1. The NPDG Motion System for Detector Array Alignment
Christopher B. Crawford
University of Tennessee
NPDG Collaboration
DNP Meeting, Nashville, TN
I will talk about how we can measure the alignment of the NPDG detectors just by looking at the change in rates from moving the detectors around.

2. Introduction
NPDG probes the Parity Violating (PV) weak hadronic interaction
Interference of strong (PC) and weak (PV) vertex
Low backgrounds: -5 x 10-8 expected asymmetry
insensitive to MOST background physics processes (PC)
The beauty of a hadronic parity violating experiment like NPDG is that we can measure the weak contribution to an interaction dominated by the strong force for two reasons:
a) the effect is enhanced by the interference between a strong and weak vertex, and
b) most of the physical backgrounds can be easily discriminated because they are parity conserving
There are a few exceptions, and I will talk about a few of them. If you list the Cartesian invariants involving the neutron and gamma kinematics, there is the normal parity violating term which goes as cos(theta), (the angle between the neutron polarization and gamma).
But there is also a parity-conserving term (with two k vectors0) which goes as sin(theta).
These two components can be discriminated by their angular dependence, but if the detector is misaligned by a small angle, the PC asymmetry will get mixed in with the observable.
UP-DOWN
Asymmetry
LEFT-RIGHT
Asymmetry
Cartesian invariants

3. Left-Right Asymmetries
Three processes lead to LR-asymmetry
PC npdg asymmetry
Csoto, Gibson, and Payne, PRC 56, 631 (1997)
np->np elastic scattering
beam steered by analyzing power of LH2
eg. 12C used in p,n polarimetry at higher energies
P-wave contribution vanishes as k3 at low energy
Mott-Schwinger scattering
interaction of neutron spin with Coulomb field of nucleus
electromagnetic spin-orbit interaction
analyzing power: 10-7 at 45 deg
0.23 x 10-8
2 x 10-8
~ 10-8
Of the three process leading to a left-right asymmetry, only the first is a real NPDG asymmetry. It was calculated to be negligible.
The second two are actually due to beam steering from the analyzing power of either nuclear or electromagnetic interactions.
Elastic scattering is predominantly S-wave because of the low neutron energy, but only the P-wave has non-zero analyzing power.
Mott-Schwinger scattering arises from the neutron spin interacting with the Coulomb field of the nucleus which appears as a B field because the neutron is moving. The cross product as the form of orbital momentum, so this is an electomagnetic spin-orbit interaction.
At low neutron energy this amplitude is much larger than the nuclear spin-orbit interaction
However, it is also suppressed because:
a) this amplitude is imaginary; suppressed because nuclear scattering amplitudes are real at low energy, and
a) also because of charge screening of electrons at small momentum transfer (high impact parameter)
So the L-R asymmetry is approximately the same magnitude as the U-D asymmetry
at 2 MeV
(Michael Gericke et al.)

4. Motivation U-D and L-R asymmetry mixing Geometry factors
from misalignment (rotation) of detectors
goal: suppression LR asymmetry by factor of
100-1 = sin(0.57 deg)
Geometry factors
account for extent of target and detector
can be measured instead of MC calculation
Detector systematics
demonstrate understanding of rates
Therefore our goal is to measure the detector alignment accurate enough to suppress the L-R asymmetry by a factor of 100, that’s about a half a degree.
Also, the cos(theta) that enters in the asymmetry formula must be averaged over finite target volume, and detector efficiency. The so-called geometry factor can be calculated by Monte Carlo, but the same technique has the capability of making a direct measurement, because the rates are averaged by exactly the same weight.
Finally, although the detectors are not optimized to measure asymmetries not rates, it is important to study the rates at at least some level to understand the detector systematics.

5. Formalism detector yield depends on distance
extract positions from the gradient
target
detector
The basic idea used to extract the detector position from gamma rates is that the rate only depends on 1/r^2, which comes from the detector solid angle, after normalizing by the neutron flux, and to this precision the gamma emission is isotropic.
For example, the yield in the top detector is constant in x, and the yield in a side detector is constant in y.
Quantifying this, we expand the denominator into variations about the nominal position, and fit the rates as a function of \delta x and \delta y to get the position (x,y).
For small variations this equation is linear, and we can just look at the gradient.
To get the angle of the detector in the x-y plane, we just take the ratio of partial derivatives of the yield.
If we could measure the gradient in all three directions, then we could extract all three coordinates from the gradient alone. However, in our case the detector only moves in the x-y plane, so we must specify the z coordinate to extract r and then x and y.
I would like to reiterate that the extracted position have already been averaged over the finite volumes and gamma detection efficiency.
3-d position
explicit z dependence
geometry factor

6. CsI(Tl) Detector Array
4 rings of 12 detectors
15 x 15 x 15 cm3 each
VPD’s insensitive to B field
detection efficiency: 84%
current-mode operation
5 x 107 gammas/pulse
counting statistics limited
The detector array has 4 rings of 12 CsI crystal each, which cover 3\pi acceptance of the LH2 target inside. The size of the crystals were chosen to absorb most of the gamma energy. Most of the rest escapes out from the detectors, though a small fraction is backscattered or leaked into an adjacent detector.
The scintillation light is collected by Vacuum Photo Diodes instead of PMT’s because of their reduced sensitivity to stray B field, for example, from the RF spin flipper.
The count rate is so high that we must use current mode detection, but the preamplifier electronics were designed carefully, that the noise is completely dominated by counting statistics. In fact, instrumental false asymmetries can be measured in a few hours while the beam is down.

7. Detector Motion Stand constructed at TRIUMF
< 0.001” position precision
extensive safety features
LabVIEW computer interface
The ~1 ton detectors are supported on an automated x-y motion stand designed and constructed at TRIUMF by Des Ramsay and Tom Ries.
You can see 3 motors driving vertical shafts, and one motor
The screws are all anti-backlash so that the positions are reproducible to better than 0.001” precision
Because the detector surrounds and is within mm of the LH2 target, safety was the major concern and there are many levels of protection. Hard mechanical stops are placed on each motor are were carefully adjusted. The motors are given barely enough current to move the table. There are also limit switch interlocks, and software limits set in the LabView computer interface.
The detectors have a range 15 mm in both the vertical and horizontal directions.

8. Data and Analysis yields measured over 5x5 grid in x and y analysis
over-determined for study of linearity
targets: B4C, Cd, LH2
analysis
detector rates normalized by beam monitors
pedestals and empty target subtracted
Y(dx,dy) fit to obtain absolute detector positions
relative detector positions compared with physical survey of array
need to be corrected for extended geometry by Monte Carlo
The detector rates were measured at each point in a 5x5 grid in x and y. We only needed to measure gradients in x and y, but the extra points were helpful to understand systematics.
Data were taken for three different targets: Boron carbide because it emits single gamma per neutron, Cadmium because of its large cross section, and just last week the hydrogen target.
The analysis was pretty straight forward. The rates were normalized by the beam current, with pedestals subtracted, and the similarly calculated empty target yields were subtracted.

9. Results - Cd target, ring 2
x = 5.6 mm y = 2.8 mm
x position (mm)
Here is an example with a middle ring and the Cd target. Each bar represents the background subtracted yield at one point on the x-y grid. The yields were fit to a plane to extract the gradients, and finally mean (x,y) position. The detectors were drawn to scale about this point as determined by a simple Monte Carlo simulation, to judge the quality of the fit. The delta x, and delta y, were averaged from the displacement between vertical and horizontal detector pairs. From this test, the positions are accurate to about 5 mm.
x position (mm)

10. Conclusions
technique for measuring detector positions demonstrated with success on Cd target
5 mm precision ~ 1 deg.
50 x suppression of L-R asymmetry
LH2 target measurements in progress
first run affected by venting of target
next run in December
In conclusion, we have demonstrated that the event-weighted detector average can be extracted from the yields as a function of small displacements to within 5 mm with a cadmium target. This corresponds to about a 50x suppression of contributions from the L-R parity conserving asymmetry. Measurements with the LH2 target are in progress, and will be continued in the next run.