Scattering Cross Section

The concept of cross section, as its name suggests, is that of effective area for collision. The cross section of a spherical target is

The angle of scattering in Rutherford scattering depends upon the impact parameter, with larger deflection occurring for smaller impact parameters. The area of a circle of radius = b = impact parameter is then the cross section for scattering above the angle associated with b, since any particle arriving with r less than b will scatter to a larger angle. Therefore, the cross section for scattering at a greater angle than some chosen angle is

Note that this expression is for alpha particles with Z_p=2. For projectiles with another charge Z_p, then you would multiply this expression by Z_p²/4.