PHYSICS ADVANCED LABORATORY I COMPTON SCATTERING Spring 2002
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1 PHYSICS ADVANCED LABORATORY I COMPTON SCATTERING Spring 00 Purposes: Demonstrate the phenomena associated with Compton scattering and the Klein-Nishina formula. Determine the mass of the electron. Background: Melissinos pp (scintillation detectors), 6-30 (scattering) and 5-65 (Compton effect and Klein-Nishina formula). Also see Brehm and Mullin pp for a discussion of the Compton effect. Skills: Protocol: Operation of scintillation detector, multi-channel analyzer, and use of radioactive sources. You will first need to determine efficiency of a NaI scintillation detector as a function of energy. After that exercise, you will measure Compton scattered photon yield and energy as a function of scattering angle and compare results with Compton formula. You should read over each part of the lab procedure before beginning work. You will need to determine the solid angles subtended by various components as noted below. This requires careful measurements of the appropriate elements of the apparatus geometry, which in turn requires that you have a thorough understanding of which geometric measurements are important in order for you to complete the experiment. You should be particularly careful in following all of the safety precautions for using radioactive sources. Always wash your hands immediately after leaving the laboratory. Part I: Scintillation detector energy and efficiency calibration. 1. Measure the distances from the central target/source location in the Compton apparatus to the front of the NaI detector housing. Measure the size of the aperture in the lead collimator for the detector. From these values, determine the solid angle subtended by the collimator aperture. Table I. Basic information on nuclides used in this experiment. Nuclide Half-life γ-ray energy (MeV) Photon emission probability (per decay) 133 Ba 10.5 y Cs y Co 5.71 y
2 . Obtain the following calibration sources: 60 Co, 133 Ba, and 137 Cs. The most intense γ-lines for these nuclides are shown in the table below. When detected with the NaI detector, there will also be a line due to annihilation radiation at MeV. 3. Based on the information sheets for these radioactive sources, determine the absolute photon flux for each of the γ-rays emitted by the sources, and determine the absolute flux entering the NaI detector through the collimating aperture. 4. Place the 60 Co radioactive calibration source in the source position. Check that the photomultiplier high voltage supply reads approximately volts. Turn on the high voltage to the scintillation detector. Observe the pulses from the detector on the oscilloscope, noting their shape and height. 5. Acquire data for this calibration source using the multi-channel analyzer (MCA) and the software on the PC connected to the MCA. Adjust the gain of the photomultiplier amplifier until the uppermost gamma line is just below the upper edge of the MCA spectrum. 6. Clear the collected spectrum and take data until you have more than 1000 counts in the most intense γ-ray peak for this particular source. Record the number of counts and the data collection time, correcting for deadtime as necessary. 7. Find and record the centroid and full width at half maximum for the peak(s). 8. Repeat steps 6 and 7 for each radioactive source. 9. Use the centroids of the peaks and the accepted values for the energies of these peaks given in the table above to determine the energy calibration for the detector assuming the calibration is linear. Plot your values and the fit obtained. 10. Using the information from steps 1, 3 and 6, determine the photon detection efficiency as a function of energy for the detector, assuming the photon flux for each source is emitted isotropically into the full 4π solid angle. Plot your values on log-log scales and determine a best-fit formula to an appropriate functional form. Part II. Compton scattering of photons. In order to be most efficient, you should complete the measurements in this section during the same laboratory period. Do not move any of the lead shielding. 1. Make appropriate measurements to determine the solid angle of the emission aperture in the lead source holder for the Compton scattering apparatus. (Note: the source will be positioned within the holder; you will need additional measurements of the source to determine the emission geometry.)
3 . Establish an energy calibration for the detector system using the same procedure performed in Part I. 3. Obtain the multi-mci 137 Cs source from its storage place. Carefully but quickly measure the dimensions of the source holder so that you can use them with the measurements in step 1 to obtain the source geometry. Do not point the source towards any part of your body (or anyone else's body either!). 4. Carefully place the source in the lead source holder of the Compton scattering apparatus. 5. Determine the solid angle subtended by the aluminum target cylinder with respect to the source when both source and target are in installed. Which solid angle limits the photon flux-- the emission solid angle or the solid angle subtended by the aluminum target? 6. From the current date and the information sheet for the 137 Cs source, you should be able to determine the activity of the source to sufficient precision that, knowing the appropriate solid angle, you will know the photon flux incident on the aluminum target. 7. Remove the aluminum target cylinder. Slide the source carriage to the 0-degree position. Begin taking data so that you have more than 1000 counts in the 137 Cs 0.66 MeV γ-ray peak. This information can provide you with a check of your solid angle measurements, source intensity, and efficiency calibration. 8. Return the aluminum target cylinder to the target position and rotate the cylinder such that the adjusting screw is perpendicular to a line connecting the source axis and the target axis. This will minimize the contribution of photons scattering from the adjusting screw. 9. Beginning with a scattering angle of 10 degrees, accumulate pulse height data with the MCA for a period sufficient to obtain more than 1000 counts in the Compton-scattered (and thus energy-shifted) 137 Cs γ-ray line. (Before each run, rotate the cylinder as in step 9.) Determine the centroid, FWHM, and area of the γ-ray peak, recording all uncertainties. Also record any information needed to make live time corrections. Following each data run, make sure that you record each spectrum so that re-analysis can be performed if necessary. 10. After the data run in step 10, remove the cylinder and take a background run for the same live time as in step 10. This spectrum should eventually be subtracted from the spectrum obtained in step 10 to remove MCA events that are not associated with scattering from the aluminum cylinder. 11. Repeat steps 9-11 at 10-degree intervals up to the maximum scattering angle you can reach without removing any shielding. The results are most efficiently
4 recorded using a table similar to Table 6.3 in Melissinos, though we do not need to record a discriminator setting. 1. When finished with data taking, return the radioactive source to storage. Turn off the high voltage to the NaI detector. Turn off the power to the electronics rack. Transfer your data runs to a diskette for any subsequent re-analysis. 13. Follow the procedures outlined in Melissinos to accomplish the following: (a) Using a graph similar to Fig in Melissinos, determine that the data obtained are consistent with the Compton relationship (b) Using your data, determine a value for the mass of the electron by performing a weighted fit to the equation in (a) to your data. [You should, as always, also determine an uncertainty for this value.] (c) Use your peak areas, peak energies, detector efficiency and solid angle measurements to determine the differential cross section for Compton scattering. (Do not use the Melissinos approach of using all counts in the spectrum.) Compare your measurements to the Thomson and Klein-Nishina dσ d = ( 1 cos θ) E E' mc dσ e 1+ cos θ = dω hom 4πε T son 0mc dσ = Ω [ 1+ ] Ω Klein Nishina d T hom son ) ) (1 cos θ )[ 1+ )] differential cross section formulae. The Klein-Nishima and Thomson values for these cross sections are given in Table II for the 66 kev line used here. 1
5 Table II. COM PTON SCATTERING CROSS SECTION E g (M ev )= γ= r(e) (fm )=.818 Cross section Angle (1-cos) Thom son Klein-Nishim (degrees) (fm ^) (fm ^)
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