In addition to being sorted based on velocity ratio, analyzer pulse height, and polar scattering angle, the data stored in the PAW ntuples need to be sorted by beam polarization state, (+) or (-), and azimuthal scattering angle, left or right. Once this is done the beam asymmetry
as defined in equation , can be determined and the spin observables calculated.
Determining the location of the left and right sectors for the asymmetry measurement, as discussed in section , is one of the places in the analysis where the use of the PAW ntuples is most beneficial. Typically the full (azimuthal) range was split into four sectors -- left, right, up, and down -- which were hardwired in the replay and analysis. This works fine in the investigation of discrete states but has problems when studying a continuum. The neutron, after being produced in the target, will pass through the series of precession magnets discussed in section . The neutron spin will be precessed to some direction, hopefully measurable in the detector, which may or may not conform to the sectors chosen. Even worse, the amount of precession is energy dependent. So the neutrons in the tail will scatter with a different asymmetry in the detector than those in the peak because they have been precessed by a different amount.
Ordinarily, the corrections for the different precessions are made by weighting the results by a factor related to precession angle. However, this is not the most efficient method because the count difference between left and right scattered neutrons will be smaller and the overall statistical uncertainty will be larger.
The polarization vector of the neutron will be altered between the target to the detector as follows:
where is the precession angle in the plane from the dump magnet, is the precession in the plane from the combination of the permanent dipole and large, electromagnetic dipole, and is the precession in the plane from the neutron solenoid. The angles are calculated by the following formula
where is the Landé g factor for the neutron, is the nuclear magneton, , and is the integral of the magnetic field over the path of the neutron. The has been mapped out for each magnet. See figure for the position of these magnets. Notice that the solenoid was not used while measuring neutrons in the or directions, and when measuring polarized neutrons the permanent dipole and dipole were set so as to cancel each other out. Using the PAW ntuples the optimum sectors (those centered at to the nominal neutron polarization) are recalculated on an event-by-event basis, subject to values of the neutron energy and the various magnetic fields.
Obviously the sectors are based only on the expected polarization components in the or directions since the detector can only measure polarization components transverse to the neutron flux direction. Despite an effort to eliminate any longitudinal component to the neutron polarization at the detector by adjusting the magnet settings and optimizing the precession angles, a small component will exist. This fraction of the polarization which was rotated to the longitudinal direction can be determined from the magnet characteristics and the small correction made to the measured neutron polarization.