Nucleon-nucleon cross sections via stochastic processes in phase space: One-dimensional scattering

Abstract

One-dimensional nucleon-nucleon scattering is simulated by Monte Carlo techniques in the quasiclassical approximation of the Wigner representation. Nucleons are represented by minimum wave packets of approximate nucleon radii, their linear dispersion offset by intrinsic harmonic oscillation, inducing phase space spin in the nucleon Wigner function. A representative set of points evolve in four-dimensional phase space in deterministic classical and stochastic quantum momentum jumps. In the extended space, the inter-nucleon one-pion exchange potential is defined locally by the point coordinates. By the geometric analogy, cross sections are computed from collision distances considered as impact parameters. Results from the parameter free one-dimensional simulation show reasonable agreement with empirical data in the energy range 0.01 GeV to 5 GeV.