Relation between nuclear and nucleon structure functions and their moments

Calculations of nuclear structure functions (SFs) ${F}_{k=1,2}^{A}(x,{Q}^{2})$ routinely exploit a generalized convolution, involving the SFs for nucleons ${F}_{k}^{N}$ and the linking SF ${f}^{\mathit{PN},A}$ of a fictitious nucleus, composed of point particles, with the latter usually expressed in terms of hadronic degrees of freedom. For finite ${Q}^{2}$ the approach seemed to be lacking a solid justification and the same is the case for recently proposed, effective nuclear parton distribution functions, which exactly reproduce the above-mentioned hadronically computed ${F}_{k}^{A}$. Many years ago Jaffe and West proved the above convolution in the plane-wave impulse approximation for the nuclear components in the convolution. We extend the above proof to include classes of nuclear final-state interactions. One and the same function appears to relate parton distribution functions in nuclei and nucleons and SFs for nuclear targets and for nucleons. That relation is the previously conjectured one, with an entirely different interpretation of ${f}^{\mathit{PN},A}$. We conclude with an extensive analysis of moments of nuclear SFs based on the generalized convolution. Characteristics of those moments are shown to be quite similar to those for a nucleon. We conclude that the above is evidence of asymptotic freedom of a nucleon in a medium and not the same for a composite nucleus.