PHYSC 3622
Experiment 2.4
6 February, 2016
Gamma ray spectroscopy and absorption
Purpose
In this experiment, you will investigate the spectra of gamma rays emitted from
radioactive nuclei and the attenuation of gamma rays in lead.
Part I
Gamma ray spectroscopy
Background
Radioactive nuclei decay by a number of modes, such as alpha or beta emission. These
processes frequently involve the emission of energetic photons as well; we call these
photons gamma rays. Their energies range from tens of keV up to a few MeV. One
example is the decay of Cs 137 , shown below:
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Cs 137 
56
Ba 137   
(1)
Approximately 94% of the time, the beta particle (electron) is emitted with 511 keV of
energy and the Ba nucleus is left in an excited state. The Ba nucleus then goes to the
ground state by quickly giving off a 662 keV gamma ray or photon. We are interested
in this photon. (In the remaining 6% of transitions, the nucleus goes directly to the
ground state and the electron is emitted with 1.17 MeV of energy.) If we were to
measure the intensity and energy of gamma rays emitted by a Cs 137 source, we would
expect to observe a single peak at 662 keV. As we shall see below, the real situation is
somewhat more complicated.
Our problem is to measure the intensity of photons (gamma rays) as a function of
energy or wavelength. We will use a scintillation counter pulse-height technique that
directly measures the intensity versus energy. Figure 1 shows a block diagram of the
apparatus.
Figure 1. Block diagram of the gamma ray spectroscopy system.
The gamma ray enters the Tl-doped NaI crystal detector where it is absorbed in
accordance with the photoelectric effect and converted into a pulse of light. The peak
intensity of the pulse is proportional to the energy of the gamma ray. This light pulse is
then converted into a current pulse by the photomultiplier tube (PMT). Again, the
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PHYSC 3622
Experiment 2.4
6 February, 2016
height of the current pulse is proportional to the energy of the gamma ray. The current
pulse is amplified and the resulting voltage signal is fed to a "sample-and-hold" circuit,
which generates a steady output voltage proportional to the peak input voltage. Next,
this voltage is converted to a number between 0 and 255 by an analog-to-digital
converter (ADC). The number generated by the ADC is once again proportional to the
voltage. Finally, this number forms the address of a single channel in the multi-channel
analyzer (MCA). The MCA has 256 channels, one for each address. Each channel is
essentially a digital counter, and the count in the selected channel is incremented by
one. Each channel in the MCA can hold up to 16,777,215 ( 2 24  1 ) counts.
Using this technique, we are able to generate a plot of the number of counts
(proportional to the gamma ray intensity) versus channel number (proportional to
gamma ray energy). By running several different sources having known emission
energies, we can make a calibration curve giving energy as a function of channel
number. The MCA contains circuits that drive a video display and that allow us to send
the data to a computer, so that we can make a hard copy. A booklet published by The
Nucleus, Inc., entitled Spectrometry Experiments with Multichannel Analyzers gives a more
complete description of the operation of the MCA. Note that our Nucleus 800 MCA is a
bit different from the one described in the booklet (for instance, the high voltage power
supply for the PMT is fixed at 1000 V).
From the above discussion, we might expect that a plot of gamma ray intensity versus
energy would show a single peak at the proper energy (662 keV for Cs 137 ). Instead, the
situation is more complex, as shown by the sample spectrum in Figure 2. The photon is
subject to Compton scattering (an elastic process) by one or more of the electrons in the
material. Thus, the photon may lose energy before it is absorbed photoelectrically.
Compton scattering is derived in the booklet and in any modern physics text; the
energy h  of the scattered photon is given by
h  

h

1  h / m0 c 2 1  cos 
,
(2)
where h is the energy of the incident photon,  is the scattering angle of the outgoing
photon, and m 0 c 2 is the rest energy of the electron. The kinetic energy Te of the
scattered electron is just
Te  h  h  .
(3)
The electron receives maximum kinetic energy when the photon scattering angle is
180°. Compton scattering gives rise to a smoothly distributed spectrum out to the
Compton edge and, frequently, a back scattering peak, as shown in Figure 2. Other
processes, which complicate the spectrum, also take place; some of them are discussed
in the booklet.
Once they are emitted, gamma rays and x-rays are the same thing. A gamma is a
photon emitted from the nucleus, while an x-ray comes from the electron cloud
surrounding the nucleus. However, the detector cannot distinguish between them. In
fact, the type of system you are using in this experiment is often attached to a scanning
electron microscope to measure the energies of the x-rays induced by the electron
beam. A computer then analyzes the spectrum and gives a printout of the chemical
elements present in the sample. (The American Institute of Physics Handbook, Chapter 8,
is a good reference.)
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PHYSC 3622
Experiment 2.4
6 February, 2016
Figure 2. The upper graph shows counts versus channel number for a Cs 137
source, while the lower graph shows the same data plotted as counts versus
energy.
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PHYSC 3622
Procedure
Experiment 2.4
6 February, 2016
Energy calibration: To begin, place the Cs 137 source in the middle tray beneath the
detector. Run several curves using different gain settings to get a feel for the
instrument. Next, do your calibration runs. Gain settings of Coarse = 20 and Fine =
1.1–1.3 are suggested. Run up 1000–2000 counts on the principal peaks for each of the
following sources: Cs 137 (662 keV), Co 60 (1.173 & 1.332 MeV) and Ba 133 (356 & 302
keV). Use the marker to indicate the peak on the screen and record the channel number
corresponding to the peak in your notebook. Using Sigma Plot, perform a linear
regression analysis to relate the energy to the channel number, obtaining an equation of
the form
E  mN  b ,
(4)
where E is the peak energy and N is the channel number; m (slope) and b (intercept)
are fitting parameters.
From your practice runs, you should have noticed that the peak channel number is a
function of the gain settings, so be sure not to change the gain settings once you have
begun to take "real" data.
Printing a spectrum: To print a spectrum, start by running the Gamma Ray Spectroscopy
program on the PC. To send data to the computer, press the Input/Output Mode button
on the MCA control panel, so that the video display reads SERIAL OUTPUT at the top.
Then press the Start button at the computer and the Start/Stop button at the MCA to
send the data to the computer. After a few seconds, the computer display should show
the spectrum.
At the computer, you can change the horizontal axis from Channel Number to Energy
and back by pressing the vs. Energy/vs. Channel button. However, you won't be able
to do this until you enter the calibration constants you obtained above. Press the
Calibrate button to enter the data. You can get a hard copy of the spectrum displayed
on screen by pressing the Print button.
Questions
Run the "unknown" source. Read the data into the computer and make a plot of counts
versus energy. Use your data and a table of the radionuclides to identify the nuclei
present in the source. Hint: The unknown source is a mixture of two isotopes, one of
which you've already looked at, along with a second isotope you haven't yet seen.
Run Cd 109 . Plot the data. What do the data show? What is the resolution of the
instrument? Note that each channel gives the number of events having energy between
E and E  dE , where dE is the resolution.
Now recalibrate the instrument for a lower maximum energy. Suggested gain settings
are Coarse = 20 and Fine = 2.0–2.4. Use the Cs 137 and Ba 133 sources to calibrate the
energy scale. Repeat the Cd 109 spectrum and make the appropriate plots (don't forget
to enter the new calibration values into the computer). What do they show? What is the
resolution of the instrument now?
Part II
Gamma ray absorption
Background
In most materials, gamma rays are attenuated exponentially, so that their intensity can
be expressed as
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PHYSC 3622
Experiment 2.4
6 February, 2016
I  I 0 e  x ,
(5)
where I 0 is the incident intensity,  is the absorption coefficient, and x is the distance.
Usually,  is reported in units of cm 1 and x in units of cm . We often use the mass
absorption coefficient  m , which is defined as
m   / ,
(6)
where  is the density of the material.
The goal of this experiment is to measure  m as a function of energy for lead.
Procedure
Figure 3 shows the arrangement of the source, the lead absorber(s) and the detector. Set
up the multichannel analyzer with Coarse set at 20 and Fine at 1.1–1.3. These settings
usually give a good readout of the Cs 137 spectrum. Select a running time that gives
about 2000 counts with the Cs 137 source placed in the middle tray. Use the on-screen
cursor to read the number of counts at the 0.662 MeV peak of the spectrum, and record
the time duration of the run as well. Now repeat the runs using the Pb absorbers, using
enough different combinations of thicknesses to obtain several points in the range of 0–
1.5 cm. The durations of these runs should be about the same as for the first (no
absorber) run.
Divide the peak counts by the duration for each run, in order to normalize the data and
give intensity. Plot your data as the logarithm of intensity vs. Pb thickness, using Sigma
Plot. Determine the slope of a least-squares straight line fit to the data, and calculate the
resulting value of  at the Cs 137 energy of 0.662 MeV. Repeat the runs for Co 60 (both
peaks) and Na 22 to obtain the values of  at other energies. Calculate the value of  m
for each  , and plot  m vs. energy. Compare your results with handbook values.
Figure 3. Arrangement of source, absorber and detector.
Questions
Describe how your results differ from the handbook values, if at all. Discuss the
discrepancies and suggest possible sources of error.
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