Abstract
In the scattering process off a nuclear or nucleon target, the Gerasimov-Drell-Hearn (GDH) sum rule for real photons ($Q^2$=0 where $Q^2\equiv -q^2$ with $q$ the photon's 4-momentum) relates static properties of the target particle's ground state to dynamic properties of all its excited states. On the other side of the $Q^2$ spectrum, the Bjorken sum rule holds in the Bjorken limit $Q^2 \rightarrow \infty$. Bjorken sum rule relates the final structure functions of the proton and neutron to the nucleon axial coupling constant in weak decay. These two sum rules belong to domains where calculations are achievable but use different degrees of freedom: hadronic degrees of freedom at low $Q^2$ versus partonic degrees of freedom at intermediate $Q^2$. Meanwhile, different methods have been used to connect the two sum rules at finite $Q^2$ values: Chiral Perturbation Theory is used to expand the GDH sum rule while Operator Product Expansion is used to expand the Bjorken sum rule.
In recent decades, improvements in polarized beam and polarized target techniques have made it possible to test theoretical predictions in the intermediate $Q^2$ region. During the Jefferson Lab (JLab) Hall A E97110 experiment, a precise measurement of polarized cross sections was performed at $0.02<Q^2<0.3$ GeV$^2$ using a polarized $^3$He target as an effective polarized neutron target. The measured data allowed us to test predictions of Chiral Perturbation Theory at very low $Q^2$. Furthermore, an extrapolation to the real photon point $Q^2$=0 tests the GDH sum rule on the neutron. In order to reach the small angles necessary for the low $Q^2$ range, a new septum magnet was installed in Hall A for this experiment. Unfortunately, the magnet was mis-wired during initial running. There were therefore two periods for this experiment: the first period had the defective magnet due to mis-wiring; while in the second period, the magnet had been fixed and was working properly. The cross sections and the asymmetries for the first period must be extracted using a difficult and unusual method employing focal plane variables in the spectrometer. In the work described in this thesis, the target-plane and focal-plane method will be established first and confirmed by elastic scattering cross section measurements from carbon foil and $^3$He targets. Cross sections and asymmetries of inelastic scattering were then extracted using the same method, which constitute the main physics results of this thesis. Preliminary results on $I_{TT}$, the integral of the polarized cross section, were also extracted and are presented in this thesis.
In addition to the data analysis of E97110, this thesis includes instrumentation work performed on the polarized $^3$He target at JLab. For the 12 GeV program of JLab, the polarized $^3$He target is being upgraded to satisfy new experimental requirements. The new target is a convection-based cell with two transfer tubes rather than a single transfer tube as in the former 6~GeV design. The first stage of the target upgrade aims to produce a 40 cm long, 10 amg target that can withstand 30 $\mu$A of electron beam current with an in-beam polarization of 55\%, doubling the figure-of-merit from the 6 GeV time. Several studies were conducted at the Test Lab of JLab on the new convection cell. Work and improvement done on the Pulse Nuclear Magnetic Resonance (NMR) polarimetry and its test results will be presented. As this thesis is written, the target is being installed in Hall C of JLab in preparation for a 6-month long running from November 2019 to May 2020.
