David Huang

Physics 225 Lab 2 Report

Experiment: Gamma Coincidence

Hypothesis to test: Using radioactive 22Na, we observed its β+ decay and the subsequent positron and electron annihilation process. In order to conserve both energy and momentum, the 2 resulting photons should be produced with an angle of 180° to each other. We detected the gamma rays emitted when the positron is captured and then measured the angular correlation between the emitted photons. We followed the procedure outlined in the lab write-up: http://vpac00.phy.vanderbilt.edu/velkovms/VUteach/PHYS226W-Spring2014/g2.pdf

Additional Procedural Information not in Write-up: we followed a procedure described and provided to us by Professor Velkovsky: http://vpac00.phy.vanderbilt.edu/velkovms/VUteach/PHYS226W-Spring2014/g2.pdf. For our experiment, we set up a two gamma ray detectors focused on a single point of radiation (22Na). We first began by calibrating the detectors. The annihilation photons release a known energy of 511 keV, whereas the de-excitation photons release energies of 1274 keV. We needed to focus our detectors to only measure the coincidences of the 511 keV annihilation photons. To accomplish this, we first adjusted the amplifier until we were able

to clearly detect both signals. From here, we calibrated the single channel analyzer. We slowly decreased the window range of the SCA by increasing the “Lower Level” and decreasing the “Upper Level” until only 511 keV signals were being detected. We then proceeded to check the physical set-up of our detectors. We made sure that they were 180° from each other, and were sitting on the same plane. This is important because our whole experiment was based on the changing angle between the detectors. A bad initial set-up would skew our results. We checked our set-up with a flat meter stick and a laser pointer.

After calibration, we were ready to begin measuring data. We measured for 25 periods of coincidences: once at 180° and twelve times at positive angles and then twelve times at the negative conjugates of the angles. We recorded the number of coincidence counts for periods of 2 minutes.

David Huang

Analysis: Our peak was very close to 180°, just off by one degree. It had a peak at 179°. This result suggests the introduction of experimental errors that could have affected our results. Likely errors include an inaccurate calibration of the angle between the two PMT detectors. Another factor could be that the two PMT detectors weren’t properly set up on a single plane. These two physical factors would affect the rate of coincidence detection because they would introduce a phase shift into our data. In our case for this experiment, a phase shift is undesirable. A third possibility would be the experiments random error that would be reduced if the experiment were run for longer.

Based off of our results, it’s likely that the effect of moving one of the detectors away from the 180° mark would be a reduced number of coincidence counts from the detectors. The largest angle we recorded data for was at ±25°. For both positive and negative angles, three coincidence counts were recorded in the two-minute periods. In order to reduce the coincidence count to 0, I would hazard to guess that we would have to move the detectors to a little more than 30°, possibly more. My prediction is based off the exponential fall-off trend of the coincidence counts as the angle was increased. This would explain the tiny width of the peak we detected. The curve is exponential in form.

We measured a distance of 20.3 cm from the source of radiation to the detectors. This was the same distance measured for both detectors. Even if these were the accurate distances, if the source isn’t properly placed on the same axis of the detectors, incorrect results would be yielded due to changing distances as the angle of the detectors were changed.

As shown to the left, I have included a blue dot to depict the above stated situation. While the

David Huang

source is equidistant to both PMT detectors initially, as one PMT moves, the distance between the two PMT detectors and the source will change. Blue arrow shows the unchanging distance for the stationary PMT, but the red arrows show the changing distances for the moving PMT detector. My group decided that we could do an error analysis for the peak based on an inaccurate placement of the source. We estimated that if we didn’t place the source on the rotational axis of the PMT detectors, we probably were off within a centimeter or so. With error analysis, we summed the product of the counts and for each angle and divided that by the sum of counts. This yields the average angle of -0.2. This is the angle at which there were an equal number of counts on either side of the angle.

We measured the diameters of the PMT detectors to be 5.6 cm. The radius of our circle is 20.3 cm. The isotropic sphere of radiation that the source gives off at a distance of 20.3 cm creates a total surface area of 5180 cm2. The PMT detectors have a surface area of 99 cm2. The PMT detectors capture about 1.91% (99 cm2 / 5180 cm2) of all the source’s radiation. We don’t need to use smaller detectors to get a narrower coincidence angular peak because the current set-up already captures a relatively small percentage of all the radiation.

Results: Our final results were very good. Below is a coincidence count histogram with varying angular deviations from 180°.

Up To -18

-18 To -15

-15 To -12

-12 To -

9

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-6

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-3

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3

_x0006_3 To 6

_x0006_6 To 9

_x0007_9 To

12

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15

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18

_x0008_18 To

21

_x0004_More

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Histogram

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We had a good distribution that peaked at 179°, but with our error margin of 1.15°, the ideal 180° peaked is reached. We found that we had a normal distribution with a standard deviation that correlated with the angular deviation from 180°. We derived a standard deviation of 5.77°. Below is our normal distribution.

David Huang

0

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HistogramC

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Discussion: My data and results support the Hypothesis. The stand deviation for our experiment was 5.77°, and we yielded a peak of 180° after accounting for a statistical error ±1.15°. Our initial peak was 179°. Because the peak of coincidence counts was measured to be at 180°, we can deduce we observed 22Na’s β+ decay and the subsequent positron and electron annihilation process. In order to conserve both energy and momentum, the 2 resulting photons were produced with an angle of 180° to each other. We think we were successful.

What’s Next: This was an interesting lab and it was very straightforward. Nothing too difficult or confusing.