Nuclear effects in $g_{1A}(x,Q^2)$ at small $x$ in deep inelastic scattering on ${}^7$Li and ${}^3$He

Abstract

We suggest to use polarized nuclear targets of ${}^7$Li and ${}^3$He to study nuclear effects in the spin dependent structure functions $g_{1A}(x,Q^2)$. These effects are expected to be enhanced by a factor of two as compared to the unpolarized targets. We predict a significant $x$ dependence at $10^{-4}÷10^{-3}\le x\le 0.2$ of $g_{1A}(x,Q^2)/g_{1N}(x,Q^2)$ due to nuclear shadowing and nuclear enhancement. The effect of nuclear shadowing at $x\approx 10^{-3}$ is of an order of 16% for $g_{1A=7}^{n.s.3/2}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$ and 10% for $g_{1A=3}^{n.s}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$. By imposing the requirement that the Bjorken sum rule is satisfied we model the effect of enhancement. We find the effect of enhancement at $x\approx 0.125(0.15)$ to be of an order of $20(55)$ for $g_{1A=7}^{n.s.3/2}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$ and $14(40)$ for $g_{1A=3}^{n.s}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$, if enhancement occupies the region $0.05\le x\le 0.2$ ($0.1\le x\le 0.2$). We predict a 2% effect in the difference of the scattering cross sections of deep inelastic scattering of an unpolarized projectile off ${}^7$Li with $M_J$=3/2 and $M_J$=1/2. We also show explicitly that the many-nucleon description of deep inelastic scattering off ${}^7$Li becomes invalid in the enhancement region $0.05<x\le 0.2$.

Comments: 29 pages, 5 figures, RevTex