6805: 1094 Activities 13

Write your name and answers on this sheet and hand it in at the end.

Postulating neutrinos

Goal: Understand the puzzle that led Pauli to postulate the existence of neutrinos.

1. Understanding decay spectra
   1. Why do nuclei undergo beta decay?
      
      
      
      
      
   2. Look at the first page of the "Beta Decay 3" slides. What exactly is plotted in the spectrum on the first page?
      
      
      
      
      
   3. From looking at the spectrum, determine the energy of the nuclear transition corresponding to the decay that is shown.
      
      
      
      
      
2. Symmetries and conservation laws
   1. Why do we believe in energy conservation as a fundamental principle of physics?
      
      
      
      
      
      
      
   2. Which fundamental symmetries and conservation laws are relevant to understand beta-decay spectra?
      
      
      
      
      
      
   3. Pauli postulated the existence of neutrinos to solve a puzzle with beta decay. Describe this puzzle in your own words, and explain how exactly it is solved by introducing neutrinos as new particles. (Hint: what should a beta decay spectrum look like if only an electron (or positron) were emitted in the process?)
      
      
      
      
      
      
   4. Nuclear beta decays are said to happen either as a "Fermi" transition or as a "Gamow-Teller" transition. What exactly is the difference, and could there be three (or more) types of transitions? (Hint: explain your answer based on conservation laws.)
      
      
      
      
      
      
      

Neutrino cross sections and detection

Goal: Understand quantitatively what it means that neutrinos are weakly-interacting particles.

1. Fundamental forces in nature
   1. Which fundamental forces are (currently) known in physics?
      
      
      
      
      
      
   2. For each of the following particles, list which of the above fundamental forces they are subject to: proton, neutron, pion, electron.
      
      
      
      
      
      
   3. What about the neutrino?
      
      
      
      
      
   4. Pauli originally used the name "neutron" for the neutrino, before it got renamed by Fermi. Obviously, they are both electrically neutral, but in what way is the neutron different from the neutrino -- and why?
      
      
      
      
      
      
      
      
2. Neutrino interactions and cross sections
   1. Look at the first page of the "Neutrinos 1" slides. At the center you can see reaction relations for neutrino capture processes. Give the corresponding beta decay relations and explain the occurrence of neutrinos and antineutrinos. What is the relevant symmetry to relate the reactions?
      
      
      
      
      
      
      
      
   2. Can you transform the formula for the capture on protons in the same way? Explain your answer.
      
      
      
      
      
      
   3. The table on the slide shows some typical cross sections for neutrino capture reactions on protons. How would you judge if these are big or small? (Think about other reactions to compare them to.)
   
   
   
   
   
   
   
   4. What exactly does the "mean free path" describe? Explain/derive the formula given on the slide. (Hint: recall the meaning of a "cross section" and manipulate the form of the equation.)
   
   
   
   
   
   
   
   
   
3. Neutrino detectors
   1. Why do nuclear reactors provide a large neutrino flux?
      
      
      
      
      
      
   2. What is Cherenkov radiation?
      
      
      
      
      
      
   3. Why are neutrino detectors typically built deep underground?
      
      
      
      
      
      
   4. What is "heavy water," and why is it advantageous to use it for neutrino detection?