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,
becomes
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
.
