Shadowing and antishadowing effects in a model for then+dtotal cross section

Abstract

Based on the multiple scattering series incorporated in the Faddeev scheme the high-energy limit of the total $n+d$ cross section is evaluated in a nonrelativistic model system where spins are neglected. In contrast to the naive expectation that the total $n+d$ scattering cross section is the sum of two $\mathrm{NN}$ cross sections we find two additional effects resulting from rescattering processes. These additional terms have different signs (shadowing and antishadowing) and a different behavior as function of the energy. Our derivation of these results which are already known from Glauber theory is based on the analytical evaluation of elastic transition amplitudes in the high-energy limit. It does not depend on the diffraction-type assumptions connected with Glauber theory. In this model of spinless Yukawa type forces (with no absorption) the total $n+d$ cross section does not approach twice the $\mathrm{NN}$ total cross section in the high-energy limit but rather approaches the total $\mathrm{NN}$ cross section multiplied by a number larger than 2. Therefore, the enhancement effect resulting from rescattering is larger than the shadowing effect, which decreases faster with energy.