Deep Inelastic Scattering of Polarized Electrons by Polarized $^3$He and the Study of the Neutron Spin Structure

TL;DR

This study measures the neutron's spin structure functions using polarized electron scattering on polarized helium-3, providing data that tests fundamental sum rules and enhances understanding of neutron spin contributions.

Contribution

It presents new measurements of neutron spin structure functions over a broad x range, testing sum rules and comparing with theoretical predictions at specific Q^2 values.

Findings

Neutron spin structure function g1^n(x,Q^2) is small and negative.

The integral of g1^n(x) over 0.03 to 0.6 is -0.028 ± 0.006 (stat) ± 0.006 (syst).

The difference between proton and neutron integrals agrees with the Bjorken sum rule.

Abstract

The neutron longitudinal and transverse asymmetries $A^n_1$ and $A^n_2$ have been extracted from deep inelastic scattering of polarized electrons by a polarized $^3$He target at incident energies of 19.42, 22.66 and 25.51 GeV. The measurement allows for the determination of the neutron spin structure functions $g^n_1 (x,Q^2)$ and $g^n_2(x,Q^2)$ over the range $0.03 < x < 0.6$ at an average $Q^2$ of 2 (GeV$/c)^2$. The data are used for the evaluation of the Ellis-Jaffe and Bjorken sum rules. The neutron spin structure function $g^n_1 (x,Q^2)$ is small and negative within the range of our measurement, yielding an integral ${\int_{0.03}^{0.6} g_1^n(x) dx}= -0.028 \pm 0.006 (stat) \pm 0.006 (syst) $. Assuming Regge behavior at low $x$, we extract $\Gamma_1^n=\int^1_0 g^n_1(x)dx = -0.031 \pm 0.006 (stat)\pm 0.009 (syst) $. Combined with previous proton integral results from SLAC experiment E143, we find $\Gamma_1^p - \Gamma_1^n = 0.160 \pm 0.015$ in agreement with the Bjorken sum rule prediction $\Gamma^p_1 - \Gamma ^n_1 = 0.176 \pm 0.008$ at a $Q^2$ value of 3 (GeV$/c)^2$ evaluated using $\alpha_s = 0.32\pm 0.05$.