Empirical Parameterization of Nucleon-Nucleon Scattering Amplitude at High Energies for Glauber Calculations and Monte Carlo Simulations

V. Uzhinsky, A. Galoyan, Q. Hu, J. Ritman, H. Xu

Published 2016-03-15Version 1

Parameterization of the nucleon-nucleon elastic scattering amplitude is needed for future experiments with nucleon and nuclear beams in the kinetic energy range 1 - 50 GeV/nucleon. The amplitude is used in Glauber calculations of various cross sections and Monte Carlo simulations of nucleon-nucleon scatterings. Usually, the differential nucleon-nucleon elastic scattering cross sections are described by an exponential expression. Fitting corresponding experimental data on $pp$ interactions at $|t|>$ 0.005 (GeV/c)$^2$ and $|t|\leq$ 0.125 (GeV/c)$^2$ we have found parameters of the expression and propose formulae for approximations of their energy dependencies in the considered energy range. The same was done for $np$ interactions at $|t|\leq$ 0.5 (GeV/c)$^2$. Expressions for the energy dependence of the total and elastic cross sections, and the ratio of real to imaginary parts of the amplitude at zero momentum transfer are also given for $pp$ and $np$ collisions. It is sufficient for the Glauber calculations in a first approximation. For more exact calculations we fit the data at $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on maximum value of $|t|$ using a two coherent exponential expression. The parameters of the fits are found for the energy range 1.5 - 50 GeV.