Extraction of Asymptotic Nucleon Cross Sections from Deuterium Data

Abstract

The effect of Fermi motion on the extraction of asymptotic total neutron cross sections from deuterium data is examined in some detail. Particular attention is paid to the threshold condition on the nucleon cross sections. Using realistic hard-core wave functions to describe the deuteron, we find that, with this added correction, the Glauber mean inverse square radius of the deuteron is experimentally determined to be 0.0212±0.005 ${\mathrm{mb}}^{-1\mathrm{}}$, in good agreement with values calculated using hard-core wave functions. Previous discrepancies in $\pi N$ and $\mathrm{NN}$ scattering are shown to be eliminated. When applied to the real photoabsorption total cross section our correction considerably reduces the neutron-proton difference, making it consistent with zero in the asymptotic region. We also examine deep-inelastic electron-deuteron scattering and show how the theory gives an excellent description of the quasielastic peak. For scattering into the continuum we find that the correction far away from threshold is ∼5%, while near the threshold it can become very large (∼30%). In terms of the neutron-proton ratio the correction is generally very small (i.e., the smeared ratio is an excellent approximation to the unsmeared) unless this ratio drops below ∼ ¼ near threshold.