As shown in figure there are really three angular cuts which have to be made on the data: , the sector half-angle; , the minimum polar scattering angle; and , the maximum polar scattering angle. It has been shown in a derivation of the FOM [Mer93] that the FOM is maximized when is a minimum, and this is true when or . Further Monte Carlo studies of this estimate show that it is valid and that the FOM is fairly insensitive to changes in the sector half-angle [Mer93]. Therefore, is used for all of the analysis in this thesis. A histogram showing the event distribution in for an average run is shown in figure .
Figure: Raw azimuthal distribution of double-scattering events in the polarimeter. is defined as a horizontal scatter to the left. The spikes are the result of finite size of the detector cells.
The sinusoidal nature of the distribution that would be expected from equation is not obvious in figure . In order to show that there is an actual asymmetry in the distribution it is necessary to take a difference between the distribution when the beam is in a state and when it is a state. The results of this subtraction can be seen in figure along with a smooth spline fit to the data which makes obvious the sinusoidal asymmetry.
Figure: Difference between the distributions in the state and the state for a single sample run. The dotted line is the actual difference in the data and the solid line is a smooth spline fit to that difference.
The polar scattering angle window also needs to be adjusted in order to optimize FOM. A raw distribution is shown in figure .
Figure: Raw histogram of the polar scattering angle, , distribution in the polarimeter. The spikes are the result of the limited position resolution of the detector cells.
A lower bound, , on the polar scattering angle is used because the events with a small have a large uncertainty in . As becomes smaller the finite position resolution of the detector cells makes it difficult to determine if a scattering took place to the left sector or right sector. The upper bound on serves to cut off the point at which the analyzing power of the reaction becomes negative. Obviously, including such events will dilute the analyzing power of the detector and reduce the FOM. This takes place at [Arn96] as shown in figure .
Figure: Calculated values for the Analyzing Power of the reaction [Arn96].
In the same manner that figure shows the difference between the distributions of the (+) and (-) beam states figure shows the full angular distribution of that same difference.
Figure: Full angular distribution of the difference between (+) and (-) beam state. is shown in the angular direction and in the radial direction. Relative height indicates the event count.
The asymmetry in the distribution of scatters from the analyzer plane is very obvious.