High-energy expansion for nuclear multiple scattering

Abstract

The Watson multiple scattering series is expanded to develop the Glauber approximation plus systematic corrections arising from three effects: (1) deviations from eikonal propagation between scatterings, (2) Fermi motion of struck nucleons, and (3) the kinematic transformation which relates the many-body scattering operators of the Watson series to the physical two-body scattering amplitude. Operators which express effects ignored at the outset to obtain the Glauber approximation are subsequently reintroduced via perturbation expansions. Hence a particular set of approximations is developed which renders the sum of the Watson series to the Glauber form in the center of mass system, and an expansion is carried out to find leading order corrections to that summation. Although their physical origins are quite distinct, the eikonal, Fermi motion, and kinematic corrections produce strikingly similar contributions to the scattering amplitude. It is shown that there is substantial cancellation between their effects and hence the Glauber approximation is more accurate than the individual approximations used in its derivation. It is shown that the leading corrections produce effects of order ${\left(2k{R}_c\right)}^{-1\mathrm{}}$ relative to the double scattering term in the uncorrected Glauber amplitude, $\hslash k$ being momentum and $R_c$ the nuclear charge radius. The leading order corrections are found to be small enough to validate quantitative analyses of experimental data for many intermediate to high energy cases and for scattering angles not limited to the very forward region. In a Gaussian model, the leading corrections to the Glauber amplitude are given as convenient analytic expressions.