{ ${/download/attachments/164080117/Table_layout.png?version=1&modificationDate=1501004539000&api=v2}$ { ${/download/attachments/164080117/Compton_pig.png?version=1&modificationDate=1502292371000&api=v2}$ { ${/download/attachments/164080117/Compton_geometry.png?version=2&modificationDate=1502292505000&api=v2}$ Set PMT to 1500v

PHA preamp gain.  Coarse = 8  Fine = 1.68

Detector set to 90deg.

PMT remained at HV = 1500v throughout all measurements.

PHA Channel measurements made by creating a region of interest in USX software and reading the centroid.  ROI was chosen to encompass symmetric portion of the peak as shown for the 356keV peak of Ba133 in the figure below.

{ ${/download/attachments/164080117/Ba133_roi_selection.PNG?version=1&modificationDate=1501090462000&api=v2}$

Calibration data using Cs137, Na22 and Ba133 sources were taken over multiple days.

PMT Energy Calibration 072017

PMT Energy Calibration  072417

PMT Energy Calibration  072517

PMT Energy Calibration  080717.  PMT has been on continuously since 072017.

Fit all three calibration data sets to a straight line.  

PHA Ch = m * Energy + b

Best fit values from the three sets of calibration data.

*Averages do not include last data pair which was taken over a week after the scattering data.

Y-intercept b: Avg = 11.6  STD = 1.4.

Slope m: Avg = 1.24  STD = 0.01.

So to get energy from PHA channel,

E = ( P - b ) / m

dE = E * ( db / ( P-b ) + dm / m )  Assuming negligible uncertainty in peak location.

{ ${/download/attachments/164080117/PHA_calib.png?version=1&modificationDate=1501101041000&api=v2}$

Does pmt gain change with angle (i.e. orientation in earths magnetic field).

Measure again on 080917.  Use 662keV line from Cs137 calibration source.  Pig closed and scatterer removed.

Include making some obviously non-symmetric selections.  The following data table contains 16 separate measurements of the centroid of the 356keV peak of Ba133.  Note that spread in measurements is exaggerated as I intentionally made my ROI selections sloppy. 

Average = 466.18

STD = 0.58

Uncertainty in the selection of the peak location is 0.1%.  

To test how sensitive the centroid estimation is to number of counts in the peak two Cs137 spectra were taken.  One where the full energy peak amplitude was about 50 ( Lo counts ) and one where the full energy peak reached about 1000 counts (Hi counts).  Visually the Hi count full energy peak appears smoother and would seem to provide a better estimate of the centroid location than the Lo count spectra.  However when each spectra is analyzed by reselecting the ROI 10 times, there is stastically no difference in the value of the centroid.

Lo Count Spectra

{ ${/download/attachments/164080117/Lo_counts.PNG?version=1&modificationDate=1502300929000&api=v2}$ Ten ROI centroid measurements:  824, 823, 824, 825, 823, 824, 825, 824, 824, 824.

Avg = 824.0  Std = 0.6

Hi Count Spectra

{ ${/download/attachments/164080117/Hi_counts.PNG?version=1&modificationDate=1502300929000&api=v2}$ Ten ROI centroid measurements: 825, 824, 825, 825, 824, 823, 824, 825, 825, 824.

Avg = 824.4  Std = 0.7

For a user with an experienced eye in selecting ROI's, using the USX programs centroid calculation provides very repeatable results.  Determination of full energy peak centroid seems to be fairly insensitive to the precise boundaries of the ROI as well as the visual smoothness of the peaks.  We have probably been having students collect data for much longer than is necessary.

{ ${/download/attachments/164080117/Energy_vs_angle.png?version=1&modificationDate=1501101093000&api=v2}$ 080717 - Take another data set over about 1.5 hours after the pmt has been on for a couple weeks straight.  5 minute runs for all angles.  Calibration data was taken on the same day as the scattering data.  This coupled with the fact the pmt has been held at HV since 072017 should minimize the effect of gain drift.

Prior to the fit the measured angles were corrected for the known 0.7 degree offset in the table scale.  The only free parameter of the fit was the electron rest mass.  The fit returned a rest mass for the electron of 513.3keV ± 1.3keV.  The reduced Chi Sq was 6.2.  However the uncertainties on the full energy peak centroids are not due to statistically random fluctuations, so a reduced Chi Sq of 1 is not necessarily expected.  

Note that this result was obtained from spectra whose run times were considerably shorter than what we have considered necessary.

{ ${/download/attachments/164080117/Compton_scatter_080717.png?version=1&modificationDate=1502303790000&api=v2}$

Can the non-zero angular acceptance of the detector produce a systematic shift in the measured energies as a function of angle.  We test for this possible systematic effect by recording and comparing spectra of the 511keV line from Na22 with that of 511keV compton scattered gammas.  We also do the comparison at 244keV using Eu152 in place of Na22.  Comparison of 511keV spectra from Na22 source and compton scattered photons at 40deg which corresponds to a scattered energy of ~511keV.

{ ${/download/attachments/164080117/511kev_spectra.png?version=1&modificationDate=1501101135000&api=v2}$ Zooming in on the full energy peaks and fitting both to gaussian functions gives.

{ ${/download/attachments/164080117/Gaussian_fits.png?version=1&modificationDate=1501533950000&api=v2}$ The table below gives the best fit parameters for a gaussian function of the form,

{ ${/download/attachments/164080117/image2017-7-31%2015%3A56%3A11.png?version=1&modificationDate=1501534571000&api=v2}$.

Both fits give a reduces chisq of about 1.5.  While the compton scattered data show a broader full energy peak, there is no meaningful shift in the location of the centroid.

Use Eu152 to get a line at 244keV which corresponds to a compton scattered angle of 108.8.

{ ${/download/attachments/164080117/244keV_comparison.png?version=1&modificationDate=1501607529000&api=v2}$ The best fit values for the gaussians are given below.  As with the 511keV energy the compton scattered data have a wider sigma, but the centroids are essentially the same.

It does not appear that there is any meaningful shift in measured energies as a function of scattering angle.  The full energy peak of the compton scattered gammas is slightly wider which may impact measurements of the differential scattering cross section.  But there should be no effect on measurements of the compton scattered photon energy.

Scan through the beam to check the 0 deg mark.  All runs at 100s live time.  Used lead collimator in detector.  ROI encompasses entire spectrum, not just full energy peak.  ROI remained unchanged for all measurements.  Dead time never exceeded ~5%, so there should be no saturation effects.  No scatterer.

Best fit parameters of fit to Gaussian.

 { ${/download/attachments/164080117/image2017-7-31%2015%3A56%3A11.png?version=1&modificationDate=1501534571000&api=v2}$ P1 = -5092

P2 = 1.56e6

P3 = 3.0

P4 = 0.7

{ ${/download/attachments/164080117/detector_scan.png?version=1&modificationDate=1501620859000&api=v2}$ The data show a 0.7° offset in the orientation of the angle scale with respect to the beam axis.  This should be added to the angle readings taken from the table scale.

Uncertainty in reading the angle markings on the table is less than ±0.5deg.  Accuracy of the scale however is unknown.