Physics 116C Lab onRadioactive Decay, Geiger Counter, Counting Statistics

V. 1.0, 4/20/2010

Introduction

The goals of this experiment are to investigate:

1. radioactive decay measurements with a Geiger counter;

2. basic data acquisition techniques with LabVIEW;

3. counting statistics (Poisson and Gaussian distributions as limits of the binomial distribution).

The experiment exemplifies a nuclear or particle physics experiment at the simplest level. A sub-atomic particle enters a detector and, through some interaction with the material of the detector,produces an electrical pulse. The pulse is amplified and recorded as an “event” in a counter readout by a computer. The events are entered into histograms for immediate monitoring and storedfor further analysis. The eventual result may be a publication in a scientific journal or, as in thiscase, a lab report.

In the experiment, you will use a LabVIEW program to record histograms of the number of de-tected radioactive decay events from a 137Cs source in a specified time interval when the measure-ment is repeated many times. When the source is far from the detector and the count interval isshort, the average number of decays per interval is small. This should yield a Poisson distribution.Moving the source closer and using a longer interval results in a larger mean number of counts perinterval and a distribution which should approach a Gaussian. Statistical tests are performed on theresulting distributions to test these hypotheses.

Material necessary for understanding the experiment (particles, interactions, detectors, radioac-tive decay) is summarized in Chapter 8 of the text by Melissinos and Napolitano.[1] Statisticalanalysis is covered in Bevington [2] plus Chapter 10 of Melissinos and Napolitano. Also refer tothe specifications of the Geiger counter tube.[3] Some possible questions to be addressed are asfollows.

• What are the energies of the particles resulting from 137Cs decay?

• What physical effects allow these particles to be detected?

• How is the Geiger counter constructed and how is the electrical pulse produced?

• What are the advantages and disadvantages of a Geiger counter as a radiation detector?

Here, X-rays and gamma rays may considered to be particles (photons) as they are emitted, scat-tered and absorbed in discrete events.

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Experiment

The block diagram of the circuit is shown in Fig. 1. The idea is to use a continuously runningcounter which can be read at regular intervals by the computer to take a set of data samples ni(number of counts in ith interval). The computer program (LabVIEW VI) then makes a histogramof ni which can be read out manually or saved to a file for comparison with statistical theory.The timing accuracy is at least of the order of a few ms, which is sufficient for this application.(Greater timing accuracy could be achieved with external gating pulses.)

The VI control panel is shown in Fig. 2 and the VI block diagram in Fig. 3. You should befamiliar with most of the elements in the block diagram at this point. The Express DAQ AssistantVI framework is used for input using counter input 0. Controls are provided for the length ofthe count interval, the number of samples, the histogram binning and whether or not to write thehistogram contents to a file (you must specify this before the run). Indicators are provided for thetotal number of counts, the sample mean and the sample standard deviation.

Figure 1: Circuit block diagram.

The salient features of the Geiger counter controller are shown in Fig. 4. It has a pair of terminalson the back marked “Oscilloscope” (bottom one is ground). The output is a fast-rising pulse withheight of approx. 2.5 V and a decay time constant≈ 200 µs superimposed on a DC pedestal≈ 5 V.

To get the required TTL logic pulse for the computer interface, we need to trigger on Geigercounter pulses exceeding a certain amplitude above the pedestal (≈ 0.6 V). That is accomplishedwith the AC-coupled Schmitt circuit in Fig. 5. The 0.01 µF capacitor at the input blocks DC whilepassing the rapidly rising leading edge of the Geiger counter pulse to the comparator “−” input.The open collector comparator output is connected to a 1 kΩ pull-up resistor, the Schmitt triggerfeedback resistor and a TTL inverter. The inverter drives the base of a 2N3904 BJT capable ofproviding a TTL-compatible signal in the properly terminated 50 Ω coaxial cable. The terminationof the cable in its characteristic impedance prevents reflected pulses which might otherwise causespurious counts. The topics of transmission lines and terminations will be covered later in thequarter.

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Figure 2: Geiger counter statistics front panel (during timing accuracy test).

Procedure

• Precautions with Geiger tube

– Leave the cable from the Geiger counter controller to the Geiger tube in place at alltimes. The connector on the controller can carry a voltage of order 1000 V. If you leavethe cable from the tube connected, nothing else can get connected to it by mistake(including fingers!).

– Leave the Geiger tube in its holder. It has a thin front window which could be broken.

• Precautions with radioactive source

– Don’t touch the source.

– Leave the source in its tray at all times. The TA or lab assistant will provide the sourcesand deal with moving them from place to place.

– Review the material in Appendix D of Melissinos and Napolitano [1] on radiationsafety. Remember that distance between you and the source is your friend.

1. Record your observations and make preliminary curves in a loose leaf notebook (preferablyquadrille-ruled engineering paper).

2. Check and turn on Geiger counter

Remember the warning above not to disturb the connection to the Geiger counter itself, butverify that it is connected to the control box HV. Turn on the Geiger counter control box, setthe HV knob fully CCW (low voltage) and turn on the Geiger counter HV. We turn on thisequipment at this point to let its temperature stabilize.

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Figure 3: Geiger counter statistics VI block diagram.

470 k!

5 nF2 kV

Amplifier

High Voltagemin " 400 Vmax = 1000 V

Oscilloscopeoutput

To internalcounter circuits

Geiger counter control box

thin micawindow LND, Inc

Model 7232filled withNe + halogen gas

Geiger counter tube

Figure 4: Geiger counter and control box.

3. Discriminator circuit

A discriminator circuit produces an output logic pulse for a (suitable amplified and shaped)detector pulse exceeding a given threshold. Wire the discriminator circuit shown in Fig. 5.Use the lower right corner of the prototype board array. Be reasonably neat and use 5 V andground busses appropriately. The input should be from the BNC connector on the left andthe output to the BNC connector on the right. Use twisted pairs of wires for the connectionsfrom the Geiger counter output to the left BNC block. The Geiger counter wires connect tothe scope output screw terminals on the back of the Geiger control box (bottom terminal isground). Also use a twisted pair for the connection to the circuit input. The output goes tothe PFI 8 input of the small connector box coupled to the DAQ card in the computer via aterminated 50 Ω coaxial cable.

4. LabVIEW VI

Load the DAQ program (called Make count samples write for.vi) and figure out what itdoes. Note how the loop delay timer waits until a fixed multiple of a system clock (inms) before reading the continuously running counter at the end of each iteration of the loop.

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C.01 µF

4.7 k" 1.0 k"

+5V

-15 V

+15 V

Vin"Oscilloscope"output fromGeiger countercontrol box

Vout to DAQ interconnect boxPFI 8 input(must be terminatedin 50 " at DAQ cardinput)

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8 LM311

Note: connect 0.01 µF capacitorbetween 5V (pin 14)and ground (pin 7)at chip

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1.0 k"1/6 7404

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2

2

+5V

+5V

10 "1.8 k"

10 k"

100 k"

2N3904

Figure 5: AC-coupled Schmitt trigger discriminator circuit and line driver for Geiger counter.

The Geiger count sample for the current interval is found by subtracting the counter readingfrom the previous iteration. This is put in an array. The zeroth and first element are deleted:the zeroth element winds up being the initial value of the counter (0) and the first elementthe value from the incomplete period of the first loop iteration (the loop is only synchronizedafter the first loop ends). This procedure will include counts outside the timer interval be-tween loop iterations so the actual interval will be slightly longer than the specified value andsomewhat variable. The effect of this on the data will be evaluated, although it is expectedto be negligible for this application. More elaborate procedures exist for critical work.

Also determine how counts are assigned at the histogram bin boundaries.

5. Test the count accuracy and repeatability for 100 ms and 1000 ms counting intervals (theseare the intervals you need for the Poisson and Gaussian distributions, respectively).

Use the signal generator to produce a 1 kHz square wave of 2 V amplitude (4 v peak-to-peak). Disconnect the twisted pair from the Geiger counter control box and instead connectthe signal generator to the input of your trigger circuit on the breadboard.

Now set your VI to count 10 samples of 100 ms. When finished, set the histogram accord-ingly for a longer run. With a longer run (50 samples, say) you can accumulate statistics onthe counting accuracy.

Record the histogram, measured number of counts with error and signal generator frequency.

Repeat for a 1000 ms counting interval.

When you are finished, disconnect the signal generator from your trigger circuit input andreconnect the twisted pair from the Geiger counter control box output.

6. Set Geiger counter operating voltage

The 137Cs source should be in the second slot from the top of the Geiger tube holder. Besure the Geiger counter control box is set to count. We will leave it in this mode at alltimes. Also, don’t push the reset button. It can generate spurious pulses in the output to thediscriminator. This source emits energetic β− particles and γ rays. Sufficiently energetic βsenter the Geiger tube through the thin window and ionize the gas to cause output pulses. Theγs can eject energetic electrons from atoms in the gas filling the Geiger tube to trigger thecounter.

(a) Finding the threshold

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Use the LabVIEW VI (not the counter control box itself–leave it counting continuously;it has a somewhat lower counting threshold).Be careful not to exceed 1000 V. If you hear a ticking sound from the counter (HVbreakdown), reduce the voltage immediately and call the TA.Set the VI to count a small number of samples (10, say) with a short count interval(100 ms). Start the VI in “repetitive” mode (recirculating arrow) and watch the to-tal number of counts per run as you slowly increase the Geiger counter HV from itsminimum setting. Find the minimum HV setting for which you get reliable counting.Record this threshold voltage. (This procedure may need to be modified.)

(b) Making a plateau curveStart at the next 50 V HV multiple above the threshold (e.g., if the threshold was 730 V,start at 750). Set the VI to acquire 10 samples with a 1000 ms count interval andstart the program. After 12 s or so, you will get a count measurement for this voltage(total counts reading). Record this and the voltage. Now increase the voltage in 50 Vincrements up to 1000 V (or 300 V above threshold, whichever is less–don’t exceed1000 V) and repeat the count measurements. You should get samples, ni, of order1000 counts each on the plateau.Make a (hand-drawn) graph of your result with error bars. We assume Poisson statisticshere, so we can estimate σi =

√ni. The threshold voltage in our discriminator is too

high to observe the linear or proportional region of the counter, but there should bea gently rising linear plateau in the Geiger region above the threshold and to the leftof any sharp rise at large voltages. Set the voltage near the center of this plateau andrecord this operating voltage (it will probably be ≈ 100 V above your first measuredpoint above the counting threshold).Fig. 6 shows a typical plateau curve and the chosen operating point. Your results mayvary somewhat.

Figure 6: Geiger counter plateau curve.

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7. Observe Geiger pulses and dead time

Sketch the pulses at four points: trigger circuit input, comparator “−” input, comparatoroutput and trigger circuit output. Note: check the output pulse at a high sweep speed to besure there are no spurious extra pulses at the end (glitches) which could be counted by the20 MHz counter. Be careful not to interfere with the proper termination of the output.

Now set the oscilloscope time base to 50 µs/division. The source should now be in thetop slot, nearest the tube. You should see additional output pulses on the same trace as thetriggering pulses. These appear at random, following a uniform distribution except near thebeginning of the trace. Estimate how long this gap lasts where no additional pulses are seen.This is the overall dead time of the circuit. Record this information.

Actually, the counter is recovering from delivering its previous pulse toward the end of thisperiod. If you hook the scope probe to the comparator “−” input, you should see small pulsesoccasionally near the end of the deadtime region below the 0.6 V threshold (scope triggerlevel needs to be set low enough to capture them). These pulses increase in size until theyreach the maximum. This is the Geiger counter “recovery” region. See if you can observethis.

8. VI file output

Optionally, an output text file of the histogram contents may be written in a spreadsheet-compatible format for further analysis.

9. Observe Poisson statistics with mean near 0

This should be done with the source in the next-to-bottom slot (away from the tube) and witha relatively short count interval (100 ms, say). The mean number of counts should be in therange of 1-3 counts; be sure it is low enough that you get a reasonable number of zero countsamples. The histogram should be set to have bin widths of one count and cover the range0-10 counts.

Do a run of 10 samples and check that the histogram of the samples ni is correct–i.e., makethe histogram by hand and see that it agrees with the computer. Include the check histogramin your lab notes (this is to verify that the software is working as expected).

Check that the count rate measured by the Geiger counter control box roughly agrees with theVI. Do this by comparing counts for a 10 s interval (total number of counts for 100 100 mstrials with the VI vs. a separate 10 s measurement with the Geiger counter scaler using itscontrols). The results should agree within statistics. If not, discuss with the instructor.

Perform and record to file an extended run under these conditions (100 samples, say) to geta histogram with good statistics. Be sure to record the conditions of the run, particularly thehistogram setup. Be sure your upper limit is such that there are no overflows. Be sure thehistogram looks reasonable before proceeding.

10. Observe Poisson statistics with mean ≈ 100 and compare with normal distribution

The source should now be in the slot third from the top. A counting interval of 1000 mswill probably be appropriate for this section. Make a histogram which includes the entiredistribution on ni (within at least 2σ) and has boundaries that are easy to understand. For

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example, if the expected number of counts were 100, you could make a histogram with lowerlimit 80, upper limit 120 and 20 bins.

Do a run of 100 samples, save the output data file for further analysis and record the his-togram in your lab notes. Make sure the histogram looks reasonable.

11. Suggested analysis and writeup

The idea is to plot the histograms and compare with Poisson (low rate) or Gaussian (highrate) statistics. For the high rate data, we want to compare with the Gaussian limit by cal-culating the number of counts expected in each bin using differences of the Gaussian cu-mulative distribution function, given the measured mean value. Use LabVIEW to producecomparison plots. Calculate and compare χ2 to the extent possible.

The writeup should be brief but complete. It should include a brief discussion of the 137Csradioactive decay sequence and Geiger tube operation (see Melissinos and Napolitano, Ch.8).[1] It should describe your procedure and the equipment used, give your results and thedegree of agreement with statistical theory.

References

[1] Adrian C. Melissinos and Jim Napolitano, Experiments in Modern Physics, 2nd. Ed., Aca-demic Press (2003).

[2] Bevington and Robinson, Data Reduction and Error Analysis for the Physical Sciences,3rd Ed., McGraw-Hill (2003).

[3] LND 7232 Geiger counter tube, LND, Inc., http://www.lndinc.com

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