On the geometric nature of high energy nucleus–nucleus reaction cross sections

Abstract

Within the context of a high energy double-folding optical potential approximation to the exact nucleus–nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the finite proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to the assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability limits for geometric reaction cross sections are determined.

Elastic differential cross sections for space radiation applications

“…Nuclear charge densities and the NN transition amplitude are parameterized to experimental data [5,11,12,[17][18][19][20].…”

“…where q = k ′ − k, q = |q|, ρ(q) is the nuclear matter density, t(e NN , q) is the NN transition amplitude, e NN is the NN CM energy, and η is the Möller frame transformation factor [7,32] used to transform from the AA to NN CM frame. Nuclear charge densities and the NN transition amplitude are parameterized to experimental data [5,11,12,[17][18][19][20].…”

“…The scattering amplitude is determined from eikonal phase factor, which is a function of the the optical potential [5,[14][15][16][17][18].…”

“…The eikonal approximation can be derived by assuming high energy and small angle scattering, which leads to a linearized propagator in the LS equation from which the eikonal scattering wave function may be obtained [7]. The scattering amplitude is determined from eikonal phase factor, which is a function of the the optical potential [5,[14][15][16][17][18].…”