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ORTEC
Experiment 3
Gamma-Ray Spectroscopy Using NaI(Tl)
Equipment Required
- Electronic Instrumentation
o SPA38 Integral Assembly consisting of a 38 mm x 38 mm NaI(Tl) Scintillator, Photomultiplier Tube, and PMT Base with Stand o 4001A/4002D NIM Bin and Power Supply o 556 High Voltage Bias Supply o 113 Scintillation Preamplifier o 575A Spectroscopy Amplifier o Easy-MCA-2k including USB cable and MAESTRO-32 software (other ORTEC MCAs may be substituted) o Personal Computer with a USB port and a recent, supportable version of the Windows operating system. o Oscilloscope with a bandwidth ≥150 MHz, e.g., Tektronix Model TDS 3032C or equivalent.
- Coaxial Cables and Connectors
o C-34-12 RG-59A/U 75-Ω Cable with one SHV female plug and one MHV male plug, 3.7-m (12-ft) length. o Five C-24-1 RG-62A/U 93-Ω Coaxial Cables with BNC plugs, 30-cm (1-ft.) length. o C-24-12 RG-62A/U 93-Ω Coaxial Cable with BNC plugs, 3.7-m (12-ft.) length. o Three C-24-4 RG-62A/U 93-Ω Coaxial Cables with BNC plugs, 1.2-m (4-ft.) length o C-29 BNC Tee Connector o C-27 100 Ω Terminator (BNC male plug)
o RSS8 Gamma Source Set. Includes ~1 μCi each of: 60 Co, 137 Cs, 22 Na, 54 Mn, 133 Ba, 109 Cd, 57 Co, and a mixed Cs/Zn source (~0. μCi 137 Cs, ~1 μCi 65 Zn). The first three are required in this experiment. An unknown for Experiment 3.2 can be selected from the remaining sources. o GF-137-M-5 5 μCi ±5% 137 Cs Gamma Source. (Used as a reference standard for activity in Experiment 3.5) o GF-057-M-20 20 μCi 57 Co Source (for Experiment 3.9)
o One each of pure metal foil absorber sets: FOIL-AL-30, FOIL-FE-5, FOIL-CU-10, FOIL-MO-3, FOIL-SN-4, and FOIL-TA-5. Each set contains 10 identical foils of the designated pure element and thickness in thousandths of an inch (Foil-Element-Thickness). o RAS20 Absorber Foil Kit containing 5 lead absorbers from 1100 to 7400 mg/cm^2. The 10 aluminum absorbers from 140 to 840 mg/cm^2 also included in this kit are not used in this experiment.
- Small, flat-blade screwdriver for tuning screwdriver-adjustable controls
- Additional Equipment Needed for Experiment 3.
o 427A Delay Amplifier o 551 Timing Single-Channel Analyzer o 426 Linear Gate o 416A Gate and Delay Generator
Purpose
The purpose of this experiment is to acquaint the student with some of the basic techniques used for measuring gamma rays. It is based on the use of a thallium-activated sodium iodide detector. The written name of this type of detector is usually shortened to NaI(Tl). In verbal conversations, it is typically simply called a sodium iodide detector.
Gamma Emission
Most isotopes used for gamma-ray measurements also have beta-emissions in their decay schemes. The decay scheme for the isotope typically includes beta decay to a particular level, followed by gamma emission to the ground state of the final isotope. The
beta particles will usually be absorbed in the surrounding material and not enter the scintillation detector. This absorption can be assured with aluminum absorbers (ref. 10). For this experiment, the beta emissions cause negligible interference, so absorbers are not specified. There is always some beta absorption by the light shield encapsulating the detector. The gammas, however, are quite penetrating, and will easily pass through the aluminum light shield.
Generally there are two unknowns that we would like to investigate about a gamma source. One is measuring the energies of the gamma rays from the source. The other is counting the number of gamma-ray photons that leave the source per unit of time. In this experiment the student will become familiar with some of the basic NaI(Tl) measurements associated with identifying a gamma- emitting radioisotope. A total time of ~6 hours is required to complete all the parts of Experiment 3 (3.1 through 3.10). Since each part is written to be fairly independent of the others, the complete series can be done in two 3-hour lab periods.
The NaI(Tl) Detector
The structure of the NaI(Tl) detector is illustrated in Figure 3.1. It consists of a single crystal of thallium activated sodium iodide optically coupled to the photocathode of a photomultiplier tube. When a gamma ray enters the detector, it interacts by causing ionization of the sodium iodide. This creates excited states in the crystal that decay by emitting visible light photons. This emission is called a scintillation, which is why this type of sensor is known as a scintillation detector. The thallium doping of the crystal is critical for shifting the wavelength of the light photons into the sensitive range of the photocathode. Fortunately, the number of visible-light photons is proportional to the energy deposited in the crystal by the gamma ray. After the onset of the flash of light, the intensity of the scintillation decays approximately exponentially in time, with a decay time constant of 250 ns. Surrounding the scintillation crystal is a thin aluminum enclosure, with a glass window at the interface with the photocathode, to provide a hermetic seal that protects the hygroscopic NaI against moisture absorption. The inside of the aluminum is lined with a coating that reflects light to improve the fraction of the light that reaches the photocathode.
At the photocathode, the scintillation photons release electrons via the photoelectric effect. The number of photoelectrons produced is proportional to the number of scintillation photons, which, in turn, is proportional to the energy deposited in the crystal by the gamma ray.
The remainder of the photomultiplier tube consists of a series of dynodes enclosed in the evacuated glass tube. Each dynode is biased to a higher voltage than the preceding dynode by a high voltage supply and resistive biasing ladder in the photomultiplier tube base. Because the first dynode is biased at a considerably more positive voltage than the photocathode, the photoelectrons are accelerated to the first dynode. As each electron strikes the first dynode the electron has acquired sufficient kinetic energy to knock out 2 to 5 secondary electrons. Thus, the dynode multiplies the number of electrons in the pulse of charge. The secondary electrons from each dynode are attracted to the next dynode by the more positive voltage on the next dynode. This multiplication process is repeated at each dynode, until the output of the last dynode is collected at the anode. By the time the avalanche of charge arrives at the anode, the number of electrons has been multiplied by a factor ranging from 10^4 to 10^6 , with higher applied voltages yielding larger multiplication factors. For the selected bias voltage, the charge arriving at the anode is proportional to the energy deposited by the gamma ray in the scintillator.
Gamma-Ray Spectroscopy Using NaI(Tl)
Fig. 3.1. The Structure of the NaI(Tl) Detector and Various Types of Gamma-Ray Interactions that Occur in the Typical Source-Detector-Shield Configuration.
The MCA listed in the Equipment Required for this experiment uses software in a supporting personal computer to operate the instrument and display the spectrum. The MCA connects to the computer via a USB cable. It is important to become familiar with the controls that are accessible via the MAESTRO-32 software. The most efficient approach may be to have the laboratory instructor provide a quick demonstration. You will need to know how to start/stop data acquisition, clear the contents of the memory, select the digital resolution, adjust the upper and lower discriminator thresholds, set the preset live time, monitor the percent dead time, read the peak positions with the mouse pointer, set regions of interest, and calibrate the horizontal scale to read in keV (energy).
One of the benefits of the MCA is the incorporation of a live time clock. This feature automatically corrects for dead time losses by measuring elapsed time only when the spectrometer is not busy processing a pulse. See references 1, 11, 13 and 14 for more information.
EXPERIMENT 3.1. Energy Calibration
3.1.1. Equipment Setup
Set up the electronics as shown in Fig. 3.2.
- Turn off power to the NIM Bin and Power Supply and the 556 HV Power Supply.
- Check that the front-panel controls on the 556 HV Power Supply are set to their minimum values. Confirm that POSitive POLARITY has been selected on the rear panel, and the CONTROL toggle switch has been set to INTernal. The 556 derives its primary power from an AC power outlet. But, for convenience, it can be inserted into a vacant location in the NIM Bin.
- Ensure that the NaI(Tl) detector assembly is properly mounted in the stand. Connect the MHV High Voltage (Bias) connector on the detector to the SHV High Voltage OUTPUT on the rear of the 556 using the C-34-12 coaxial cable. Note that the connectors are different on each end of this high voltage cable. One connector is specific to the MHV connector used on the detector, and the other is matched to the SHV connector on the rear of the 556 HV Supply.
- Using the C-24-1 coaxial cable, connect the anode output of the NaI(Tl) detector assembly (BNC connector) to the INPUT of the 113 Preamplifier. Set the 113 INPUT CAPacitance to 200 pF. The polarities of the anode output of the photomultiplier tube and the preamplifier are both negative.
- Remove the 575A Amplifier from the NIM Bin and check that the slide switches accessible through the side panel are all set to 0.5 μs. That selection ensures that the shaping time constant is set to 0.5 μs. Insert the amplifier back into the NIM Bin.
- Connect the power cable from the 113 Preamplifier to the PREAMP. POWER connector on the rear of the 575A Amplifier.
- Using a C-24-12 coaxial cable, connect the OUTPUT of the 113 Preamplifier to the INPUT of the 575A Amplifier.
- Select the NEGative input polarity on the 575A Amplifier.
- Using a C-24-4 coaxial cable, connect the UNIpolar OUTput of the 575A Amplifier to the analog INPUT of the Easy-MCA. Using the USB cable, connect the USB port on the rear of the Easy-MCA to the USB port on the supporting computer. Ensure that the MAESTRO-32 software that operates the Easy-MCA has been installed on the computer.
- Turn on the power to the computer and the NIM Bin and Power Supply.
There are two parameters that ultimately determine the overall gain of the system: the high voltage furnished to the phototube and the gain of the spectroscopy amplifier. The gain of the photomultiplier tube is quite dependent upon its high voltage. A rule of thumb for most phototubes is that, near the desired operating voltage, a 10% change in the high voltage will change the gain by a factor of 2. The desired high voltage value depends on the phototube being used. Consult your instruction manual for the phototube and select a value in the middle of its normal operating range. Sometimes, the detector will have a stick-on label that lists the percent resolution and the voltage at which that resolution was measured. In that case, use the high voltage value on that label. Lacking those sources to specify the operating voltage, check with the laboratory instructor for the recommended value. The operating voltage will likely fall in the range of +800 to +1300 Volts.
- Set the voltage controls on the 556 High Voltage Power Supply to the operating voltage recommended for the detector. Turn on the POWER switch on the 556.
- Using the MCB Properties menu in the MAESTRO-32 software, set up the acquisition conditions for the Easy-MCA. Select a conversion gain of 1024 channels for the pulse-height range of 0 to +10 Volts. Turn the GATE to Off. For a starting value, the lower level discriminator threshold can be set to about 100 mV (10 channels). Set the upper level discriminator to full scale, or slightly higher. Initially, the preset time limit can be turned off. Your laboratory instructor may have additional recommendations for the set-up of the Easy-MCA.
Gamma-Ray Spectroscopy Using NaI(Tl)
Gamma-Ray Spectroscopy Using NaI(Tl)
3.1.2. Pole Zero Cancellation Adjustment
The NaI(Tl) detector produces a pulse of charge that lasts for about 1 μs at the anode output of the photomultiplier tube. The preamplifier collects that charge on the input capacitance and turns it into a voltage pulse at the preamplifier output. Because the anode pulse has a negative polarity, and the 113 Preamplifier is non-inverting, the voltage pulse at the preamplifier output has a negative polarity. The decay time of the scintillation controls the shape of the leading-edge response of the preamplifier output pulse. For the 250-ns decay time constant of the NaI(Tl) scintillator, the fall time (10% to 90% of the pulse height) on the leading edge of the voltage pulse will be approximately 0.55 μs. Within about 1 μs, the absolute value of the pulse amplitude reaches its maximum excursion. Subsequently, the voltage pulse decays back towards zero Volts with an exponential decay that is characterized by a 50 μs time constant. That decay time constant is nominal, and could lie anywhere in the range of 30 to 80 μs.
In the amplifier, the long exponential decay of the preamplifier must be replaced by the shorter exponential decay selected by the shaping time constant switches on the amplifier. This is the function of the Pole-Zero Cancellation circuit near the input of the amplifier. The adjustment of the Pole-Zero Cancellation to achieve exact replacement will be implemented in the next series of steps. For more information on pole-zero cancellation, consult references 1, 11 and 12.
- Disconnect the Amplifier UNIpolar OUTput from the Easy-MCA and connect it instead to the Channel 1 (CH1) input of the oscilloscope. Select Auto triggering on CH1 in the oscilloscope, a vertical scale of 5 V per major division and 1 μs per major horizontal division. Adjust the vertical position of the baseline in the display to the centerline of the display. Make sure the input impedance of channel 1 is set to 1 MΩ.
- Place the 137 Cs source from the gamma source kit (Eγ = 0.662 MeV) in the stand ~2 cm below the front surface of the NaI(Tl) crystal.
- Observe the signal on the oscilloscope. It should look approximately like the yellow signal in Figure 3.3, except the vertical and horizontal scales will be different. There should be an intense signal at the top of the range of pulse heights, and a distribution of less intense pulses at lower amplitudes. The intense signal at the top of distribution is the full-energy signal from the 662-keV gamma ray. If no signals are observed, try adjusting the oscilloscope triggering and the vertical scale to find the signals.
- Once you are able to display the signals, adjust the amplifier coarse and fine gain controls to make the amplitude of the full-energy signal from the 662-keV gamma rays approximately 10 Volts. It may be useful to change the oscilloscope triggering mode from Auto to Normal at this point.
- Change the oscilloscope horizontal scale to 50 μs per major division.
- Change the vertical scale to 100 mV per major division. Re-adjust the triggering and vertical position so that the baseline before and after the pulses aligns with the main horizontal scale line across the middle of the display.
- Turn the PZ ADJ screwdriver adjustment on the front panel of the 575A Amplifier clockwise and/or counter-clockwise, as needed, to make the observed pulses return to baseline as quickly as possible after each pulse without any undershoot. Consult references 1, 11 and 12 for more guidance.
CAUTION: On some oscilloscopes, the 10-V pulse amplitude may cause an overload of the oscilloscope amplifiers on the more sensitive vertical scales. When this happens the recovery of the trailing edge of the pulse will appear distorted, making it impossible to make a valid PZ adjustment. If this problem is suspected, start with the 5 V per major division scale and increase the vertical scale sensitivity one step at a time. For each increase in vertical sensitivity verify that the shape of the trailing edge differs from the shape on the previous scale setting in proportion to the change in the scale factor. When abrupt distortion is encountered on the more sensitive vertical scale, return to the previous, less sensitive scale to make the PZ adjustment.
It may be useful to try different horizontal scales ranging from 10 μs to 100 μs per major division while making the pole-zero cancellation adjustment.
3.1.3. Adjusting the Gain for Recording Spectra
- Set the oscilloscope vertical scale to 1 Volt per major division, and the horizontal scale to 1 μs per major division. Adjust the triggering and vertical position if needed to observe the signals.
- Reduce the amplifier gain to set the 662-keV pulse height to approximately 2.4 Volts.
Fig. 3.3. Oscilloscope Signal.
Gamma-Ray Spectroscopy Using NaI(Tl)
Note that 100 counts in a channel corresponds to a 10% standard deviation, 10,000 counts yield a 1% standard deviation, and 1 million counts are needed to achieve a 0.1% standard deviation. Consequently, the vertical scatter in the spectrum will begin to appear acceptable when the rather flat continuum at energies below the Compton edge has more than a few hundred counts per channel.
- Plot the spectrum accumulated in step 1 with a linear vertical scale. Mark the photopeak, the Compton edge and the backscatter peak (if discernable) on the spectrum as indicated in Figure 3.4.
- Determine the channel number for the 662-keV peak position.
- After the 137 Cs spectrum has been read from the MCA, save it in a file that you designate for possible later recall. Erase the spectrum, and replace the 137 Cs source with a 60 Co source from the gamma source kit.
- Accumulate the 60 Co spectrum for a period of time long enough for the spectrum to be similar to that in Fig. 3.5.
- Save the 60 Co spectrum for possible later recall and plot the spectrum.
EXERCISES
a. From the 137 Cs and 60 Co spectra determine the photopeak positions and fill in items 1, 2, and 3 in Table 3.1. These peak positions are most conveniently determined with the mouse pointer in the spectra displayed on the computer screen.
b. From items 1, 2, and 3 in Table 3.1, make a plot of energy of the photopeaks vs. channel number. Fig. 3.6 shows this calibration for the data taken from Figs. 3.4 and 3.5. If other calibration sources are available, additional data points can be added to Fig. 3.6. The other entries in Table 3.1 will be filled out in Experiment 3.3.
c. Use the energy calibration feature of the MCA and compare the results with those found in Exercise b.
d. Does the straight line for the energy calibration intercept channel zero at zero energy? If there is a finite zero intercept, what could cause the offset?
Table 3.
Item Energy (MeV) Channel No.
- 0.662-MeV photopeak 0.
- 1.17-MeV photopeak 1.
- 1.33-MeV photopeak 1.
- Compton Edge 137 Cs
- Backscatter 137 Cs
- Compton edge for^
(^60) Co 1.33-MeV gamma ray
- Backscatter^
(^60) Co for 1.33-MeV gamma ray
- Backscatter^
(^60) CO for 1.17-MeV gamma ray
Fig. 3.5. NaI(Tl) Spectrum for 60 Co.
Fig. 3.6. Energy Calibration Curve for NaI(Tl) Detector.
EXPERIMENT 3.2. Energy Analysis of an Unknown Gamma Source
3.2.1 Purpose
This experiment uses the calibrated system of Experiment 3.1 to measure the photopeak energies of an unknown gamma-ray emitter and to identify the unknown isotope.
3.2.2. Procedure
- Erase the 60 Co spectrum from the MCA, but do not change any of the gain calibration settings of the system.
- Obtain an unknown gamma source from the instructor. Accumulate a spectrum for the unknown source for a period of time long enough to clearly identify its photopeak(s). From the calibration curve, determine the energy for each photopeak.
EXERCISE
Use refs. 7 and 8 to identify the unknown isotope.
EXPERIMENT 3.3. Spectrum Analysis of 60 Co and 137 Cs
3.3.1. Purpose
The purpose of this experiment is to explain some of the features, other than the photopeaks, usually present in a pulse-height spectrum. These are the Compton edge, the Compton continuum and the backscatter peak.
3.3.2. Relevant Information
The photopeak is created when the gamma-ray photon interacts in the scintillator via the photoelectric effect. The photon encounters an orbital electron that is tightly bound to a nucleus. The entire energy of the photon is transferred to the electron, causing the electron to escape from the atom. The gamma-ray photon disappears in the process. As the photoelectron travels through the scintillator, it loses its energy by causing additional ionization. At the end of the process, the number of ionized atoms is proportional to the original energy of the photon. As the electrons re-fill the vacancies in the ionized atoms, visible light photons are generated. This is the source of the scintillation, wherein the number of visible photons is proportional to the original energy of the gamma-ray. Consequently, the event populates the photopeak in the spectrum. This peak is often called the full-energy peak, because a two-step interaction, a Compton scattering followed by a photoelectric interaction, also contributes a small number of events to the full-energy peak.
The Compton interaction is a pure, kinematic collision between a gamma-ray photon and what might be termed a free electron in the NaI(Tl) crystal. By this process, the incident gamma-ray photon gives up only part of its energy to the electron as it bounces off the free electron. The recoiling electron loses energy by causing ionization as it travels through the crystal. Thus the number of visible photons in the resulting scintillation is proportional to the recoil energy of the Compton electron. The amount of energy transferred from the gamma-ray photon to the recoiling electron depends on whether the collision is head-on or glancing. For a head-on collision, the gamma ray transfers the maximum allowable energy for the Compton interaction. Although it involves a photon and an electron, the interaction is similar to a billiard-ball collision. The reduced energy of the scattered gamma ray can be determined by solving the energy and momentum conservation equations for the collision. The solution for these equations in terms of the scattered gamma-ray energy can be written as
where
Eγ' is the reduced energy of the scattered gamma-ray, γ', in MeV,
θ is the scattering angle for the direction of γ' relative to the direction of the incident gamma-ray, γ,
Eγ is the energy of the incident gamma-ray, γ, in MeV,
Gamma-Ray Spectroscopy Using NaI(Tl)
EXPERIMENT 3.4. Energy Resolution
3.4.1. Purpose
The purpose of this experiment is to measure the resolution of the NaI(Tl) detector.
3.4.2. Relevant Equations
The resolution of a spectrometer is a measure of its ability to resolve (i.e., separate) two peaks that are fairly close together in energy. Fig. 3.4 shows the gamma spectrum that was plotted for the 137 Cs source. The resolution of the photopeak is calculated from the following equation:
Where δE is the Full Width of the peak at Half of the Maximum count level (FWHM) measured in number of channels, and E is the channel number at the centroid of the photopeak.
In Fig. 3.4 the photopeak is in channel 280 and its FWHM = 32 channels. From Eq. (7), the resolution is calculated to be 11.5%. It is standard practice to specify the quality of the NaI(Tl) detector by stating its measured percent resolution on the 662-keV photopeak from a 137 Cs radioactive source.
EXERCISE
Calculate the resolution of the system from your 137 Cs spectrum. Record this value for later reference.
EXPERIMENT 3.5. Activity of a Gamma Emitter (Relative Method)
3.5.1. Purpose
In Experiments 3.1 and 3.3, procedures were given for determining the energy of an unknown gamma-ray source. Another unknown associated with the gamma-ray source is the activity of the source, which is usually measured in Curies (Ci); 1 Ci = 3.7 x 10 10 disintegrations/second. Most of the sources used in nuclear experiments have activities of the order of microcuries (μCi). The purpose of this experiment is to outline one procedure, called the relative method, by which the activity of a source can be determined.
In using the relative method, it is assumed that the unknown source has already been identified from its gamma-ray energies. For this example, assume that the source has been found to be 137 Cs. Then all that is necessary is to compare the activity of the unknown source to the activity of a standard 137 Cs source that will be supplied by the laboratory instructor. For convenience, call the standard source S1 and the unknown source U1.
3.5.2. Procedure
- Place source S1 ~4 cm from the face of the NaI(Tl) detector (or closer, if necessary to get reasonable statistics). Accumulate a spectrum for a period of live time, selectable on the MCA, long enough to produce a spectrum similar to Fig. 3.4.
- Use the cursor to determine the sum under the photopeak. In the example shown in Fig. 3.4, this would correspond to adding up all counts in channels 240 through 320. Define this sum to be ΣS1. The easiest and most reliable way to measure this sum is to set a Region of Interest (ROI) across the peak (channels 240 through 320, in the example). Once a Region of Interest is set, the MAESTRO-32 software can display the total number of counts in the region of interest (Gross Area) when the mouse pointer is placed in the ROI. This is the sum over all channels in the ROI. If you are having difficulty learning how to set an ROI or to read the Gross Area of the ROI, consult the instruction manual for the software, or ask for guidance from the laboratory instructor.
- Clear (erase) the MCA spectrum. Remove source S1 and replace it with source U1, positioned exactly the same distance from the crystal as S1 was. Accumulate a spectrum for the same period of live time that was used in step 1. Sum the peak as in step
- Call this sum ΣU1.
- Clear the spectrum from the MCA. Remove source U1 and accumulate background counts for the same period of live time that was used in steps 1 and 3 above.
Gamma-Ray Spectroscopy Using NaI(Tl)
Gamma-Ray Spectroscopy Using NaI(Tl)
- Sum the background counts in the same channels that were used for the photopeaks in steps 2 and 3 above. Call the sum Σb.
EXERCISE
a. Solve for the activity of U1 by using the following ratio:
Where AS1 is the activity of the standard source, S1, and A (^) U1 is the calculated activity of the unknown source, U1. NOTE: Since the efficiency of the detector is only energy dependent, the standard and unknown sources do not have to be the same isotope. It is necessary only that their gamma energies be approximately the same (±10%) in order to get a fairly good estimate of the absolute gamma activity of the unknown. However, this relaxation of the comparison requirements may be invalid if one of the sources has a more complicated decay scheme, or if the gamma-ray decay fraction is different for the two isotopes.
b. Check the nominal activity listed on the label attached to the unknown source. How closely does your calculated value match that number?
c. Increasing the detector-to-source distance results in longer counting times to achieve adequate precision in the counting statistics, as a result of the Inverse Square Law (see Expt. 2.5). What is the other way that the source-to-detector distance significantly affects the accuracy of the relative activity measurement?
EXPERIMENT 3.6. Activity of a Gamma Emitter (Absolute Method)
3.6.1. Purpose
The activity of the radioactive source used in Experiment 3.5 can be determined by the absolute method. The purpose of this experiment is to outline the procedure for this method. Here, the source to be measured will be called U1.
3.6.2. Procedure
- Place a source U1 (of unknown activity) approximately 10 cm away from the face of the detector.
- Measure the distance, s, from the middle of the source thickness to the front surface of the NaI(Tl) detector
- Acquire a spectrum long enough to accumulate at least 10,000 counts in the photopeak, and note the elapsed live time, t (^) L.
- Set a region of interest over the photopeak such that all the counts in the peak are included. Record the sum of the counts in the region of interest, ΣU1.
- Clear the spectrum, remove the source, accumulate background for the same live time, and sum the background, Σb, in the same region of interest.
- Use the following formula to calculate the activity of U1. The units in equation (9) are disintegrations per second.
Where
tL is the live time in seconds,
εp is the intrinsic peak efficiency for the gamma-ray energy and detector size used (Fig. 3.7 and ref. 10),
f is the decay fraction of the unknown activity, which is the fraction of the total disintegrations in which the measured gamma ray is emitted (refs. 7 and 8 and Table 3.2)
G = [area of the detector (cm^2 )] / [4πs 2 ], and
s is the source-to-detector distance in cm.
Gamma-Ray Spectroscopy Using NaI(Tl)
I 0 is the intensity before the absorber,
μ is the total mass absorption coefficient in cm 2 /g, and
x is the density thickness in g/cm 2.
In this experiment, the intensity will be measured as the net counts in the photopeak divided by the elapsed live time. Net counts means the background contribution has been subtracted from the total counts in the region of interest (ROI) set across the photopeak. The density thickness is the product of the density in g/cm 3 times the thickness in cm.
The half-value layer (HVL) is defined as the density thickness of the absorbing material that will reduce the intensity to one half of its original value. From Eq. (10):
If I/I 0 = 0.5, and x = HVL, then In(0.5) = –μ(HVL) and hence
In this experiment we will measure μ for lead at 662 keV using the gamma rays from 137 Cs. The accepted value for μ at that energy is 0.105 cm^2 /g. Values for other materials can be found in references 8 and 15.
Background Subtraction : Two different methods can be used for background subtraction. In Experiments 3.5 and 3.6, the background contribution was determined by measuring the counts when the radioactive source was absent. This is a useful scheme if there is some risk that a natural background is producing a peak that overlaps the photopeak of the radioisotope that is the primary subject of the measurement. There is an alternative method that is productive when it is not feasible to remove the source under investigation, or when other gamma-rays from the source generate a Compton continuum under the peak of interest. In this latter scheme, the counts in background regions on either side of the peak are measured, and an interpolation is employed to estimate the background under the peak. The MAESTRO-32 software can perform this latter calculation of the Net Counts in the region of interest. It generally uses the first three channels and the last three channels of the region of interest to calculate the interpolated background and subtract it. Thus, the ROI should be set up so that the first three and the last three channels are in the flat background regions to either side of the peak. Use the Gross Area readout from the ROI when a separate background spectrum will be acquired for background subtraction. Employ the Net Area when it is desirable to subtract the local background interpolated from both sides of the peak in the spectrum. In Experiment 3.7, use the Net Area to subtract the background.
3.7.3. Procedure
- Place the 137 Cs source about 5.0 cm from the NaI(Tl) detector, and accumulate the spectrum for a preset live time that is long enough for the net counts under the 662 keV peak (ΣCs – Σb) to be at least 6000 counts. Determine (ΣCs – Σb) by employing the Net Area feature of the ROI readout. Record the net counts for zero mg/cm^2 in Table 3.3.
- Clear the MCA and insert the minimum thickness of lead from the absorber kit between the source and the detector. Accumulate the spectrum for the same period of live time as in step 1 above. Determine (ΣCs – Σb). Record the absorber thickness and the net counts for that thickness in Table 3.3.
- Repeat the process as the thickness of lead absorber is incremented in steps of no less than 1,000 mg/cm^2 and no more than 1,600 mg/cm^2. It will be necessary to use various combinations of the lead absorbers to achieve an approximately uniform step size. Continue the process until the total thickness of lead exceeds 13,200 mg/cm 2 , or the counting rate has dropped below 1/4 of the initial value with no absorber.
Table 3.3. Data for Mass Absorption Coefficient.
Absorber Absorber Thickness (mg/cm^2 ) ΣCs – Σb 1 0 2 3 4 5 6 7 8
EXERCISES
a. Using semilog graph paper, plot I vs. absorber thickness in mg/cm 2 , where I = (ΣCs – Σb)/(live time). Determine the HVL from this curve, and calculate μ from Eq. (12). How does your value compare with the accepted value of 0.105 cm 2 /g?
b. The μ for aluminum at 662 keV is 0.074 cm^2 /g, and the density of aluminum is 2.70 g/cm^3. What is the half-thickness of aluminum in mg/cm^2 and in cm? Why is the half-thickness of aluminum so much larger than the half-thickness for lead? How does the mass absorption coefficient depend on atomic number?
EXPERIMENT 3.8. Sum Peak Analysis
3.8.1. Explanation and Relevant Equations
Fig. 3.5 shows the two pronounced peaks from a 60 Co radioisotope. Their origin is documented by the 60 Co decay scheme illustrated in Fig. 3.8. Most of the time (>99%), the decay occurs by β–^ emission to the 2.507 MeV excited state of 60 Ni. Subsequent decay to the ground state always occurs by a 1.174 MeV gamma-ray emission to the 1.3325 MeV level, followed almost simultaneously by the 1.3325 MeV gamma emission to the ground state. Experiment 19 will demonstrate that these two events are in coincidence, and have an angular correlation that deviates from an isotopic distribution by only 16%. For the purposes of this experiment we can assume that each of these gamma rays are isotropically distributed. In other words, if γ 1 departs in a particular direction, γ 2 can go in any direction that it wishes. The range of available angles (directions) for each of the two gamma-rays covers the 4π steradians of a sphere centered on the point source. There is a certain probability that γ 2 will go in the same direction as γ 1. If this occurs within the resolving time of the detector, the energies of γ 1 and γ 2 will be summed in the scintillator. Hence a sum peak will show up in the spectrum. Adopting the definitions in Experiment 3.6, the number of counts, Σ 1 , under the γ 1 peak is given by:
where A is the activity of the sample, t (^) L is the live time for the measurement, ε 1 is the intrinsic photopeak efficiency at the γ 1 energy, and f 1 is the fraction of the total decays in which γ 1 is emitted. Similarly, the sum Σ 2 for γ 2 is given by:
Using the basic concepts behind equations (13) and (14), the number of counts in the sum peak, Σs, can be expressed as:
where W(0°) is a term that accounts for the angular correlation function (ref. 16 & 17). For the case of 60 Co, W(0°) ≈ 1.0, f 1 ≈ f 2 ≈ 1.0, and Eq. (15) can be approximately expressed as:
3.8.2. Purpose
This experiment, will confirm that the sum peak for 60 Co has an energy of 2.507 MeV, and that the number of counts in the sum peak is given by Eq. (16).
Gamma-Ray Spectroscopy Using NaI(Tl)
Fig. 3.8. The Decay Scheme of 60 Co.
where Eγ = hv is the original energy of the gamma-ray photon, h is Planck's constant, v is the oscillatory frequency of the photon, and E (^) B is the binding energy of the electron in its host atom. The probability of a photoelectric interaction occurring is dependent on the atomic number of the absorbing material and the energy of the gamma-ray or x-ray photon. Although it is difficult to write an exact analytical expression for this probability, it can be shown that, for low-energy photons
where k is a proportionality constant, Z is the atomic number, and n is usually a number between 4 and 5.
Taking the logarithm of both sides of the equations yields
For this experiment, the gamma-ray energy will be held constant at Eγ = 122 keV, while the atomic number of the absorber is varied. Consequently, the terms within the square brackets in equation (20) will be constant. Thus, plotting the mass absorption coefficient versus the atomic number on log-log graph paper should produce a straight line with a slope equal to n.
3.9.3. Procedure
The setup for this experiment is the same as for Experiment 3.7.
- Place the 20 μCi 57 Co source between 4 and 10 cm from the front surface of the NaI(Tl) detector on the cylindrical center line of the scintillator crystal. Accumulate a spectrum on the MCA for a 100-second live-time. Determine the number of counts in the entire spectrum divided by the live time. If this number is not between the limits of 2000 counts/second and 8,000 counts/second, adjust the source position to bring the counting rate within that range. Obviously, a higher counting rate will shorten the time taken to complete the experiment. But, too high a counting rate will distort the gain of the photomultiplier tube. If you notice a shift in the photopeak position at the higher counting rates, reduce the counting rate to eliminate the peak shift. In no case should the source-to-detector distance be less than 4 cm.
- Once the optimum source position is determined, accumulate a spectrum for a live time period long enough to get reasonable statistics in the 122 keV peak. As in Experiment 3.7, the net counts above background in the peak area should be at least 10, counts.
- Table 3.4 shows the half-value layer thicknesses for the various pure-element foils, along with typical foil thicknesses. Use Table 3.4 to determine the number of foils to insert between the 57 Co source and the NaI(Tl) detector to reduce the counting rate by a factor of 2. For some elements, it will not be possible to achieve a thin enough absorber, or a thick enough absorber to approximate the half-value layer. In those cases choose a thickness that comes as close as feasible to the half-value layer.
- Clear the MCA memory contents. Insert enough aluminum foils between the 57 Co source and the detector to get as close as possible to the half- value layer thickness. Accumulate a spectrum for the same live time as employed in step 1. From the change in the net counts in the 122-keV peak and the known absorber thickness, calculate the mass absorption coefficient of aluminum.
- Repeat steps 2 through 4 for the other thin absorbers, Fe, Cu, Mo, Sn, Ta, and Pb from the absorber kits. NOTE: the counting time might have to be increased as the atomic number of the absorber is increased.
Gamma-Ray Spectroscopy Using NaI(Tl)
Table 3.4. Elemental Foil Parameters
Foil Element
Individual Foil Thickness (^) Density (g/cm 3 )
μ @ 122 keV in cm 2 /g
Half Value Inches cm g/cm 2 Layer in g/cm 2 Al 0.030 0.0762 0.206 2.70 0.154 4. Fe 0.005 0.0127 0.099 7.80 0.272 2. Cu 0.010 0.0254 0.226 8.89 0.321 2. Mo 0.003 0.0076 0.069 9.00 0.685 1. Sn 0.004 0.0102 0.074 7.30 1.020 0. Ta 0.005 0.0127 0.211 16.60 2.592 0. Pb 0.039 0.0986 1.119 11.35 3.376 0.
Gamma-Ray Spectroscopy Using NaI(Tl)
EXERCISES
a. On log-log graph paper, make a plot of μ vs. Z from your experimental data. (Alternatively, plot the ln(μ) versus the ln(Z) in an Excel spreadsheet). Draw a straight line through the data points and calculate the value of “n” in equations (19) and (20) from the slope of that straight line. How do your results compare to the theory?
b. How does the inability to match the half-value layer thickness affect the accuracy of the measurement?
EXPERIMENT 3.10. The Linear Gate in Gamma-Ray Spectroscopy
3.10.1. Purpose
The purpose of this experiment is to learn how to set up the analog and logic signal alignment when employing a linear gate to restrict the categories of nuclear events that are analyzed. The demonstration will involve limiting the analyzed events to only those appearing in the photopeak.
3.10.2. System Set-up
- Begin with the setup and energy calibration used in any of the prior experiments from 3.1 through 3.9. The system will be altered according to Figure 3.9.
- Turn off the NIM Bin Power Supply, and insert the 427A Delay Amplifier, the 551 Timing SCA, the 426 Linear Gate, and the 416A Gate and Delay Generator in the NIM Bin. Turn the NIM Bin Power on again.
- Place a BNC Tee on the INPUT to the 427A Delay Amplifier. Connect one arm of the Tee to the 575A Amplifier UNIpolar OUTput using a short 93-Ω coaxial cable. Connect the other arm of the Tee to the DC INPUT of the 551 Timing SCA via a short 93-Ω cable.
- Using a short 93-Ω cable, connect the OUTPUT of the 427A to the 426 analog INPUT.
- Connect the POSitive OUTput of the 551 to the POSitive INPUT of the 416A with a short 93-Ω cable.
- Using a short 93-Ω cable, connect the POSitive DELAYED OUTPUT of the 416A to the ENABLE input of the 426 Linear Gate.
- Connect the analog OUTPUT of the 426 Linear Gate to the analog INPUT of the Easy-MCA.
- Ensure that the rear-panel switches on the 551 are both set to the INTernal position.
- On the front panel of the 551, set the μsec switch to the 0.1 – 1.1 μsec range, and turn the DELAY dial to its minimum value.
- On the 551, set the INT/NOR/WIN switch to the NORmal mode.
- On the 551, set the LOWER LEVEL dial to 50 mV (5/1000). Set the UPPER LEVEL dial to 10 V (1000/1000).
- On the 416A, set the DELAY dial to its minimum value, and the delay range switch below it to 1.1 μsec.
Fig. 3.9. Block Diagram of the Electronics for Gamma-Ray Spectrometry with a Linear Gate Interposed.
Gamma-Ray Spectroscopy Using NaI(Tl)
- Save a record of the full spectrum for your report. Record the UPPER and LOWER LEVEL dial settings for this spectrum
- Erase the spectrum, and start a new spectral acquisition while raising the LOWER LEVEL threshold on the 551 SCA. Increase the LOWER LEVEL setting until all energies below the photopeak are eliminated from the spectrum. This may require repeated erasing and restarting of the acquisitions as the threshold is adjusted.
- Reduce the UPPER LEVEL threshold on the 551 SCA until all pulse heights above the photopeak are eliminated.
- Save a record of the spectrum limited to the photopeak for your report. Record the UPPER and LOWER LEVEL dial settings for this spectrum.
EXERCISE
a. With the additional modules inserted, there are at least two factors that may have changed the energy calibration of the spectrum in this experiment compared to the previous experiments. What are those factors? It will not be necessary to re-calibrate the horizontal (energy) scale, as long as the features of the spectrum are readily identifiable for the purposes of Experiment 3.10.
3.10.6. Replacing the 426 Linear Gate with the MCA Linear Gate
Currently, external linear gates are rarely used in nuclear measurements, because virtually all commercially-available MCAs incorporate a linear gate. It turns out that it is much easier, and more convenient, to design a high-quality linear gate into the MCA. The previous set of measurements demonstrated what is happening in the linear gate. The next set of measurements shows how to meet the needs of the linear gate imbedded in the MCA.
Because the goal of the MCA is to measure the maximum height of the analog pulse, it automatically closes its linear gate after the peak amplitude of the pulse has been captured. Consequently, the linear gate logic pulse does not need to last more than a few tenths of a microsecond past the peak amplitude of the analog pulse. Different MCAs have diverse requirements for when the linear gate logic pulse must begin relative to start of the analog pulse. Some designs require that the logic pulse arrive slightly before the start of the analog pulse. Others simply require that the logic pulse be present at the time the peak amplitude of the analog pulse is captured.
In the following set of measurements, the alignment requirements of the Easy-MCA gating function will be investigated.
3.10.7 Procedure
- Starting with the set-up in experiment 3.10.5, remove the 426 Linear Gate from the system.
- Connect the 427A Delay Amplifier OUTPUT directly to the Easy-MCA analog INPUT.
- Connect the 416A POSitive DELAYED OUTput to the GATE input of the Easy-MCA.
- Turn the 416A gate WIDTH screwdriver adjustment to its maximum clockwise limit (4 μs).
- Via the MAESTRO-32 software, check the ADC properties, and ensure that the Gate function is turned off.
- Acquire a spectrum and confirm that the full spectrum, including the Compton continuum and the photopeak are being acquired. Save a copy of this spectrum for your report. NOTE: If the dc offset of the baseline between pulses has changed significantly at the MCA INPUT, it may be necessary to optimize the lower level threshold accordingly on the MCA. If the Percent Dead Time is abnormally high, even when the radioactive source is removed, raise the lower level threshold until the dead time is less than 1%. Otherwise, do not worry about this threshold for the purposes of the remainder of this experiment.
- Using the MAESTRO-32 software, select the Coincidence Gate function. This allows acquisition of a spectrum for only those analog pulses that are accompanied by a logic pulse at the GATE input of the Easy-MCA.
- Acquire a spectrum. If the settings on the 551 have not been changed from the prior experiment, only the 137 Cs photopeak should be acquired, with all events eliminated above and below that peak. Save a copy of that spectrum for your report.
- Increase the DELAY dial setting on either the 551 or the 416A until the MCA no longer acquires a spectrum. Reduce the DELAY dial setting until the MCA just reliably acquires a spectrum. Record the new DELAY dial settings.
- Reduce the WIDTH screwdriver adjustment (counterclockwise) on the 416A until the MCA will no longer acquire a spectrum. Turn the WIDTH adjustment until the MCA reliably acquires a spectrum.
- Reduce the LOWER LEVEL setting on the 551 to 100 mV (10/1000) and increase the UPPER LEVEL setting to 10 V (1000/1000).
- Repeat steps 9 and 10.
- Display the analog signal from the 427A on channel 1 of the oscilloscope. Trigger the oscilloscope on the positive pulses with the triggering threshold set just above the noise on the baseline.
- Observe the POSitive DELAYED OUTput pulse from the 416A on channel 2 of the oscilloscope.
EXERCISE
b. Make a sketch of the analog and logic pulses showing their time relationship.
If the timing requirements of the MCA linear gate are not well known, the above procedure can be employed to determine those requirements. Alternatively, it is usually safe to adjust the gating logic pulse to span the entire analog pulse.
References
- G. F. Knoll, Radiation Detection and Measurement, John Wiiley and Sons, New York (1979).
- J. B. Birks, The theory and Practice of Scintillation Counting, Pergammon Press, Oxford (1964).
- S. M. Shafroth, Ed., Scintillation Spectroscopy of Gamma Radiation, Gordon and Breach, London (1967).
- K. Siegbahn, Ed., Alpha, Beta and Gamma Spectroscopy, North Holland Publishing Co., Amsterdam (1968).
- P. Quittner, Gamma Ray Spectroscopy, Halsted Press, New York (1972).
- W. Mann and S. Garfinkel, Radioactivity and its Measurement, Van Nostrand-Reinhold, New York (1966).
- C. M. Lederer and V. S., Shirley, Eds., Table of Isotopes, 7th Edition, John Wiley and Sons, Inc., New York (1978).
- Radiological Health Handbook, U.S. Dept. of Health, Education,and Welfare, PHS Publ. 2016. Available from National Technical Information Service, U.S. Dept. Of Commerce, Springfield, Virginia.
- 14th Scintillation and Semiconductor Counter Symposium, IEEE Trans. Nucl. Sci. NS-22(1) (1975).
- R. L. Heath, Scintillation Spectrometry, Gamma-Ray Spectrum Catalog, 1 and 2, Report No. IDO-16880. Available from the National Technical Information Center, U. S. Dept. of Commerce, Springfield, Virginia. Electronic copy available at http://www.inl.gov/gammaray/catalogs/catalogs.shtml.
- Ron Jenkins, R. W. Gould, and Dale Gedcke, Quantitative X-ray Spectrometry, Marcel Dekker, Inc., New York, 1981.
- Introduction to Amplifiers at http://www.ortec-online.com/Solutions/modular-electronic-instruments.aspx.
- Introduction to CAMAC ADCs and Memories at http://www.ortec-online.com/Solutions/modular-electronic-instruments.aspx.
- Dale Gedcke, Application Note AN63, Simply Managing Dead Time Errors in Gamma-Ray Spectrometry, http://www.ortec- online.com/Solutions/modular-electronic-instruments.aspx.
- J. H. Hubbell+ and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest, NISTIR 5632, 1996, http://www.nist.gov/physlab/data/xraycoef/index.cfm.
- A. C. Melissinos, Experiments in Modern Physics, Academic Press, New York (1966).
- R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York (1955).
Gamma-Ray Spectroscopy Using NaI(Tl)
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