The GDH Sum-Rule in few-body systems.

Alexandre Deur
for the Jefferson Lab E94-010 GDH Collaboration.

University of Virginia, Charlottesville.

In this talk I will present the measurement of the extended GDH integral evolution from intermediate to low \( Q^{2} \) on the \( ^{3} \)He and neutron.

One of the main goals of Jefferson Lab is to understand the transition between the nuclear domain (low \( Q^{2} \), nucleon and meson degrees of freedom) and the perturbative QCD domain (large \( Q^{2} \), quark and gluon degrees of freedom) of the strong interaction. It has been pointed out that the extended GDH sum-rule [2] was a unique tool to study this transition domain.

This experiment [1] was carried out in the Hall A of the Thomas Jefferson National Accelerator Facility. In order to achieve such a study on the neutron we used a high-density polarized \( ^{3} \)He target. We measured the spin dependent inclusive \(
\overrightarrow{^{3}He}(\overrightarrow{e},e') \) cross sections. From them we extract the two spin structure functions \( g^{^{3}He}_{1}(Q
^{2},\nu ) \), \( g^{^{3}He}_{2}(Q^{2},\nu ) \) and the GDH integrand \( \sigma ^{TT}(Q^{2},\nu )/\nu \). The GDH sum rule stands also for \( ^{3} \)He and provides valuable information on its nuclear structure. After a brief description of the experimental setup and having discussed the extraction of the neutron information from the \( ^{3} \)He data, we will present our results and give an outlook on future perspectives.



[1] Z.-E. Meziani, G. Cates, J.-P. Chen et al., Jefferson lab experiment E94010.

[2] D. Drechsel, S.S. Kamalov G. Krein and L. Tiator. The Generalized Gerasimov -Drell-Hearn Integral and the Spin Structure of the Nucleon. Phys.Rev. 59 094021. (1999);

[3] X. Ji and J. Osborn. Generalized Sum Rules for Spin Dependent Functions of the Nucleon. J.Phys. G27 127 (2001).