SQUARE45

Consider a positively charged projectile particle with charge

q_1

and momentum

\vec{p}_1

, scattering off a target nucleus with charge

Q

and mass

M

. The interaction potential is the Coulomb potential:

V(r) = \frac{k Q q_1}{r}

. The scattering amplitude

f(\theta)

is derived from the differential cross-section

\frac{d\sigma}{d\Omega}

. For small-angle scattering, the classical trajectory analysis yields the scattering angle

\theta

and the momentum transfer

\vec{q}

. The differential cross-section is given by:

\frac{d\sigma}{d\Omega} = \left( \frac{k Q q_1}{4 E} \right)^2 \frac{1}{\sin^4(\theta/2)}

where

E

is the initial kinetic energy and

\theta

is the scattering angle.

Rutherford Scattering Experiment