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Experiment7_High-Resolution-Gamma-Ray-Spectroscopy_v071415OLD.pdf

ORTEC ® Experiment 7

High-Resolution Gamma-Ray Spectroscopy

Equipment Required

Purpose

Gamma-ray energies will be measured with a High-Purity Germanium (HPGe) detector and research-grade electronics. The principles behind the response characteristics of the detector are explained. The high-resolution measurement results are contrasted with those obtainable from the NaI(Tl) (sodium iodide) scintillation detector previously explored in Experiment 3.

Introduction

Most of the experiments in this series are written for use with lower-cost detectors and electronic modules. However, in this experiment, which illustrates the superior resolution capabilities of the high-performance HPGe detector systems, research-grade signal processing modules have been incorporated to fully utilize the detector’s capabilities.

Many colleges, universities, and national research laboratories have Nuclear Spectroscopy Centers that employ high- resolution gamma-ray spectrometry to investigate decay schemes of radioisotopes. Given the plethora of isotopes, opportunities continue to arise in exploring the details of the decay schemes. Improved energy resolution allows additional lines to be found in spectra. Occasionally, a doublet is discovered, whereas earlier measurements with NaI(Tl) detectors indicated only a single energy line.

High-Purity Germanium (HPGe) detectors are also extensively used to detect and monitor radioactivity in the environment, and to detect contraband radioisotopes and fissionable material. It is the excellent energy resolution of the HPGe detector that enables ultra-low detection limits in these applications.

• GEM10-70/CFG-SV-70/DWR-30 Coaxial Germanium Detector System (Includes detector, preamplifier, cryostat, liquid-nitrogen dewar, and 12-ft. cable pack); typical specifications: 10% relative efficiency, 1.75 keV resolution at 1.33 MeV, 41:1 peak-to-Compton ratio.

• 659 5 kV Detector Bias Supply

• 672 Spectroscopy Amplifier

• 480 Pulser

• Four each C-24-4 RG-62A/U 93-Ω Coaxial Cables with BNC Plugs, 4-ft. (1.2-cm) length

• C-29 BNC Tee Connector

• 4001A/4002D NIM Bin and Power Supply

• EASY-MCA-8K System including a USB cable, and MAESTRO software (other ORTEC MCAs may be substituted)

• TDS3032C Oscilloscope with bandwidth ≥150 MHz

• GF-057-M-20* 20 µCi 57Co (272-d half life). A license is required for this source.

• GF-137-M-20* 20 µCi 137Cs (30-y half life). A license is required for this source.

• GF-060-M-10* 10 µCi 60Co (5.3-y half life). A license is required for this source.

• GF-228-D-10* 10 µCi 228Th (698-d half life). A license is required for this source.

• Personal Computer with a USB port and Windows operating system

• Small, flat-blade screwdriver for tuning screwdriver- adjustable controls

• OPTIONAL FOR EXPERIMENT 7.4

• POSK22-10* 10 µCi 22Na thin source for observing positron annihilation peak broadening. A license is required for this source.

• Foil-AL-30 10 ea ½-inch (1.27-cm) dia. Aluminum foils, 0.030-inch (0.076 cm) thick

• Foil-NI-10 10 ea ½-inch (1.27-cm) dia. Nickel foils, 0.010-inch (0.025 cm) thick

*Sources are available direct from supplier. See the ORTEC website at www.ortec-online.com/Service-Support/Library/Experiments- Radioactive-Source-Suppliers.aspx

Decay schemes for isotopes are included in refs. 10 and 12. More recent information on certain nuclei can be found in ORTEC’s Nuclide Navigator Master Library software package (Model C53-B32). An up-to-date on-line resource for such information is sponsored by:

National Nuclear Data Center Building 197D Brookhaven National Laboratory Upton, NY 11973-5000 Phone: (631) 344-2902 Fax: (631) 344-2806 Email: [email protected] Internet: http://www.nndc.bnl.gov

In Experiment 3, gamma-ray spectroscopy with NaI(Tl) detectors was studied. The typical energy resolution that can be obtained with NaI(Tl) is circa 7% for the 0.662 MeV 137Cs gamma-ray line. For NaI(Tl) detectors, the resolution is a strong function of energy. The resolution is primarily controlled by the statistical fluctuation of the number of photoelectrons produced at the photocathode surface in the photomultiplier tube. Table 7.1 illustrates some typical resolutions for a NaI(Tl) detector as a function of the gamma-ray energy. Note that it is conventional to express the resolution in percent for NaI(Tl) detectors.

Where

E is the energy of the peak,

δE is the FWHM of the peak in energy units, and

k is a proportionality constant characteristic of the particular detector.

The development of germanium detectors in the late 1960s completely revolutionized gamma spectroscopy. Fig. 7.1 illustrates the striking contrast in results obtained with the two common types of gamma-ray detectors. Compared to NaI(Tl), there is a factor of 30 improvement in the full-width at half-maximum (FWHM) resolution. As a result of this improved resolution, many nuclear energy levels that could not be resolved with NaI(Tl) detectors are easily identified by using HPGe detectors.

Concurrently, the development of lithium- drifted silicon detectors [Si(Li)] with drastically- improved energy resolution revolutionized x-ray spectrometry. These Si(Li) devices are studied in Experiment 8.

The purpose of this experiment is to explore some of the properties of HPGe detector systems. This experiment deals only with the

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Experiment 7 High-Resolution Gamma-Ray Spectroscopy

Fig. 7.1. A Portion of a 60Co Spectrum, Illustrating the Energy Resolutions and Peak-to-Compton Ratios for a Coaxial HPGe Detector Compared to a NaI(Tl)

Detector.

Table 7.1. Typical Resolutions of a Na(Tl) Detector for Various Gamma-Ray Energies.

Isotope Gamma Energy (keV) Resolution (%)

166Ho 81 16.19

177Lu 113 13.5

133Te 159 11.5

177Lu 208 10.9

203Hg 279 10.14

51Cr 320 9.89

198Au 411 9.21

7Be 478 8.62

137Cs 662 7.7

54Mn 835 7.26

207Bi 1067 6.56

65Zn 1114 6.29

22Na 1277 6.07

88Y 1850 5.45

The information for this table was taken from IRE Trans. Nucl. Sci. NS-3(4), 57 (Nov. 1956). “Instrinsic Scintillator Resolution,” by G. G. Kelley et al., quoting results from F. K. McGowan, et.al.

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practical aspects of making measurements with these detectors. To understand the properties of these detector systems, the following brief review of gamma-ray interactions and pair-production processes is included.

Gamma-Ray Interactions in HPGe Detectors

Fig. 7.2 shows graphs for the three important gamma-ray interactions in both germanium and silicon. The absorption cross sections for germanium are of interest in this experiment. The corresponding values for silicon will be used in Experiment 8.

When a gamma-ray photon enters a detector, it must produce a recoil electron by one of three processes before it is recorded as an event: (1) the photoelectric effect, (2) the Compton effect, or (3) pair production.

In the photoelectric process, the gamma-ray or x-ray photon transfers all of its energy to an electron in the detector. Consequently, the photon vanishes. The recoiling electron loses energy by causing ionization of the detector material, resulting in a trail of electron-hole pairs. The bias voltage applied across the detector sweeps the electrons and holes to opposite electrodes, where the charge is collected to form the preamplifier pulse. For the photoelectric process, the total charge in the output pulse from the detector is proportional to the energy of the gamma-ray or x-ray that produced the interaction. These events will show up as full-energy photopeaks in the spectrum.

In the Compton process, the photon is scattered from an electron that is essentially not bound to an atom. Because the scattering angle can vary from 0 to 180 degrees, there is a range of energies that can be transferred from the photon to the recoiling electron. The scattered photon survives and carries off the remainder of the energy. It is the recoiling electron that loses energy by ionizing the detector material. Consequently, the charge collected from the detector will yield a distribution of pulse amplitudes at the preamplifier output up to some maximum pulse height. This maximum pulse height corresponds to the Compton edge in the energy spectrum, as explained in Experiment 3. There is a statistical probability that each Compton scattering event has an approximately equal chance to produce a pulse with any height up to this maximum. Thus, Compton events will provide a well-distributed low-energy continuum in the spectrum.

In large detectors with high peak-to-Compton ratios, some Compton events also contribute to the full-energy peak, when the scattered photons undergo one or more additional interactions, and finally terminate in complete absorption by the photoelectric interaction.

The pair-production process can also provide a total absorption of the gamma-ray energy. The gamma-ray photon enters the detector and creates an electron-positron pair. All the energy of the initial photon is transferred to the electron- positron pair. Consequently, the initial photon disappears in the process. From the law of conservation of mass and energy, it follows that the initial gamma-ray must have an energy of at least 1.022 MeV, because it takes that much energy to create both the negative and positive electrons. The net mass that is produced is two electron masses, and this satisfies the law of conversion of energy, E, into mass, m, i.e., E = mc2. If the initial photon has an energy in excess of 1.022 MeV, that excess energy is transferred into the recoil energies of the positron and electron. Both the positron and the electron lose energy by causing ionization of the atoms in the detector. Once the positron is moving slowly enough, it can be captured by a free electron, and the two can combine. In this annihilation of the positron with an electron, both particles disappear, and their rest mass energies are converted into two photons travelling in opposite directions, with each photon having an energy of 511 keV. Note that the sum of the energies of these two annihilation gamma rays is 1.022 MeV.

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Experiment 7 High-Resolution Gamma-Ray Spectroscopy

Fig. 7.2. Relative Probability (Cross Sections in Barns/Atom) for Each of the Three Types of Gamma-Ray Interactions in Ge and Si as a

Function of Energy.

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The optional experiment 7.4 explores this process of positron annihilation when the

positron is obtained from β+ decay of a 22Na radioactive source.

Fig. 7.3 illustrates what happens in the detector in the pair-production process. In Fig. 7.3 the e– (ordinary electron) will produce a pulse whose magnitude is proportional to the energy of e–, i.e., Ee–. The positron, e

+, will produce a pulse proportional to its energy, Ee+ . Since these two pulses are produced simultaneously, the output pulse from the detector would be the sum of the two pulses. When the

positron annihilates in the detector, the annihilation radiation γ1 and γ2, will be produced. In Fig. 7.3, both γ1 and γ2 are shown escaping from the boundaries of the detector without making any further interactions. (Note: Eγ1= Eγ2 = 0.511 MeV). Thus, in this example, an energy of exactly 1.022 MeV escapes from the detector, and is subtracted from the total energy that entered the

detector. It is possible for only one, either γ1 or γ2, to make a photoelectric interaction in the detector while the other escapes. In such cases, the total energy absorbed is 0.511 MeV less than the original incident gamma-ray energy. It is also possible for both gammas to make photoelectric interactions without escaping, with all the original energy being left in the detector. Therefore, in the spectrum being measured, there will be three peaks for each incident gamma-ray having an energy well in excess of 1.022 MeV. These peaks, labeled Full-Energy Peak, Single-Escape Peak, and Double- Escape Peak, will be separated by 0.511 MeV increments. Fig. 7.4 shows a typical spectrum that would be obtained for an incident gamma-ray energy of 2.511 MeV. The lower end of the spectrum that shows the Compton distribution has not been included. The Single-Escape Peak occurs at 2.00 MeV (Eγ – 0.511 MeV), and the Double-Escape Peak occurs at 1.49 MeV

(Eγ – 1.022 MeV). Of course, the full-energy peak represents those events for which there was a combination of pair production and photoelectric effect in which all the energy was absorbed in the detector.

Now refer again to Fig. 7.2, and specifically to the curves for the interaction in germanium. The absorption cross section, plotted in the y direction, is a measure of the relative probability that an interaction will occur in a thin slab of the germanium detector. These probabilities of relative interactions, for the most part, determine the shape of the observed spectrum. For example, a photon with an energy of 100 keV has an absorption cross section of approximately 55 barns/atom for the photoelectric process. The corresponding Compton cross section is about 18 barns/atom. There is no pair production. These two cross sections are in the approximate ratio of 3:1, at 100 keV, implying that there are 3 times as many photoelectric interactions as Compton interactions. Fig. 7.5 shows the shape of a spectrum that could be expected for measurement of the 100 keV energy events.

The shape of the spectrum changes drastically from 100 keV to 1 MeV. Fig. 7.6 shows the gamma spectrum that could be expected for the 1 MeV gammas incident on a thin HPGe detector. From Fig. 7.2, the ratio of Compton cross section to photoelectric cross section is approximately 90; so, in Fig. 7.6, the sum of the counts in the

Compton distribution is Σc = 90,000 and the sum of the counts in the photopeak is Σpp = 1000.

Experiment 7 High-Resolution Gamma-Ray Spectroscopy

Fig. 7.3. The Process of Pair Production in a Ge Detector.

Fig. 7.4. Typical Spectrum for an Incident Gamma-Ray Energy of 2.511 MeV, Showing the Full-Energy, Single-

Escape, and Double-Escape Peaks.

Fig. 7.5. A Typical Spectrum Expected for a 100 keV Photon in

a Thin HPGe Detector.

Fig. 7.6. A Typical Spectrum Expected for a 1 MeV Photon in a Thin HPGe Detector.

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Experiment 7 High-Resolution Gamma-Ray Spectroscopy

The relative efficiencies for HPGe and Si(Li) detectors can also be approximated from Fig. 7.2. For example, at

Eγ = 400 keV the photoelectric cross section for germanium is 6 barns/atom, and that for silicon is approximately 0.1 barn/atom. This is a ratio of 60:1, and indicates that there will be 60 times as many counts under the photopeak for a germanium detector as for a silicon detector at 400 keV, assuming that the detectors are the same size. This ratio of detector efficiencies reflects the fact that the photoelectric cross section varies as Z5, where Z is the atomic number of the absorbing material. The atomic number of Ge is 32 and for Si it is 14. The ratio of these two numbers raised to the 5th power is 62.2, which agrees remarkably well with the above cross-section ratios. Higher atomic numbers offer greater photopeak efficiencies.

Fig. 7.2 shows that the cross-section for photoelectric absorption drops rapidly with increasing energy. From 300 keV to 3 MeV, the Compton-scattering cross-section dominates. The higher the energy, the more deeply the gamma-ray can penetrate the detector before it interacts with an electron. Consequently, the efficiency can be improved by increasing the dimensions of the Ge detector along the original direction of the photon, and in directions perpendicular to the path of the photon. According to the Beer-Lambert law for absorption (Experiments 2 and 3), a larger detector increases the probability that the photon will interact in the detector. If the initial interaction is a Compton scattering, the larger detector dimensions improve the chances that the scattered photon will be stopped by a photoelectric absorption before it leaves the detector volume, placing the event in the full-energy peak. Consequently, a larger detector improves the ratio of counts in the full-energy peak to the counts in the Compton continuum. This improves detection limits for weak peaks that would be obscured by statistical fluctuations in the Compton continuum from higher-energy gamma rays.

Detector Structure

Basically, a HPGe detector is a very large semiconductor diode, with a reverse bias voltage applied to its two electrodes to deplete virtually all free charge carriers from the bulk of the detector. Small detectors can be obtained in the planar geometry that is similar to the structure of the silicon charged-particle detectors studied in experiments 4, 5 and 6. Figure 7.7 illustrates the planar geometry. The detector is a cylinder of HPGe with electrodes applied to its two circular ends.

Significantly larger detectors benefit from using the coaxial geometry depicted in Fig. 7.8. The P-type HPGe (GEM) is the type of detector used in this experiment. The detector is composed of a large cylinder of high-purity germanium. A hole is drilled from one end, along the centerline of the cylinder. One electrode is applied to the outer surface of the cylinder and to the closed end. The other electrode is applied to the inside surface of the central hole. The surface of the end from which the hole is drilled (open end) is passivated to reduce surface leakage currents between the two electrodes. The coaxial detector shape is mounted in the end cap of the cryostat, with the cylindrical axis of the detector diode aligned coaxially with the centerline of the end cap. The closed end of the detector is located a few millimeters behind the circular surface of the end cap.

The detector and the first amplifying stage of the preamplifier are operated near the boiling temperature of liquid nitrogen (77°K) to reduce noise. Consequently, the detector and the first stage of the preamplifier are mounted in a vacuum cryostat. The cryostat establishes operation at the desired low temperature via a copper cooling rod dipped in the liquid nitrogen contained in the associated dewar. Operation at the cryogenic temperature dramatically reduces the leakage current in the HPGe detector and also diminishes thermally generated noise in the FET input stage of the preamplifier. The preamplifier feedback capacitor and feedback resistor are also cooled to reduce their noise contribution. As will be seen next, decreasing these sources of noise improves the energy resolution.

Fig. 7.7. The Structure of a 16 mm Diameter, 10 mm Deep Planar Detector.

Fig. 7.8. Configurations of Coaxial Germanium Detectors

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Energy Resolution

The energy resolution of a HPGe detector is described by equation (2).

where

ΔEtotal is the full width at half maximum amplitude (FWHM) of the gamma-ray peak at energy E in the spectrum. ΔEnoise is the contribution from the noise caused by the detector leakage current and the preamplifier. It is most readily measured as the FWHM of a pulser peak artificially introduced into the spectrum by injecting a pulser signal into the input of the preamplifier. The noise contribution is independent of the gamma-ray energy. But, it does depend on the shaping time constant of the spectroscopy amplifier. If the shaping time constant is too small or too large, the noise contribution will be higher than the optimum. Check the detector data sheet for the optimum shaping time constant to minimize the noise. The optimum will likely lie in the range of 3 to 6 microseconds.

ΔEion describes the variation in the number of electron-hole pairs generated as a result of ionization statistics. It depends on the average energy required to create an electron-hole pair (i.e., є = 2.95 eV), the energy of the gamma-ray, E, and the Fano factor, F. Note that the same units of energy must be used throughout equation (2). The Fano factor accounts for the fact that the ionization process lies somewhere between completely independent random ionization events at one extreme (F = 1), and an absolutely deterministic conversion of energy into electron-hole pairs at the other extreme (F = 0). For HPGe a Fano factor, F ≈ 0.1, indicates the process is closer to the latter than the former condition.

ΔEincomplete accounts for the variation in the ability to collect all of the electron-hole pairs that are created by the ionization process. Primarily, this applies to electron-hole pairs that recombine before they can be collected, or charge carriers that fall into traps while drifting to their respective electrode. Additionally, there is potential for a ballistic deficit effect when the shaping time constant is too small. For large coaxial HPGe detectors the charge collection time can vary from 50 to 700 ns, depending on the position at which the charge was created. If the amplifier shaping time constant is not large compared to these collection times, the pulse height will show additional fluctuations caused by random variations in the charge collection times. If the incomplete charge collection term is ignored in equation (2), spectral resolution measurements may lead to an inflated value for the implied Fano factor.

Maximum Counting Rate Deduced from the Percent Dead Time

Because gamma rays arrive at the detector with random spacing in time, the width of the pulse from the amplifier limits the counting rate that can be processed without distortion. Probably the most efficient way to ensure that the maximum counting rate is not exceeded is to adjust the source-to-detector distance so that the percent dead time observed on the Multichannel Analyzer is less than 63%. The dominant dead time in the gamma-ray spectrometer specified for this experiment is a paralyzable (a.k.a., extending) dead time (ref. 11, 14 and 15). For a paralyzable dead time, the maximum analyzed throughput is accomplished when the dead time is 63%. Operation at counting rates that yield slightly less than 63% dead time will provide optimum performance.

Further Information on HPGe Detectors

Consult references 11, 13, 14 and 15 for further details on HPGe detectors.

Experiment 7 High-Resolution Gamma-Ray Spectroscopy

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Experiment 7 High-Resolution Gamma-Ray Spectroscopy

EXPERIMENT 7.1. Energy Resolution with a HPGe Detector

CAUTION

The instructor will provide the HPGe detector and instructions for its use. Before attempting to use the detector, carefully read the instruction manual. This is a very expensive detector system and must be handled very carefully.

Procedure

1. Turn off power to the 4001A/4002D NIM Bin and the 659 5-kV Detector Bias Supply. Turn the 0–5 kV dial on the 659 to its minimum value (full counter-clockwise).

2. Install the 659, 480 and 672 in the 4001A/4002D NIM Bin and interconnect the modules as shown in Fig. 7.9. The preamplifier is mounted as an integral part of the HPGe detector and the preamplifier input is internally connected to the detector in the cryostat.

3. Using the cable bundle supplied with the detector, connect the preamplifier power to the PREAMP power connector on the rear panel of the 672 Spectroscopy Amplifier. Connect the preamplifier signal output to the NORMal INPUT of the 672 Amplifier. Connect the Test Input of the preamplifier to the ATTENuated OUTPUT of the 480 Pulser. Connect the Bias Voltage input on the preamplifier to the 0–5 kV OUTPUT on the rear panel of the 659 bias supply. Connect the BIAS SHUTDOWN on the rear of the 659 to the Auto HV Shutdown connector on the preamplifier.

4. Connect the UNIPOLAR OUTPUT of the 672 Amplifier to a Tee on the Channel-1 Input on the oscilloscope. Connect the other arm of that Tee to the analog signal INPUT on the EASY-MCA-8K.

5. Connect the BUSY output of the 672 to the BUSY input on the EASY-MCA-8K. Connect the PUR (Pile-Up Rejector) output of the 672 to the PUR input of the EASY-MCA-8K.

6. Ensure that the EASY-MCA-8K is connected to the supporting computer via the USB cable, and that MAESTRO is installed on the computer.

7. Set the module controls as follows:

• 672 Amplifier: GAUSSIAN UNI SHAPING, AUTO PZ, 6-µs SHAPING TIME, NORMal (+) INPUT, AUTO BLR RATE.

• 480 Pulser: POSitive polarity, OFF.

• 659 0–5 kV Detector Bias Supply: Leave at zero until all other connections have been made. The GEM HPGe detector specified for this experiment requires a positive bias voltage. But, consult the instructions for the detector to determine both the bias polarity and the bias voltage required for the detector. Check the polarity indicated on the 659 front-panel POS/NEG LEDs when the bin power is turned on. Make sure the indicated polarity is correct for the detector. Apply the correct bias voltage with the correct polarity when ready to operate the detector.

8. Turn on the Bin power. Turn on the Detector Bias Supply, and adjust the voltage to the value required for the detector.

9. Via MAESTRO, select a Conversion Gain of 8192 channels full scale for the MCA digital resolution. Set the Lower Level Discriminator to circa 80 channels and the Upper Level Discriminator to 8192 channels. Check that the Gating function is turned off.

Fig. 7.9. System Block Diagram for the Gamma-ray Spectrometer.

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10. Place the 60Co source approximately 1 cm from the face of the detector. Adjust the gain of the 672 Amplifier so that the 1.333 MeV gamma has an amplitude of +8 V at the amplifier unipolar output. The two lines for 1.173 and 1.333 MeV should be quite easily seen on the oscilloscope. Lock the FINE GAIN dial on the amplifier to discourage accidental changes in the established energy calibration. The recommended settings in step 7 are correct for the specified GEM detector. But, a different detector model may have the opposite polarity for the preamplifier output signal. If that is the case, change the amplifier input polarity switch so that the UNIPOLAR OUTPUT has a positive polarity.

11. Check that the percent dead time when acquiring a spectrum on the MCA is <63%. Adjust the source-to-detector distance to meet this condition, if necessary.

12. To make the PZ adjustment, switch the BLR RATE switch to the PZ position for the duration of this adjustment. The 672 Amplifier controls have been set up to utilize the Automatic Pole-Zero Adjustment feature. To observe its operation, turn the oscilloscope to the most sensitive vertical scale. Select a horizontal scale of 50 microseconds per major division. Push the LIMIT pushbutton on the 672 front panel near the UNIPOLAR OUTPUT. On the oscilloscope, observe that this pushbutton limits the pulse amplitude and prevents distortions that would otherwise be caused by overloading the oscilloscope input.

13. While continuing to depress the limit switch, briefly press the AUTO PZ pushbutton on the front panel of the 672. The red BUSY LED should light up, and you should be able to track the automatic adjustment of the PZ on the oscilloscope. Confirm that the PZ is correctly adjusted. You can opt for a manual adjustment by moving the PZ switch from AUTO to MANual, and adjusting the screwdriver control as learned in previous experiments. But, the AUTO PZ adjustment will probably be more accurate. After the PZ adjustment has been accomplished, return the BLR RATE switch to the AUTO position. For an explanation of the BLR (baseline restorer) function, see ref. 14, and the specification sheet or instruction manual for the 672 Amplifier.

14. Make an acquisition on the MCA for a long enough period of time to create a well-defined spectrum as illustrated in Fig. 7.10.

15. Save a copy of the 60Co spectrum on the internal hard drive for potential later use.

16. From the positions of the two photopeaks, make a calibration curve of energy (y direction) vs. channel number (x direction) and determine the keV per channel.

17. Remove the 60Co source and turn on the 480 Pulser. Using the ATTENUATOR switches and PULSE HEIGHT dial, place the pulser peak approximately mid way between the two 60Co peaks in the spectrum. Acquire enough counts to achieve a well-defined pulser peak in the spectrum. Save this spectrum on the internal hard disk for potential later reference.

EXERCISES

a. What is the FWHM resolution in keV for the two photopeaks? How does this compare in value with the detector’s resolution specifications? What is the FWHM resolution of the Pulser peak?

b. Presume that ΔEincomplete = 0 in equation (2). Using your measured resolutions on the two peaks from 60Co and the

Pulser peak, calculate the effective value of the Fano factor, F, in equation (2b). How does your value compare to the referenced value of F = 0.1? Why does your result differ from the referenced value?

c. Using your measured value for the Fano factor and the Pulser resolution, calculate the values for ΔEtotal from equation (2), to fill in the blank column in Table 7.2.

d. Make a plot of the data in Table 7.2 on linear graph paper.

Experiment 7 High-Resolution Gamma-Ray Spectroscopy

Fig. 7.10. Locating the Peaks and Compton Edges in the 60Co Spectrum with the HPGe Gamma-ray

Spectrometer.

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Experiment 7 High-Resolution Gamma-Ray Spectroscopy

e. From the 60Co spectrum, determine the energies of the Compton edges associated with the two gamma-ray energies. How do these compare with the values that were calculated from the formula used in Experiment 3?

EXPERIMENT 7.2. Photopeak Efficiency and Peak-to-Compton Ratio

Compared to NaI(Tl) detectors, the energy resolution with HPGe detectors is better by a factor of 30 or more. This dramatic …