Compton Scattering

Introduction

In 1923 Compton discovered that when a beam of x-rays of well-defined wavelength is scattered through an angle by sending the radiation through a metallic foil, the scattered radiation contains a component of a well-defined wavelength which is longer than the original wavelength. This phenomenon is called the Compton effect.

Equipment

Procedure

1. Set up the equipment according to the diagram. High voltage needs to be applied to the detector. Turn on the power to the high voltage supply. After waiting a minute for the tube to warm up properly, flip the switch labeled HV. The signal from the detector is fed to an amplifier before it can be used by the multichannel scaler board in the computer.

2. Turn on the hand-held Geiger counter and place it near you. Whenever working with radiation you must be careful to be aware of where the sources are located. Sweep the area with the counter so that you become familiar with its function. When you remove sources from their lead housings, use the counter again. Turn off the Geiger counter only after you have returned the sources to their housings (but DO remember to turn it off then so the batteries do not wear out too fast!).

3. The software can be started by selecting Start -> Programs -> Genie 2000 -> Gamma Acquisition & Analysis . To communicate with the data acquisition card, select File -> Open Datasource; click on Source: Detector, select GAMMARAY and click Open. You are now ready to start acquiring gamma ray counts (on the Y axis) as a function of gamma ray energy (on the X axis); this is a “Pulse-Height Analyzer” (PHA) spectrum. Explore the various software options to identify the gamma ray peak from the radioactive source, and tally the total number of counts. Note that if you save a spectrum using File -> Save As… , the saved file is in a proprietary format (.CNF) that can only be reopened with the Canberra software. To produce a simple ascii dump of the channel contents, follow the procedure: Analyze -> E. Reporting… -> Template Name: Datadmp.tpl , then Execute . The data file produced is in:

 C:\Genie2k\Repfiles\   

(look at the date and time of files there) and can be opened with any spreadsheet program. An Excel template that contains a macro and instructions for parsing the data can be found here.

4. Record the complete spectrum of the 137Cs source and a few other sources in PHA mode, using the known energies of the peaks to calibrate the energy scale. Note that the range of the spectra on the screen is a function of the photomultiplier (PMT) voltage, and if the PMT voltage is not appropriate, the relevant peaks may be off scale. Note also that from one lab session to the next, if the high voltage is different, the peaks will be in different locations. A PMT voltage of about 1 kV is a good place to start. Some relevant energies for major peaks:

  • 60Co: 1.173, 1.332 MeV

  • 57Co: 0.014 MeV

  • 22Na: 0.511, 1.275 MeV

  • 137Cs: 0.662 MeV

  • 133Ba: 0.080, 0.276, 0.302 MeV

5. Put the large 137Cs source in its holder, insert a scattering rod and measure the spectrum as a function of the angle of the source. From this, verify that Compton scattering occurs. Determine the Compton wavelength shift and compare to the theoretical one. Determine the functional dependence of  l’-l on angle, i.e., plot l’-l vs (1-cosθ). Compare the slope to the known value for the mass of an electron.

                        6. It is also possible to measure the differential cross section by making measurements of the yield by integrating under the peaks in the PHA spectrum. Calculate the differential cross sections and compare them to the classical Thomson cross section and to the fully quantum mechanical Klein-Nishina cross section.

References

           Any modern or atomic physics textbook such as Eisberg (Fundamentals of Modern Physics) will discuss the interaction of radiation with matter and the fundamentals of Compton scattering. See also:

Compton, Am. J. Phys. 29, 817 (1961).

Bartlett, Am. J. Phys. 32, 120 (1964).

Burns and R. Singhal, Am. J. Phys. 46, 646 (1978).