INTERACTION OF GAMMA RAYS WITH MATTER - EXPERIMENT 9

Equipment used:

radioactive sources: 207Bi, 137Cs, 22Na, and 24Na; NaI(TI) crystal and PMT with associated electronics; multichannel analyzer card in personal computer
 

Objectives:

  1. to consider the interaction of gamma rays with matter as illustrating the electromagnetic interaction
  2. to record spectra obtained when gamma rays interact with a scintillation crystal, and to associate each feature of a spectrum with the corresponding interaction mechanism
  3. to calibrate the scintillation spectrometer and determine its energy resolution


Interaction Mechanisms

Gamma rays are electromagnetic radiation with wavelength l of less than about 1 nm = 10-9 m. This corresponds to an energy of greater than 1.6 x 10-16 Joule or 1 keV. Gamma rays are emitted when nuclei undergo transitions from higher-energy to lower-energy states.

There are three principal mechanisms by which gamma rays interact with matter: the photoelectric effect, Compton scattering, and pair production. Each is a consequence of the electromagnetic interaction.

(a) Photoelectric effect. You have already considered the photoelectric effect from the standpoint of ejection of electrons from a metal cathode. A minimum energy (work function) had to be provided to overcome the relatively weak attraction of a chunk of metal for an electron. Similarly an electron can be ejected from an atom by radiation with sufficient energy to overcome the binding of the electron to the atom. If the incident photon has energy Eg , the electron is ejected - usually from the innermost (K) electron shell - with kinetic energy Ee = Eg - B, where B = binding energy of the electron. The probability s of ejection of photoelectrons depends on both the photon energy Eg and the number (Z) of electrons per atom. It can be expressed approximately in terms of,

for low (<100 keV) photon energies. At higher energies, the probability of ejection varies more slowly with energy and varies with a slightly higher power of  Z.

(b) Compton scattering. The g photon scatters from, and imparts energy to, an electron. By treating the scattering as a collision between two particles and writing down equations for conservation of total energy and the components of momentum (with photon energy Eg and momentum Eg /c), you can derive a number of relationships.

(1) The wavelength shift of a photon which has scattered through an angle q.

Note: The electron rest energy and Compton wavelength are found as follows.

h/(moc) = 2.43 x 10-12 m

(2) Thus, the energy acquired by the electron when it is struck by a photon is Ee.

Note that there is a maximum value of the energy the electron can acquire, namely,
 
 

corresponding to the case in which the photon is "backscattered," scattered back in the direction from which it came. However, the energy acquired by the electron may be any value down to 0, depending on the angle q through which the photon scatters. The theoretical number of electrons as a function of their energy Ee is shown in Fig. 1.

Figure 1. Theoretical energy distribution of Compton electrons, struck by photons of initial energy Eg .
The probability of Compton scattering drops smoothly with increasing energy. Below ~100 keV it is less probable than ejection of photoelectrons, but above this energy it is more probable.

(c) Pair production. If it has sufficient energy, a photon may be converted into an electron-positron pair. Clearly the minimum energy necessary equals the sum of the rest-energies of the electron and positron,

2 mo c2 = 2 x 0.511 MeV = 1.022 MeV.

(In this case it is easy to see why pair production must take place in the presence of a nucleus or electron; something has to absorb the photon's momentum Ey/c !) Any additional photon energy beyond this minimum goes into kinetic energy. The probability of pair production must be zero below 1.022 MeV; pair production becomes more likely than Compton scattering only for photon energies above several MeV.

Figure 2 summarizes qualitatively the relative probabilities s of the three mechanisms as a function of photon energy.

DETECTION OF GAMMA RAYS

In this experiment, gamma rays are detected by a scintillation crystal made of thallium-activated sodium iodide, abbreviated NaI(TI). The energy deposited in the crystal is converted to a flash of light, whose intensity is proportional to the energy of the gamma ray. This is converted to a voltage pulse by a photomultiplier tube (PMT, for short) and associated electronics.

The detection process is as follows (Fig. 3):

1. The g -ray interacts with the NaI(TI) crystal and produces radiation which is predominantly in the ultraviolet region. The light output resulting from one photon's hitting the crystal lasts about 10-6 sec.

2. The radiation strikes the cathode of the PMT and produces low energy electrons by means of the photoelectric effect.

3. High voltage applied to the PMT accelerates the photoelectrons down a series of electrodes ("dynodes"), where more electrons are produced by secondary emission.

4. The electron current at the final electrode (anode) is integrated, and an output voltage pulse is formed.

The amplitude of the output voltage pulse is proportional to the energy lost by the g -ray in the crystal. However, the pulse is only a fraction of a volt high. For analysis, it must be amplified while retaining the linear relationship between g ray energy and output voltage. The amplified voltage pulses are sorted by a multichannel analyzer, a "voltmeter with a memory" which records how many pulses in each voltage "channel" (hence g ray energy) were produced. This is the gamma ray spectrum.



GAMMA RAY SPECTRA

An idealized spectrometer would give you a "spike" of a single voltage corresponding to a single gamma ray energy deposited. In practice, electronic noise in the spectrometer, as well as statistical fluctuations in the process of converting photon energy to voltage, broaden the peak even when only a single gamma ray energy is deposited (Fig. 5). The narrowness of the experimental peak is a measure of the quality of the detector. We define the resolution of the detector as DE, where DE is the full width of the peak at half maximum (FWHM). Sometimes this is expressed as DE /E or (DE /E) x 100%. The significance of D E is this: if two gamma rays produce mean responses E1 and E2, they will be resolved if |E2 – El | > DE.

When a gamma ray of energy Eg strikes the scintillation crystal, so long as the full energy is collected within a microsecond, a voltage pulse corresponding to Eg results. This is so even though the collection process may be somewhat complicated. For example in the photoelectric effect, the ejected electron has energy Eg - B, which it gives up to the crystal primarily by colliding with electrons and exciting or ionizing the atoms. Photons, emitted as several atoms de-excite or capture electrons to fill vacancies (including that left by the

original photoelectron!), can be collected at the photocathode and their energies added, together corresponding to the full energy Eg . Similarly in Compton scattering, if the energies of both the electron and the scattered photon are collected within a microsecond, a voltage pulse corresponding to Ey results.

However, even when gamma rays of only a single energy enter the scintillation crystal, the full energy is not always collected, so the spectrum is more complicated than a single peak. Some features to look for include the following.

  1. Compton continuum - The incident g -rays scatter off electrons in the scintillator, give up a part of their energy which depends on the angle of scatter, and then leave the crystal. This gives rise to a continuous spectrum of energy deposited in the crystal by the struck electrons; the energy distribution looks like Fig. 1. The maximum electron energy is referred to as the "Compton shoulder." The Compton continuum is increased in intensity if photons are detected after being scattered into the scintillator by Compton collisions with electrons in the surroundings (e.g. walls, the PMT, even the source material itself).
  2. Backscatter peak - This effect is due to photons Compton - scattering through 180° and then depositing their energy in the crystal. As an illustration of backscattering, if Eg = 0.51 MeV, the expression for Emax tells us that the struck electron acquires energy of 0.34 MeV, so the scattered photon retains 0.17 MeV, which is therefore the energy of the "backscatter peak." Scattered electrons range downward in energy from the Compton shoulder, so energy conservation requires that scattered photons must range upward in energy from the backscatter peak.
  3. Escape peaks - Consider the case of pair production, where a g -ray of energy Eg > 2 mo c2 is annihilated and an electron-positron pair is formed. The charged particles give up their kinetic energy Eg - 2 mo c2 to the scintillation crystal, then the positron encounters some electron in the crystal and they annihilate each other. Depending on whether both, one, or neither of the two resulting annihilation quanta are absorbed in the crystal, the resulting peak corresponds to Eg , Eg - mo c2, or Eg - 2 mo c2. The latter two are referred to respectively as a "single-escape peak" and a "double escape peak." When studying a new isotope, the experimenter must take care not to interpret escape peaks as full-energy g -ray peaks.
  4. Summing - If two gamma rays strike the detector within about a microsecond of each other, their energies can be added together and recorded as a single sum peak. This is especially likely if the detector is large and close to the source, or if the source is strong.


Radioactivity is always present. Sources include long-lived natural radioactive isotopes in ordinary building materials and even in your own body. The radiation emitted constitutes a background present in addition to the radiation from the sources you are trying to study. To avoid being confused by the background, whenever you record a spectrum of a weak source, background counts must be eliminated by shielding the detector or subtracting the background spectrum.

RADIATION SAFETY

The radioactive sources used in this experiment are only a few microcuries in strength, and they are all sealed, so they actually pose no significant health hazard. However we will follow good safety procedure. Horseplay involving the sources is forbidden. While the sources are not dangerous, like any radioactive source they should be treated with respect and properly handled. Only the instructor is to handle the sources, and he/she will wash hands after handling the sources. When any source is not in use, it is to be stored behind lead shielding. In the event of any accident which results in spilled radioactivity, do not attempt to clean it up yourself. Block off the area of the spill and call the professor in charge of the course.

Remember: If for safety reasons you choose not to work directly with radioactive sources, you are given the option of performing the experiment with stored data instead. See the instructor to arrange a time when you can do this.



 

USING THE GAMMA RAY SPECTROMETER

Do not turn off the power to the electronics, except for the personal computer and printers. The high voltage supply and amplifier may be safely left on all the time.

The size of the NaI(TI) crystal determines its efficiency in detecting gamma rays, and the attached phototube determines the high voltage and amplification required. You should note down the size of the NaI(TI) crystal provided at your laboratory station.

Detailed description of the use of the PCA-II software is given on a separate page.

The software allows you to calibrate each spectrum, so that arbitrary voltage units ("channels") are converted to photon energy. To calibrate, you specify the energy that corresponds to each of two or more full-energy peaks; to reduce extrapolation error these should be far apart. Because the peaks in the scintillation spectrum are broad, and because you are extrapolating (or interpolating) over a sizable energy range, your gamma ray energy values are only accurate to ±10 keV or ±20 keV, where 1 keV = 1.60 x 10-16 joules. (It is much easier to locate exactly the much narrower full-energy peaks in a spectrum recorded with a high-resolution germanium spectrometer, and so calibration is much more precise with such a detector.)

Gamma Ray Spectroscopy with the PCA-II Card

Again we use the PCA-II card and software, which you first used in the K-capture atomic spectroscopy experiment, to convert the personal computer into a multichannel analyzer. The software really is user-friendly; the commands on the pull-down menus mean about what you'd expect them to mean. Suggestions are provided below for initial choices of parameters. Try to refrain from exploring all the possibilities of the software so you do not get distracted from learning the physics.

(F#) denotes a Function Key. Toggle between the spectrum window and the command area by clicking the right mouse button.

I. Starting PCA Software

A. At the C:\PHY293> type mca and then enter (<-)
II. Setting up to record a spectrum   (Use the mouse to choose from the menu bar.)
A. Setup
1. Identification. Enter a caption for this spectrum.   2. Memory Group. Quarter. Choose Division 1 through 4.   3. Conversion Gain. Gain should be 512.   4. Vertical scale. Scale should be Log.   5. Expanded Display. Choose Expand 512 to display the whole spectrum. Choosing 256, 128, or 64 allows you to zoom in on part of the spectrum.   B. Mode  
1. PRA (Pulse Height Analysis) (In each of the next three, when you select the first choice, next time you call the menu the other choice will be presented.)   2. Add (Subtract)   3. Live Time (Real Time)

4. No overlap (overlap).

    C. [F3] - Preset Time in seconds, how long you want to count a spectrum.


III. Recording a Spectrum

A. [F1] toggles Acquire (Stop) to start or stop recording a spectrum. Many menu choices are not allowed while a spectrum is being acquired.

B. You can erase a spectrum after [F1] - Stop by pressing Ctrl and [F2].


IV. Calibration

A. Record the calibration spectrum in the Division 1 of the memory.  
Suppose you are using a two-point calibration using the 75 keV Pb X-ray emitted in the decay of 207Bi and the 1275 keV gamma ray emitted in the decay of 22Na. A reasonable procedure would be to record the 207Bi spectrum for 60 s, then set the first ROI (see below) on the 75 keV peak, and then put the cursor on the 1063 keV peak. Next add in that same division the spectrum of 22Na recorded for 60 s; set the second ROI on the 1275 keV peak, and proceed with the calibration routine.
 
B. Setting an ROI (Region of Interest)
  1. [Esc] to select ROI menu. Move the cursor to the low-energy side of the ROI, then [F9]. Move the cursor to the high-energy side of this ROI, then [F10]. You should select only an isolated piak for a calibration line, and you should choose the ROI to extend about 5 channels onto the "flat" region on each side of the peak.

2. You can delete an ROI with [Del], and you can toggle on/off the shading of the ROI with [Alt] and R.
 

C. Calculate energy corresponding to channel number.
  1. Calc; Calibrate; Enter units keV

2. Locate Peak 1 by putting the cursor within the ROI on Peak 1. <Enter>. Type in the energy for this peak.

3. Repeat for each calibration peak. When you have entered the last calibration peak, type <Enter> again, and you will be told that calibration is terminated.

D. Saving the Calibration spectrum
  1. File; Save Binary File; Filenane; enter Calib.spm
 
E. Automatically calibrating all divisions of the memory
  1. Options; Run a Batch File; Filename; enter calib.nbe
V. Recording additional spectra After you have calibrated all divisions by the above procedure, you may record a spectrum in any of the divisions and read the peak location in energy instead of channels.
 
VI. Printing out spectra
    1. Options; Call a User Program; Execute Filename enter setcolors.exe
    2. Shift-Print Screen.
    3. To return to color display repeat step A.

FOR YOUR REPORT

You are to obtain and analyze gamma ray spectra as described below. You should print out each of the spectra. Write the results of your measurements directly on these hardcopy spectra.

  1. Calibrate the spectrometer using the 1275-keV full-energy peak from 22Na and using the 75-keV Pb x-ray. (This x-ray is emitted, for example, when 207Bi decays to 207Pb by capturing an orbiting electron; the vacancy thus created in the [Pb!] electron shell is filled by an electron from a higher orbit, and an x-ray photon is emitted.) Check your calibration against the known 511-keV energy of annihilation radiation following emission of positrons by 22Na.
  2. Record a spectrum of 137Cs. Point out the full-energy peak, the Compton shoulder, the Compton continuum, and the backscatter peak. From the 662-keV energy of the full-energy peak, predict the corresponding energies of the Compton shoulder and backscatter peak, and use the predictions to confirm your identification of these features. (In this decay there is also emitted the 32 keV x-ray of 137Ba.)

  3.  

     

    Record another spectrum of 137Cs in which you deliberately reduce the backscatter peak by removing the lead brick behind the source, with everything else unchanged. When you do this, one peak disappears from the spectrum in the vicinity of 100 keV. Identify what it is, and explain why it arises only when the lead brick is put in place.

  4. Determine the energy resolution of the scintillation spectrometer at E = 662 keV. Its value is quoted in percent.

  5. Gamma ray detectors using germanium instead of a sodium iodide scintillation crystal will give a resolution of 0.1% or better. While a germanium detector has much better energy resolution, you pay a price (in addition to $$$!); its efficiency for detecting gamma rays is much less than for NaI(TI).
  6. Record a spectrum of 24Na. This isotope has a half-life of 15 hours, and the source was made expressly for this week's experiment by neutron irradiation of Na2CO3 at the Ohio State University nuclear reactor. This isotope emits gamma rays of energy 2754 keV and 1369 keV. Both of these gamma rays have sufficient energy to give rise to pair production. Annihilation of the positron with an electron results in two 511-keV photons, one or both of which may escape from the detector and give rise respectively to a single-escape or double-escape peak. What would be the energies of these peaks? Can you observe such escape peaks with your detector? Would you expect these escape peaks to be more prominent in a spectrum recorded with a 3" x 3" detector or with a 2" x 2" detector? Explain.
  7. Record a background spectrum; note how slow the counting rate is. You are given a spectrum recorded for a long time with your calibration. Identify sources by energies of peaks. Here are some possible candidates:
40K: 0.01% of all potassium on earth is 40K, which is radioactive with a half life of 1.3 billion years. It emits a 1461-keV gamma ray. (There is a lot of potassium in building materials and in your body.)

208TI: This isotope, historically called Th C", is part of the decay chain of Th-232, which has a half life of 14 billion years. It emits gamma rays of 511, 583, 860, and 2614 keV.
 


 Pre-Lab Questions


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 Dr. S.D. Marcum or  Dr. J.M. Yarrison-Rice