The analyzing power of a detector is a function of scattering angle, , and neutron energy. Ideally the detector should be calibrated using neutrons of known polarization at a variety of energies covering the range of interest. This sort of calibration was the purpose of another proposed experiment, E384, carried out at IUCF. However, the results of that experiment are not available at the time this thesis is being written. The primary reason that this calibration data has not been analyzed is that it was recently determined that the high-energy beamline polarimeters (described in section 4.1.3) had not been characterized for proton energies below MeV. That means that the analyzing power of the beamline polarimeters was not known at those energies so the proton polarization and, therefore, the polarization of neutrons from a calibrating reaction was not known. This, in turn, meant that the neutron detector could not be calibrated with neutrons of known polarization at those lower energies. A measurement of the high-energy beamline polarimeters at the appropriate energies is the focus of an experiment taking place in spring of 1997.
In the interim a reasonable amount of calibration data was taken at MeV during the E385 and E387 experiments, so, in fact, it is possible to determine the analyzing power of the detector for 200 MeV neutrons. Calculations of the analyzing power for free n-p scattering show that it has a fairly flat distribution between MeV, which is the range of interest for data from the INPOL detector. Figure shows data for an old IUCF neutron polarimeter of similar design to the INPOL detector.
Figure: Effective analyzing power of an old IUCF neutron polarimeter. The square data points are values measured using neutrons from the IAS reaction. The crosses are the results of calculations based on free n-p scattering. The asterisks are the calculated values reduced by a factor of 0.85 [Tad85].
The data shown were taken using neutrons from the IAS reaction which produced neutrons of the same polarization as the incident protons . It appears that the data fit the shape of the free np scattering calculations, just slightly rescaled. This phenomenon was also observed at LAMPF for the energy range of MeV [Che93]. The conclusion then is if the detector's analyzing power is found at 200 MeV the distribution can be assumed to be flat back to MeV, until a more precise determination can be made based on improved polarimeter calibrations.
The detector calibration at MeV was carried out using the reaction. This reaction is a pure Gamow-Teller transition. The expected value of for such a transition is and that value has been confirmed experimently [Rap90] at 200 MeV with an absolute uncertainty of for this particular reaction. Therefore,
for 200 MeV neutron detected in the INPOL polarimeter. A sample energy spectrum from the reaction is shown in figure .
Figure: Sample spectrum. The ground state is the most prominent feature. The smaller peaks at lower neutron energy are the result of beam contamination of the type discussed in section 4.1.3. The peak at the higher neutron energy than the ground state is the result of contamination in the target.
Another useful feature of the target is its relatively large cross section for the reaction ( mb/sr). This means that it does not take long to gather sufficient statistics to make a statement about . Also, the lack of any state near the ground state means that the resolution requirements are fairly relaxed and thicker targets can be used to further increase the rate at which statistics are gathered.
In practice equation is not precisely the equation used to calculate the effective analyzing power. Recall from section that the beam polarization flips every seconds, and that this can be used to eliminate experimental asymmetries. By defining a quantity, equation could be rewritten as
In using this equation the assumption must be made that the detectors acceptance and efficiencies are the same for left and right scattered particles which is, perhaps, untrue. It is possible to overcome this difficulty without knowing the left/right asymmetries by defining the quantity
where the superscripts indicate whether the beam is in a (+) or (-) state. In this way any efficiency or acceptance factors associated with a given scattering direction will cancel out assuming that the detector efficiency is independent of the proton spin orientation. Equation then becomes [Tad85]
to second order in , where is half the difference between the polarization of the beam in the (+) state versus the (-) state, and is the average polarization between the two states. For the current experiment the difference is taken to be negligible. The average proton beam polarization for the calibration runs was .