Physics 418, Homework Assignment
Due in Class, Wednesday, January 28, 2004

1. Consider a scattering apparatus which has the following components:

• a source of $\alpha$-particles with kinetic energy 8.4 MeV and a flux of $3.0 \times 10^{6}$ particles/$\rm cm^2/sec$ in a beam with a transverse area of 1 mm$^2$;
• a Gold target (density = 19.3 g/cm$^3$) with transverse dimensions larger than the beam, and thickness of 2.6 $\mu$m,
• an alpha detector subtending a solid angle $\Delta \Omega$ = 0.001 steradians which can be moved to different positions in the polar angle, $\theta$.

1. Make a table of the number of $\alpha$-particles per second hitting the alpha detector when it is placed at angles of 5$^{\circ}$, 10$^{\circ}$, 30$^{\circ}$, 60$^{\circ}$, 90$^{\circ}$ and 120$^{\circ}$.
2. Plot these results in a graph. Use a vertical log scale for the number of particles, and a horizontal linear scale using $\sin(\frac{\theta}{2})$.

2. Repeat Problem 1, but replace each Gold nucleus by a hard sphere with radius, R = $9.5 \times 10^{-15}$ m.

3. Re-plot the data in 1(b), but change the horizontal axis from $\theta$ to the momentum transfer squared,

$$\begin{eqnarray*} p^2 & = & 2 (mv)^2 (1 - \cos(\theta)) \\ & = & 4 (mv)^2 \sin^2(\frac{\theta}{2}) \end{eqnarray*}$$