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Gamma-ray Attenuation in Lead – Variation with Energy
- Introduction
Gamma rays are emitted when an excited nucleus decays from an excited state down to the ground state. Usually (e.g. in the case of the laboratory radioactive sources used here) these excited states have been populated following the beta decay of an unstable nuclide. The two gamma-ray sources here, (^137) Cs and 60 Co, are beta-decaying nuclides, decaying to 137 Ba and 60 Ni respectively, both of which are
stable. These two nuclei are left in excited states, decaying to the ground state by gamma-ray emission. In the case of the beta decay of 137 Cs, one gamma ray in 137 Ba is emitted – of energy 0.663 MeV. In the case of 60 Co decaying to 60 Ni, two gamma rays are emitted – of energies 1.173 and 1.333 MeV.
Gamma radiation is very penetrating and can be, of course, harmful to human tissue (though not with the intensities used here). It is clearly very important from a safety point of view to understand how gamma radiation interacts in matter so that we can be properly protected. Indeed, nuclides such as this (especially 137 Cs) are readily created in nuclear reactors. It is also extremely important for the design of radiation detectors to have a full appreciation of how gamma rays interact in matter.
- Gamma-ray interactions in matter
If a beam of gamma rays of a given energy are incident on an absorber, the reduction in intensity of the beam is given by the following equation:
R = R 0 exp (− μ mx ) (1)
Where R 0 is the number of gamma-rays hitting the absorber (over a fixed time), and R is the number which pass through without interacting at all. x is the thickness of the absorber, measured as mass
per unit area (e.g. in units of g cm-2 ) and μm is called the mass attenuation coefficient (e.g. in
units of cm^2 g-1 ). Clearly the larger the values of x and μm, then the greater the absorption of the
radiation. The mass attenuation coefficient depends on the density of the material and the energy of
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the gamma ray. One can also define a half-thickness, x1/2, defined as the mass per unit area required to reduce the intensity of the radiation by a factor of two.^1
m
x
2
1 =^ (2)
In this experiment you will measure the mass attenuation coefficient and the half-thickness for the two gamma-ray sources, by measuring count rates with a varying thickness of lead placed in between the source and the detector.
There are two main processes by which gamma rays (of these energies) can interact in material. The first of these is the photoelectric effect, in which the full energy of the gamma ray is completely absorbed (i.e. the gamma-ray disappears). The second is called the Compton effect, in which the gamma ray loses only part of its energy. In this latter case, of course, the gamma ray has not disappeared, but we can tell from the measured energy that it has undergone an interaction.
Of course, to measure gamma-radiation we need to have a thick detector so that the gamma ray interacts in the detector! In the detector itself, therefore, we will also have these two effects taking place as well as in the absorbers that we will use. This complicates matters a little!! However, if we observe a gamma ray that deposits it’s full energy in the detector, then we know that it has not interacted at all in the absorber. It is the count rate for such gamma rays that we shall measure. That is, in equation (1), R 0 is the measured count (over a fixed time) with no absorber present for full-energy gamma rays in the detector, and R is the count (over the same time) of such gamma rays with an absorber present.
1 Note that equations 1 and 2 are almost identical to the equations for radioactive decay rates: A = A 0 exp(− λ t )and
T 1 2 = 0. 693 λ.
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- Experimental Procedure
The equipment should be switched on, and the required voltage for the detector (marked on the detector itself) should be applied. Do not adjust the gain on the amplifier, as this has been set already for the experiment.
(a) Setting the voltage threshold
In this first of the experiment, you are to determine the voltage threshold required for the analyser in order to select the amplified voltage pulses from the detector that correspond to events in which the gamma ray has deposited its full energy in the detector. Choose one of the two sources (either 137 Cs or (^60) Co). The source should be placed on the very bottom of the lead castle. Do not handle the source
yourself (even with tweezers) – the lecturer or demonstrator will get the source for you and place it in the lead castle. Turn the threshold voltage down to 0.25V. Set the scaler-timer to record the number of counts in a 20s period, and press the “start” button. The timer will stop automatically after 20s. Repeat the process, increasing the threshold voltage in 0.25V intervals, recording the counts. Plot a graph by hand as you go, to save time. You do not need to perform any error analysis at this point. Stop the measurements when the count rate has reduced to a typical background count (a few counts per second). Your graph should look something like…
Volts Larger voltage pulses, corresponding to the full energy of the gamma ray
Smaller pulses, where the gamma-ray has lost part of its energy inthe absorber or detector
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0
2000
4000
6000
8000
10000
12000
0 1 2 3 4 5 Threshold Volts
Counts /20s
From the graph, as indicated, approximately identify the point at which the graph levels out at a very low count. At this threshold voltage, all the gamma rays from the source have been cut out. Reduce the threshold voltage to 80% of this value. This will be sufficient to let through to the scaler-timer all the events where the gamma ray has deposited its full energy in the detector.
(b) Absorption in lead
With the threshold set, we can now begin the measurements. With no absorbers present, set the preset time on the scaler-timer to be sufficient to record about 10000 counts. This time will depend on the strength of the sources, but should be around 20s. Keeping this preset time, place an absorber on the shelf provided and record the counts. Repeat this process for at least 10 different absorber thicknesses (use combinations of absorber sheets to get a good spread of thicknesses). You should ensure that the counts reduce by at least a factor of three over the range of absorbers used.
(c) Background Count
Now you should measure the background count with the source removed from the lead castle. The background comes from naturally occurring radioactive nuclei in the environment (especially in concrete), a little from the man-made sources in the lab (but not much) and some from cosmic rays. Record the background count in a time-period of at least 100s. This background should now be
