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

TL;DR

This paper investigates nuclear effects on spin-dependent structure functions in polarized $^7$Li and $^3$He targets at small $x$, predicting significant shadowing and enhancement effects that impact deep inelastic scattering measurements.

Contribution

It models nuclear shadowing and enhancement effects on $g_{1A}(x,Q^2)$ in polarized nuclei, highlighting their $x$ dependence and the breakdown of many-nucleon descriptions in certain regions.

Findings

Nuclear shadowing causes ~16% reduction at $x \\approx 10^{-3}$ for $^7$Li.

Enhancement effects can reach up to 55% at $x \\approx 0.15$ for $^7$Li.

A 2% difference in scattering cross sections is predicted for different $M_J$ states of $^7$Li.

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 $10^{-4} \div 10^{-3} \leq x \leq 0.2$ 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 $0.05 \leq x \leq 0.2$ ($0.1 \leq x \leq 0.2$). 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 $0.05 < x \leq 0.2$.