Subatomic Physics

6.12. References 191
(c) Show that the electron can be treated as a massless particle for this
problem.
6.8. Verify Eq. (6.20) and find the next term in the expansion.
6.9. Assume that the probability distribution is given by (x = |x|)
ρ(x) =ρ0 x ≤ R
ρ(x) =0 forx>R.
(a) Compute the form factor for this “uniform charge distribution.”
(b) Calculate 〈x 2 〉 1/2 .
6.10. 250 MeV electrons are scattered from 40 Ca.
(a) Use equations given in the text to compute numerically values of the
cross section as a function of the scattering angle for the following assumptions:
(a1) Spinless electrons, point nucleus.
(a2) Electrons with spin, point nucleus.
(a3) Electrons with spin, “Gaussian” nucleus [Eq. (6.23)].
(b) Find experimental values for the cross section and compare with your
computations. Determine a value for b in Eq. (6.23).
6.11. (a) What are muonic atoms?
(b) Why can muonic atoms be used to study nuclear structure?
(c) Compute the energy of the 2p − 1s muonic transition in 208 Pb under
the assumption that Pb is a point nucleus. Compare with the observed
value of 5.8 MeV.
(d) Use the values computed and given in part (c) to give an order-ofmagnitude
estimate of the nuclear radius of Pb (whose actual nuclear
charge radius is ≈ 6fm).
6.12. Use Eq. (6.18) to determine the normalization constant N in Eq. (6.24).
6.13. Use the values given in Eq. (6.27) to find an average value for the internucleon
distance in a nucleus.