PHY492 Spring 2001 Nuclear and Elementary Particle Physics

Homework set 1 Due date: Friday, 2/2/2001

Please clearly state your assumptions, number the equations and indicate logical connections between different lines.

1. [5+5+5+5+5+5 pt] Rutherford scattering

Consider the scattering problem of a particle with charge ze inthe Coulomb field of a very heavy nucleus of charge Ze.

a. Derive a relationship between the impact parameter b and the scattering angle q.

b. Derive a scattering cross section.

c. Derive an angular differential scattering cross section.

d. State all assumptions you made in your derivation and briefly justify each one of them.

e. Calculate the total cross-section for the scattering of a 15 MeV a-particle by a gold nucleus through an angle greater than 15^o.

f. For the same system, plot the differential scattering cross section ds/dW versus the scattering angle for the angular range of 10^o < q < 60^o

2. [5+5 pt] Decay

a. Williams 2.5

b. Williams 2.10

3. [5+5 pt] Cross section

a. Williams 2.12

b. Williams 2.13