Physics 422: Nuclear Physics
Homework III
Due Feb. 7
1. Program the Bethe-Bloch formula stopping power formula. Your program should take
as input the medium properties (density, atomic mass and number) and ion properties
(energy, charge, and mass) and output the energy loss per distance traveled by the ion
in the medium. Use it to calculate the energy loss per distance (MeV/micron) for the
following: (a) 5 MeV alpha in Nickel, (b) 5 MeV alpha in air, (c) 5 MeV electron in Nickel,
and (d) 10 GeV proton in Nickel.
2. (F-H 6-4) At the Los Alamos Meson facility a beam of π + ’s with laboratory kinetic
energy of 200 MeV hit a 50 cm long liquid hydrogen (proton) target. What fraction of
the pions undergo π + + p scattering? (Consult Fig. 5.29 for the cross section; look up the
density of liquid hydrogen.)
3. (F-H 6-11) An electron of 500 MeV kinetic energy strikes a lead nucleus at rest. (a)
What is the maximum possible momentum transfer?, (b) What is the recoil energy of
the lead nucleus when the electron transfers the maximum momentum?, (c) Treating the
problem relativistically, show that the electron in this case can be treated as a massless
particle. Specifically, how does the numerical value for the maximum momentum transfer
change when the electron mass is neglected?
4. (F-H 6-13 - modified) Assume the charge probability distribution (i.e. charge density)
of a particle is given by: ρ(r) = N e−αr , (r = |~r|). (a) Compute the normalization constant
N such that the particle has a total charge of e?, (b) Compute the form factor for this
particle., (c) Calculate < r2 >1/2 for this distribution.
5. (F-H 6-15) (a) What are muonic atoms?, (b) Why can muonic atoms be used to study
nuclear structure?, (c) Calculate the Bohr energy levels of muonic atoms. Explain why
the screening due to the electrons be safely ignored. (d) Compute the value of the 2p→1s
muonic transition energy in 208 Pb under the assumption that the lead nucleus is a point
charge. Explain qualitatively why this value differs from the experimental value of 5.8
MeV.
6. Assume the lead nucleus is a uniform spherical charge of radius, R. Use first order
perturbation theory to calculate the value of R needed to fit the 5.8 MeV experimental
value for the 2p→1s muonic transition energy in 208 Pb. (The perturbation is the difference between the point charge potential and the potential of a uniform spherical charge
distribution which can be found in your Physics 200 textbook.)