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

TL;DR

This paper provides a comprehensive parameterization of nucleon-nucleon elastic scattering amplitudes for beam momenta between 5 and 50 GeV/c, facilitating improved Glauber calculations and Monte Carlo simulations in nuclear physics.

Contribution

It introduces new formulae for the momentum dependence of scattering parameters, covering the 5-50 GeV/c range, filling a gap between existing high and low energy parameterizations.

Findings

Parameterizations for $pp$ and $np$ interactions across the specified momentum range.

Expressions for total, elastic cross sections, and amplitude ratios at zero momentum transfer.

Fits to experimental data using exponential models for accurate simulations.

Abstract

A parameterization 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 parameterizations of the amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} \leq$ 5 GeV/c. Our paper is aimed to cover 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 $|t|>$ 0.005 (GeV/c)$^2$ and $|t|\leq$ 0.125 (GeV/c)$^2$ have been fit. We propose formulae to approximate the beam momentum dependence of these parameters in the momentum range considered. The same was done for $np$ interactions at $|t|\leq$ 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 $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on the maximum value of $|t|$ using an expression based on two coherent exponential. The parameters of the fits are found for the beam momentum range 2 -- 50 GeV/c.