## Scattering from a Hard Sphere

Assume a low energy beam is incident upon a small, hard sphere of radius . We will assume that so that only the partial wave is significantly affected by the sphere. As with the particle in a box, the boundary condition on a hard surface is that the wavefunction is zero. Outside the sphere, the potential is zero and the wavefunction solution will have reached its form for large . So we set

For very low energy, and

The total cross section is then which is 4 times the area of the hard sphere.

Jim Branson 2013-04-22