Extraction of the n structure function $F_2^n$ from inclusive scattering data on composite nuclei

Abstract

We consider a generalized convolution, linking Structure Functions (SF) $F^N_2$ for nucleons, $F^A_2$ for a physical nucleus and $f^{PN,A}$ for a nucleus, composed of point-nucleons. In order to extract $F_2^n$ we employ data on $F_2^{p,A}$ and the computed $f^{PN,A}$. Only for $Q^2\approx 3.5 {\rm GeV}^2$ do data permit the extraction of $F_2^A(x,3.5)$ over a sufficiently wide $x$-range. Applying Mellin transforms, the above relation between SF turns into an algebraic one, which one solves for the Mellin transform of the unknown $F_2^n$. We present inversion methods leading to the desired $F_2^n$, all using a parametrization for $C(x,Q^2)=F_2^n(x,Q^2)/F_2^p(x,Q^2)$. Imposing motivated constraints, the simplest parametrization leaves one free parameter $C(x=1,Q^2)$. For $Q^2= 3.5 {\rm GeV}^2$ its average over several targets and different methods is $<C(1,3.5)>=0.54\pm0.03$. We argue that for the investigated $Q^2$, $C(x\to 1,3.5)$ is determined by the nucleon-elastic ($NE$) part of SF. The calculated value is near the extracted one and both are close to the SU(6) limit 2/3.