Empirical parametrization of the nucleon-nucleon elastic scattering amplitude at high beam momenta for Glauber calculations and Monte Carlo simulations

A parametrization of the nucleon-nucleon elastic scattering amplitude is needed for future experiments with nucleon and nuclear beams in the beam momentum range of 2-50 GeV/c/nucleon. There are many parametrizations of the amplitude at P-lab > 25-50 GeV/c, and at P-lab <= 5 GeV/c. Our paper is aimed at covering the range between 5-50 GeV/c. 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. Corresponding experimental data on pp interactions at vertical bar t vertical bar > 0.005 (GeV/c)(2) and vertical bar t vertical bar <= 0.125 (GeV/c)(2) have been fit. We propose formulas to approximate the beam momentum dependence of these parameters in the momentum range considered. The same was done for np interactions at vertical bar t vertical bar <= 0.5 (GeV/c)(2). Expressions for the momentum 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. These results are sufficient for a first approximation of the Glauber calculations. For more exact calculations we fit the data at vertical bar t vertical bar > 0.005 (GeV/c)(2) without restrictions on the maximum value of vertical bar t vertical bar using an expression based on two coherent exponentials. The parameters of the fits are found for the beam momentum range 2-50 GeV/c.