Read:
- Textbook section 8.2
- Bigelow, Chapter 5 (the handout).
Use the program NUCRAD to learn about interactions of radiation with matter. This program has now been installed on the PC’s in Rooms 221 and the Modern Physics Lab. Do the exercises below and hand in the answers with needed graphs. No formal narrative report is required.
Goals:
- Learn about the photoelectric effect, Compton edge.
- Learn about energy loss mechanisms for electrons.
- Learn about mechanisms for energy loss for other particles.
1) Computer exercise:
What is the probability that a 0.662 MeV gamma ray from Cs^137 undergoes photoelectric absorption
- in 1 cm of lead
- in 1 cm of silicon
- in 1 cm of aluminium ?
What are the attenuation coefficients (sometimes called mean free paths) of a 0.662 MeV gamma ray in
- Pb
- Si
- Al ?
2) Computer exercise:
You wish to measure the 0.847 MeV gamma ray from Co^56 with a NaI detector; however, the higher energy gamma rays are an unwanted background, especially the one at 1.238 MeV.
Find the optimum thickness of the NaI crystal. (Hint: use a figure of merit based on # 0.847’s absorbed/# 1.238’s absorbed).
3) Computer exercise on electron backscattering:
Since electrons go through many scatterings over their path, there is a significant probability for an electron to escape from an absorber through the face that it entered. This effect can be important for electron detectors, electron microscopy, chip manufacturing etc. Study electron backscattering from two materials: Al, Pb.
- For each material, determine how electron backscattering changes as a function of the material thickness for a fixed energy.
- Find electron backscattering trends as a function of energy
- Find electron backscattering trends as a function of material (does A or Z of the material matter ?)
Plot your results as a function of thickness, energy to justify your answers.
4) Computer exercise: Transmitted energy for protons:
- Calculate the “stopping power” for 1 MeV, 10 MeV, 100 MeV protons in Al using a graph or table of stopping power from NIST. Estimate the energy lost by protons passing through 50 microns of Al and compare with results from NUCRAD. Discuss the differences in the energy spectra of the transmitted protons for the three different energies.
- Pick one of the energies above and repeat for a much larger thickness (e.g. 200 microns). How does the spectrum, most probable transmitted energy and average transmitted energy change ?
5) Calculation/computer exercise:
- Calculation: [Starting from a simple diagram for Compton scattering, verify equation (5.18), the equation for the location of the Compton edge.] (N.B. We will measure this spectrum with our NaI crystal and phototube in the upcoming Nuclear Spectroscopy Lab).
- Simulation and Calculation: Find the location of the Compton edge analytically and by simulation for (a) 0.511 MeV, (b) 1.28 MeV and (c) 1.78 MeV lines using the NaI detector simulation.
Is the Compton edge useful for energy calibrations ?
6) Computer exercise:
- Consider the response spectrum for 1.78 MeV gamma rays 10 cm from the detector. What processes contribute to the features in the spectrum ?
- Examine 0.662 MeV and 2.5 MeV gamma ray spectra. Explain the features and why these differ.
7) Try running simulations for muons and protons at 100 MeV.
- Qualitatively, how do the results differ from those for electrons and photons ? Focus on absorption, transmission and multiple scattering.
- Can you explain the differences in terms of physical processes for muon and proton interactions ?
Notes:
- Mean free path is 1/mu where I(t)=I_0 e^{-mu t}
- Stopping power S = – dE/dx where E is the energy of the particle and x is the thickness traversed.
- Mass Stopping power is 1/rho (dE/dx)
The CUPS programs can also be downloaded from http://www.phys.hawaii.edu/~teb/installcups.exe Comments: (make a directory called “cups”. You have to run the patch that will allow the programs to run on Pentium PC’s. This patch is included in the self-extracting package).
Last modified October 1, 2018
Tom Browder