CINCH NucWik

Developed By
Department of Chemistry
Radiochemistry
University of Helsinki

Students get familiar with gamma spectrometry using a single channel analyzer (SCA) as a pulse height analyzer. First, the students get introduced to basic operation principles of SCA. Then, it will be demonstrated, how to determine half-life of a radionuclide by performing multiple gamma measurements over several half-lives of the radionuclide, and then draw a semilogarithmic graph with count rate results as a function of time.

The studied radionuclide in this exercise is ¹³⁷Cs, having gamma radiation energy of 662 keV and half-life of 30 years (decay scheme is presented in the figure below). The counting area of the single channel analyzer adjusted to be corresponding the area of the ¹³⁷Cs photopeak by measuring the spectrum of ¹³⁷Cs. The activity of an unknown sample will be measured by utilizing the determined measuring setting. In addition, we practice the use of a simple radionuclide generator, ¹³⁷Cs/^137mBa, and determine the half-life of ^137mBa by measuring the gamma radiation of the eluted solution.

1. The operating principle of a single channel analyzer
A simple pulse height analyzer is a single channel analyzer. It consists of an amplifier, energy analyzer and pulse counter. The sorting of the pulses to be analyzed is done with two threshold discriminators. The lower threshold discriminator limits the size of the pulses to be analyzed so that only pulses that are bigger than a certain limit, that is, gamma quanta exceeding a certain minimum energy, E, will be registered. The maximum size of the pulses to be registered is controlled with the window settings (width of the energy window, ΔE) of the analyzer. Thus, the size of the pulses to be analyzed is controlled so that only pulses having the size between the voltage values determined by the threshold discriminators, are registered (see the figure below). The whole energy area of interest can be analyzed by keeping the width of the window constant and by changing (sweeping) the value of the lower threshold discriminator. This procedure can be done with some single channel analyzers also automatically.

An example of the use of a pulse height analyzer. The hatched area represents the observed (registered, counted part) gamma spectrum.

The relation between pulse height and gamma energy can be obtained by calibrating the energy area of the analyzer by using calibration standards. In a calibration standard, proportions of gamma energies and gamma quanta of all the radioactive decay of the calibration standard are known accurately. The gamma spectrum of a gamma emitter with only one gamma quantum, such as ¹³⁷Cs, consists of a so-called photopeak and Compton continuum in the lower channels. The photopeak is approximately of the Gaussian shape. The location of the tip of the peak represents the energy of the ¹³⁷Cs gamma quantum (662 keV) and the area of the peak represents the intensity, that is, the activity of the gamma radiation (see the next figure).

The gamma spectrum of ¹³⁷Cs determined with a Na(I) crystal detector.

2. Determination of half-life
Half-life, for which a symbol t1/2 is used, is the time during which the amount of the decaying nuclei (or activity) is decreased by half. This is described by the equation

𝐴= 𝐴₀ ∙ 2^-t/t½

Activity can be calculated at any given time, when the half-life (t1/2), original activity (A₀) and passed time (t) are known.

The graph of the equation 𝐴= (𝑡) is an exponential function. By taking the logarithm of it, we get the equation 𝑙𝑛𝐴 = − ln2/t½ ∙ 𝑡 + 𝑙𝑛𝐴₀
the graph of which lnA = f(t) is a line with a slope of ln2/t½ and the intersection with y-axis of lnA₀.

The activity of the sample is usually measured multiple times in a row for several half-lives when determining the half-life. Obtained activities/counting rates are plotted in semi-logarithmic scale as a function of time. The best possible fit is fitted through the data points. Half-life can be determined by simply taking the time from x-axis at which the activity has decreased by half (see the following figure).

Determining the half-life of a nuclide graphically in semilogarithmic scale. R_n on y axis denotes net count rate.

If the half-life is very short, the measuring time can be a big portion of the half-time. In such a case, the activity of the sample can change radically between the start and stop of the measurement. However, this will not cause error in the half-life if the subsequent measuring intervals are as long, provided that the activity is associated in the same moment in time (for example, on the halfway of the measurement).

3. Calibration of the equipment and measuring the spectrum of ¹³⁷Cs

First we will determine the gamma spectrum of ¹³⁷Cs with a single channel analyzer, having Na(I) scintillation crystal as a detector. Other components of the measurement system are analyzer/amplifier and power supply/pulse counter (next figure). The resolution of the equipment for 662 keV energy is measured from the determined spectrum. In addition, measurement area covering the photopeak of ¹³⁷Cs (see the previous third figure) will be selected with which the counting rates of the standard sample (known ¹³⁷Cs activity) and unknown sample will be determined. The activity and the statistical limit of error of the unknown sample will be calculated with the measured counting rates.

The block diagram of single channel analyzer equipment.

a) Calibration of the energy scale

• Connect the equipment as in the previous figure
• Connect the current to the power supply counter and amplifier-analyzer and adjust the high voltage (e.g. to 1000 V, to the appropriate value stated by the high voltage source manufacturer)
• Place the “integral/window” switch to “window” position. In “integral” selection all pulses above the noise level can be counted, while in “window” selection only pulses between selected voltage range are registered
• Adjust the potentiometer to value 320 (that is, the lower threshold of the energy window will be adjusted to 640 keV because the whole scale 1000 of the potentiometer will represent 2000 keV after this adjustment)
• Adjust the width of the energy window to 2%. That means that the width of the energy window is 40 keV (thus energy window 640-680 keV is good for the 662 keV peak of ¹³⁷Cs)
• Set the counter on for “continuous measurement” in time setting and set the source to the measurement station of the Na(I) crystal
• Adjust the amplification of the analyzer with fine gain and coarse gain knobs so that the counting rate in the counter is at its maximum (662 keV peak in the window)

→ The energy scale of the analyzer is now calibrated to correspond 2000 keV.

• Remember to write down the settings and the information about the equipment!

b) Determination of the ¹³⁷Cs spectrum

• Measure the ¹³⁷Cs standard sample by keeping the energy width (ΔE) constant (2%) and increasing the lower threshold (called as Baseline-E) of the window
• Plot the measured counts as a function of voltage (energy spectrum)
• Choose the values of the lower threshold and width of the window so that the photopeak of ¹³⁷Cs will be in the window
• Calculate the resolution (R) for the 662 keV peak with the equation
  

𝑅=ΔE/E (%),
where ΔE is the full width at half maximum and E is the energy corresponding to the center of the peak (see the illustration below)

Determination of the energy resolution of a gamma spectrometer.

c) Determination of the activity of an unknown ¹³⁷Cs sample

• Measure the counting rates of a standard sample with known activity, an unknown sample and background with the settings obtained in parts a) and b) in the same geometry
• Calculate the activity and the standard deflection of activity (σA) using the counting rates

4. Determination of half-life
In the second part of the work the half-life of ^137mBa will be determined. ^137mBa is the daughter nucleus of ¹³⁷Cs that decays by emitting a 662 keV gamma quantum (this was shown in the first figure). ^137mBa is obtained from a ¹³⁷Cs/^137mBa generator. The long-lived parent nuclide ¹³⁷Cs is adsorbed onto the generator and it produces by decaying continuously its short-lived daughter nuclide ^137mBa. The latter can be then chemically separated (eluted) with a suitable solvent that does not elute ¹³⁷Cs. In the ¹³⁷Cs/^137mBa generator, ¹³⁷Cs is adsorbed on a sodium cobalt hexacyanoferrate ion-exchanger, which is a very effective adsorbent material for cesium. The ^137mBa that is produced in the ion exchanger can be eluted with 0.1 M NaCl-solution (e.g., 0.9% NaCl in 0.04 M HCl) from the column. The ^137mBa sample that is eluted from the generator is measured at constant intervals to obtain multiple data points altogether for about an hour, until there is no more barium in the sample, but only possibly ¹³⁷Cs as an impurity. Background measurement is also performed. The half-life of ^137mBa is determined graphically from the measured net counting rates of ^137mBa. In addition, the mean error (σRn) and the relative error (σRn/Rn) of the counting rates of ^137mBa will be calculated at the start and end of the first measurement series.

• Elute the sample from the ¹³⁷Cs/^137mBa generator into a small tube (Eppendorf or other type)
• Start immediately the measurement of time and take the sample into measurement (for example, in a Styrofoam rack), measurement time in the beginning can be 30 s
• Write count rate value from this and later measurements to the formsingle_channel_analyser_exercise_form_for_students.pdf, which is part of the working report
• Repeat the measurement at constant intervals (first every minute)
• When the counting rates are decreasing lengthen the measuring time for 100 s and repeat every 2 minutes
• Finally measure background for at least 5 min (can be done also at the start of the work)
• Calculate the net counting rates of ^137mBa and mark them in semilogarithmic paper as a function of time (center of the measurement). Plot a line through the data points
• Determine the half-life of ^137mBa graphically according to the work instructions
• Calculate the mean uncertainty (σRn) and relative uncertainty (σRn/Rn) of the net counting rates of ^137mBa in the start and end of the first measurement series
• How does the relative uncertainty change and why?

During the work, lab coat, safety glasses, and gloves are used for personal protection. Radioactive samples will be saved and later disposed by the Supervisor.

• Single channel analyzer

• Eppendorf tubes or similar small plastic tubes suitable for single channel analyzer
• a Styrofoam rack or similar

• Cs-137/Ba-137m Isotope Generator

The acceptable work report should contain the following sections

• brief description of the performed exercise; motivation, instrumental setup and settings
• calculations requested in the previous sections 1-4
• graph containing net count rates of ^137mBa in semilogarithmic scale as a function of time
• filled exercise form (from the 4th part of the exercise)
• brief conclusions from the results, including discussion of changing uncertainty in measured count rates

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