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Experiment X Emission Spectrum of ¹³⁷Cs

Purpose

The purpose of this and the following experiment is to introduce nuclear measurement techniques, and to investigate some of the properties of nuclear radiation. For this experiment, the energy spectrum of ¹³⁷Cs is measured using a Single Channel Analyzer (SCA).

Introduction

The naturally occurring ¹³³Cs is a stable nucleus. However, an isotope of cesium, ¹³⁷Cs, which is a common fragment of the fission process of ²³⁵₉₂U, is unstable due to an excess of neutrons. This isotope has a half-life of 30.17 years and it decays via beta^- (b^-) to ¹³⁷Ba, i.e.,

¹³⁷

₅₅

¹³⁷

₅₆

⁰

_-1

Often the daughter nucleus, ¹³⁷₅₆Ba*, is in an excited state and when it decays to the ground state it emits a gamma-ray (g-ray) with an energy of 662 keV. (The symbol * indicates that the nucleus is in the excited state.) In addition to the beta particle, an anti-neutrino,n-bar, is also emitted. However, we will not be concerned with this particle for this experiment.

¹³⁷

₅₆

¹³⁷

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g-rays are highly energetic electromagnetic waves. Electromagnetic waves are called photons. The energy of a photon is given by E = hf = hc/l where h (=6.63×10^-34 J·s) is the Planck's constant, f is the frequency of the wave and l is the wavelength.

The g-ray emitted as a result of ¹³⁷Cs decay can induced a number of reactions as it passes through matter.

There are three types of interactions that the photon can undergo.

1. Compton effect (Figure 10.1) - In this process, a photon is scattered off from a stationary electron (or nucleus). The scattered photon loses some energy and thus has a lower frequency than the incident photon. The amount of energy lost depends on the angle, f. The higher the angle, the greater the energy lost. If l is the wavelength of the incident photon, then the wavelength of the scattered photon is given by

where the factor

is called the Compton wavelength and m_o is the rest mass of the electron. When f = 180°, the photon is back-scattered, i.e., it returns in the direction it was traveling.

2. Photoelectric effect - A photon may knock an electron completely out of an atom and in the process it completely disappears. All the energy of the photon is transferred to the electron.

3. Pair production (Figure 10.2) - A photon is converted into an electron and a positron. (A positron has the same rest mass (511 keV) as an electron but has a positive charge, +e.) In pair production matter in the form of an electron and a positron is created from pure energy according to Einstein's energy equation, E = mc².

When an electron is ejected from an orbit at low energy level, it leaves behind an empty state. This permits another electron from a higher energy level to make a transition to the lower level. When this occurs, the electron gives off an x-ray photon.

For this experiment our objective is to identify as many of the above processes as possible using a single channel (energy) analyzer. The photons are detected using a scintillation counter.

The scintillation counter is one of the most commonly used detectors of g and aradiation. A NaI crystal containing a small amount of thallium is mounted on a photomultiplier tube and this assembly is encased in a light tight covering. When a gray or charged particle enters the NaI crystal, collisions with the electrons in the crystal create excited atomic states near the thallium impurities. When these excited states decay, a pulse of visible and near ultraviolet light is emitted from the crystal. The light pulse strikes the "photocathode" of the photomultiplier tube causing electrons to be emitted by the photoelectric effect. The electrons from the photocathode are accelerated by an electric field to a series of plates. At each plate a colliding electron knocks out several more electrons. The resulting "cascade" is a multiplication of the electron current. The "gain", or multiplication factor, of the photomultiplier tube is about 10. The electrical pulse from the photomultiplier is fed to a Single Channel Analyzer which decides whether the height of the pulse, i.e., the energy of the original g or aray, is within the chosen range. If so, the pulse is further amplified, then fed to a "scaler" which counts the number of pulses over a set interval of time. It should be noted that the scintillation system has an overall efficiency of about 5% for grays (meaning that about 5 grays are counted for each 100 striking the NaI crystal). The efficiency depends upon the energy of the radiation, the size of the crystal, and other parameters.

Hook up and calibration procedure

NOTE: Make sure that all power switches are off, and the high voltage (H.V.) controls are set to zero before you connect or remove the cables.

1. With the power off connect the scaler/timer and the NaI probe to the (HV connections on the rear panel of the Amplifier/Analyzer using the signal and HighVoltage cables. (See Figure 10.3).

2. Turn on the scaler and the Analyzer, and set the scaler high voltage control to 1400 volts.

3. Set the analyzer mode switch to "window" and the baselineE (or lower level discriminator LLD) to 65.2% (6.52 turns).

4. Set the window width or DE to 2% and place the ¹³⁷Cs source directly under the detector in the near bottom slot of the holder.

5. Very slowly increase the fine gain control, watching for a sharp rise and fall in the count rate meter reading. If no such marked peak of count rate is observed as the fine gain control is increased over its entire range, increase the coarse gain by one step. Repeat the slow increase of the fine gain. As soon as the sharp peak in count rate is observed, adjust the fine gain to the point at which maximum count rate is obtained.

The single channel analyzer is a Pulse Height Analyzer (PHA) for one channel. The Baseline is a "lower level discriminator" (LLD) which only passes electrical pulses which are greater that the LLD. With the mode switch on "Window", the windowDE control acts as an "upper level discriminator" (ULD). The ULD stops all pulses with heights greater than the ULD. Thus only pulses with heights between the LLD and ULD are amplified and counted. On the other hand if the mode switch is on "integral" all pulses above the LLD are counted.

As ¹³⁷Cs has a known gray peak at 662 keV (0.662 MeV), we use this to calibrate the SCA. With the baseline set to 65.2%, and the "window width" set to 2%, we count all grays with energies between 652 keV to 672 keV. So we have 1% range = 10 keV, with a full scale calibration of 1 MeV (1,000 keV = 100%).

Once the calibration as outlined above is completed DO NOT adjust the gain setting.

6. Turn the computer on and run "Quattro Pro". Load the template "Energy spectrum.wb3" into memory.

7. Lower the Base-line on the SCA to 0% and count for a 20 second interval. Record your data on the Quattro Pro spreadsheet. Reset the counter then raise the Base-line to 2% and repeat the 20 second count. Repeat the count by raising the Base-line 2% each time until 100% of the analyzer's range is reached. Don't forget to record your reading for each of the 20 second interval on your spreadsheet.

8. Follow the on-line instructions and create an xy plot with number of counts on the ordinate and energy in keV on the abscissa (x-axis).

Analysis

Identify the 32 keV x-ray peak from the ¹³⁷Ba daughter, the 75 keV x-ray peak from the Pb shield, the Compton scatter region and the 662 keV gamma-ray peak from the ¹³⁷Cs. Use Figure 10.4 as your guide.

Calculate the full-width-at-half-maximum (FWHM) of the gamma-ray peak in units of keV. Divide the FWHM by the peak energy (662 keV) and express as a percentage. Compare your data to Figure 10.4 and comment. (FWHM is a measure of how well a line is resolved.)

Answer the following questions.

1. Based on the principle of energy conservation would you expect to see pair-production from the 662 keV gray?

2. Explain why there are very few counts for energies greater than 700 keV.

3. Explain why there is a broad range of energy resulting from the Compton scattering. Use Equation 10.1.

4. Why are there more counts for the x-ray lines than the g-ray line?