. Inelastic scattering. Very little is known theoretically, and the peripheral as well as the statistical model does not work very satisfactorily. Although rough estimates of production rates and spectra can be made, we are far from having any knowledge about the relevant amplitudes. 2. Small-momentum-transfer elastic scattering. Here, recent work on amplitudes, starting with the Mandelstam representation, Regge poles, and the multiperipheral model,1 has at least yielded definite predictions which can be compared to experiments. One of these is that the elastic differential cross section should behave as $$\frac{d\sigma_{el}}{dt}\ =(\frac{d\sigma_{el}}{dt})_{t=0}\ \cdot F(t)(\frac{s}{2m^2})^{2[\alpha(t)-1]}$$ (1) for fixed t (momentum transfer squared) and s (center of momentum energy squared) going to infinity. 3. Large-angle elastic scattering. Here again, very little is known. The approximations to the Mandelstam representation, peripheral and multiperipheral models, and the Regge pole hypothesis all fail. It seems, however, that the statistical model describes the situation fairly well. The reason is that large-angle elastic scattering is related to small impact parameters, i.e., central collisions, in which practically all center of momentum energy becomes available for particle production—the very condition for establishing thermodynamic equilibrium.