absorption of gamma rays

8/6/2019 Absorption of Gamma Rays

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ABSORPTION OF GAMMA RAYS

Gamma rays is the name given to high energy electromagnetic radiation originating fromnuclear energy level transitions. (Typical wavelength, frequency, and energy ranges are:0.0005 to 0.15 nm, 2 1018 to 6 1020 Hz, and 10 keV to 2.5 MeV, respectively.) The termsgamma rays, nuclear x-rays, and high-energy photons are often used interchangeably.Gamma rays traversing matter are absorbed due to a number of processes. The ability of asubstance to absorb gamma rays is expressed by the absorption coefficient for that substance.In this experiment an attempt will be made to verify the theoretical expression describing theabsorption of gamma rays as a function of absorber thickness, and the absorption coefficientsfor lead and aluminum for gamma rays from 137Cs will be measured and compared toaccepted values.

Theory:Gamma ray absorption is a random type of process; it is not possible to say whether a

particular gamma ray will interact with the absorber or pass through unaffected. Theprocesses by which gamma ray absorption occur are: 1) the photoelectric effect; 2) Comptonscattering, and; 3) pair production. The photoelectric effect and Compton scattering arediscussed in experiments 5 and 6 respectively. Pair production is the process whereby, in thevicinity of a nucleus, a photon (gamma ray) spontaneously materialises into an electron and apositron. Pair production can only occur for gamma ray energies 1.02 MeV. In all three ofthese processes the gamma ray is either scattered away from the incident direction orcompletely absorbed. That is, if a detector is placed on the opposite side of the absorber,along the incident direction of a beam of gamma rays, only those gamma rays which did notinteract with the absorber will be detected.An expression can be derived which gives the number,N, of gamma rays that will passthrough an absorber without interacting, as a function of the absorber thickness and theincident number of gamma rays. Consider a number,No, of gamma rays incident on anabsorber of thicknessx. Suppose the absorber is divided into n sections of equal thickness x(see Figure 1).

Figure 1


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Since gamma ray absorption is a random process, it is reasonable to expect that the change inthe number of gamma rays, N, due to absorption in a section of the absorber, is proportionalto the number of gamma rays incident on the absorber section and the absorber sectionthickness: 23 Sep 08 Gamma.2


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i.e. NNx (1)That is, the likelihood of a gamma ray interacting increases as the thickness of the absorberthickness increases, and increasing the number of incident gamma rays increases the numberthat will be absorbed. To make equation (1) an equality, define , the absorption coefficient,as the constant of proportionality. is a measure of the effectiveness of a given type ofabsorber. Also, note that Nis intrinsically negative since the number of gamma rays isdecreasing due to absorption. N=Nx (2)The relative change in the number of gamma rays, due to absorption, isNNx= (3)Consider the absorber to be separated into its n sections:Figure 2

Figure 2

The number of gamma rays remaining after each section of the absorber is traversed is givenby;NNNNNNNNNx111== = oooo()

()NNNNNNxNx2211===111o()andNn =No(1 x)n is the number remaining after passing through the complete absorber.23 Sep 08 Gamma.3


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Now recall that x =x/n.NNxnnon= 1 (4)Note that the above analysis assumes that the number of gamma rays changes linearly overthe width of each absorber section.i.e. forN1,N1 =NoNox = c1 + c2x c1, c2 constantsHowever, the proper expression isN1 =NoNx, whereN decreases continuously as thegamma rays pass through the absorber section. This problem can be overcome by takingsmaller and smaller section thicknesses. Therefore, from equation (4):NNNxnNex== = limlimnnnono1 (5)whereNo is the incident number of gamma rays, andNis the number transmitted through theabsorber of thicknessx. The above result can be obtained directly from equation (3) byintegration:

NNxdNNdxdNNdxNNxNNexNNxx====limlnln00implies=oooThat is, the number of gamma rays remaining decreases exponentially as the absorberthickness is increased. Although the desired result follows rather easily by integratingequation (3), such is not always the case. In this instance, equation (3) can be written asdNdxN=23 Sep 08 Gamma.4


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which is an easily solved differential equation. However, for some types of problems, thedifferential equation may be quite complicated. In that case, it is useful to use an iterativetype of solution as was done initially. Also, note that the iterative calculation lends itselfrather nicely to computer programming.Apparatus:

The source used in this experiment is 137Cs, which emits gamma rays with an energy of 0.662MeV. There are four lead absorber disks of thickness 1.0 mm, 1.6 mm, 3.2 mm, and 6.5 mm(each 0.1 mm), and numerous aluminum absorber plates whose thicknesses are stamped onthe plate ends.The source is collimated to provide an incident beam of gamma rays, and the detector is well-shielded and collimated to reduce background counts and to detect only those gamma rayswhich come directly from the source.The detection and analysis system consists of a NaI(Tl) scintillation crystal andphotomultiplier tube connected to a high voltage supply and a multichannel analyser (MCA)connected to a PC.Gamma rays passing into the NaI(Tl) crystal cause flashes of light (scintillations) inside thecrystal. These flashes of light release electrons from the photocathode of the photomultiplier

tube (by the photoelectric effect). The high voltage applied to the photomultiplier tube causesthe electrons to be channelled through the various stages of the tube, with amplification of thenumber of electrons occurring at each stage. The result is a pulse at the output of thephotomultiplier tube, the voltage of the pulse being proportional to the energy deposited inthe crystal by the gamma ray. After linear amplification the voltage pulse is digitized by theanalogue-to-digital-converter (ADC) in the multichannel analyser, and the computer monitordisplays the number of pulses versus channel number. The channel number is directlyproportional to the photomultiplier tube pulse voltage and hence to deposited gamma rayenergy. The monitor thus shows the energy distribution of the gamma rays being detected. Adiagram of the apparatus is shown in Figure 3.Figure 3

Gamma.5 Procedure and Experiment:NOTE: In the theory section, the discussion involved the number of gamma rays. However,

since the source emits gamma rays continuously in all directions, the termsNandNoshould have been defined as numbers of gamma rays per unit area per unit time.


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This will not affect the results, though, as long as counts are normalised to a constanttime interval. (i.e. convert to counts per second or counts per minute, or counts in 5minutes, etc.) The area over which measurements are made is constant because theactive frontal area of the scintillation crystal does not change.

Also, recall that for a random process such as absorption of radiation, the experimentaluncertainty in a count measurementNis given byN. Thus the relative uncertaintyNNNNN==1decreases as the number of counts recorded increases. Therefore, the longer the time intervalover which counts are recorded, the better the experimental accuracy. For example, suppose aone minute measurement yields 100 counts and a four minute measurement yields 400counts. Although the result in both instances is a count rate of 100 counts/min, in the firstcase the result is (100 100)/1 min = 100 10 counts/min, while in the second case it is (400 400)/4 min = 100 5 counts/min.When performing a counting experiment a compromise must be reached between the amountof time available for the experiment and the desired accuracy. When choosing time intervalsfor the counts to be made in this experiment, be sure that all of the measurements can bemade in the lab period, and remember that as the absorber thickness is increased the count

rate will decrease, so longer time intervals will be required to maintain a desired degree ofaccuracy.1. Turn on the power and high voltage switches on the scintillation amplifier/high voltage

power supply. Check that the settings are:

COARSE GAIN: 160FINE GAIN: 14.00HIGH VOLTAGE: 11.00 kV

If any of these settings are different, consult your lab instructor.

2. Allow five minutes for the high voltage power supply to warm up.

3. The system is now ready for use.4. Ensure that the two large lead bricks are in front of the source. It will be assumed that

these bricks absorb all radiation from the source that would otherwise strike the detector.Measure the background radiation (due to other sources in the building, cosmic rays, theearth, etc.) by counting for 600 seconds.

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Record the total number of counts obtained in all channels of the display (see softwareinstructions).

The background rate is the number of counts detected divided by 600 seconds. This

background rate must be subtracted from your measurements to obtain the rate due to thesource only. Once the background measurement has been completed, remove the twolead bricks. (DO NOT REMOVE ANY OF THE OTHER LEAD SHIELDING THATSURROUNDS THE SOURCE).

5. Visually check that the absorber holder is in line with, and about midway between, thesource and detector.

6. With no absorber, measure the incident gamma ray count rate. Use a time of 100 s. Thespectrum (energy distribution) of gamma rays that you observe is due to characteristics ofthe detector system. The incident gamma rays are monoenergetic at 0.662 MeV. As wellas measuring the gamma count rate as described above, record the channel number of thegamma energy peak.

7. Measure the thicknesses of the 4 available lead absorber disks.

8. Measure the gamma ray count rate and peak channel number for all possible combinations(15) of the four lead absorber disks. Remember to set and record the count time, andto increase the count time as the absorber thickness is increased.

9. Measure the gamma ray count rate and peak channel number for the aluminum plateabsorbers. Use the available C clamp to ensure that the plates are mounted vertically(perpendicular to the incident gamma rays). Since aluminum is not as effective anabsorber as lead, and since most of the plates are approximately the same thickness, takemeasurements for no plate, one plate, two plates, etc. until all the aluminum plates arebetween the source and detector. (BE SURE TO RECORD THE THICKNESS OF

EACH PLATE AS IT IS USED.)

Software Instructions

UCS30 USB DEVICE

1. Turn on the UCS30.

2. Double-click on the UCS30 icon on the desktop or single-click on the icon in the QuickLaunch toolbar.

3. Click on the Mode menu and select PHA (Direct In), the 3rditem on the list.

4. Data acquisition is controlled using the buttons on the toolbar. For the most part, the

functions of these buttons is obvious, and a ToolTip will appear if you hover over abutton.

Data acquisition is begun by clicking the GO button.

Data acquisition is stopped by clicking the STOP button.

Data is deleted using the eraser button (3rd from left).

Data can be acquired for a pre-set time by clicking the clock button. Ensure that LiveTime is selected.


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To determine the total number of counts in some region, or to determine the channelnumber/energy of a peak in the spectrum, a region of interest (ROI) must be defined. Thisis

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done using the ROI button. A ROI is defined by placing the cursor at the left edge of thedesired region and then clicking with the left mouse button and dragging the cursor to theright edge of the region. The ROI will change colour to show the region that has been

selected. The total number of counts in the region is given by the GROSS number (notthe NET number). The CENTROID is the channel number or energy of the peak withinthe ROI. To clear the ROI, go to Settings ROIs.

The vertical axis can be toggled between a linear or logarithmic scale with the Y/logbutton. The vertical axis scale is changed by moving the slider at the far right side of theprogram window.

Analysis

For each set of results (lead and aluminum) plot the natural logarithm of the gamma ray countrate (corrected for background) versus absorber thickness.

i.e. Plot ln Nversusx. According to theory, sinceNNex=o

ln N= ln No x

SinceNo and are constants, the theoretical prediction is that ln Nversusx is linear with aslope of .

Do your results verify the theoretical relationship between count rate of transmitted gammarays and absorber thickness?

Determine the experimental values of the absorption coefficients for lead and aluminum forgamma rays from 137Cs. How do your values compare with the accepted values of 1.21 cm1

and 0.202 cm1 respectively?

In your report discuss any sources of error which may be inherent in the design of theexperiment. (HINT: Consider the geometry of the apparatus and the processes by whichgamma rays interact with matter.) What assumptions were made in the theory? Do theseassumptions hold for the actual experiment? Would you expect your values to be higher orlower than the accepted values? Explain.)

Which absorber type is more effective, lead or aluminum? Try to think of a few reasons toexplain why.

How does the energy (peak channel number) of the transmitted gamma rays vary withabsorber thickness? Discuss.

absorption of gamma rays

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