In

particle physics, one usually does

scattering experiments to get information on, well, particles.
The earliest such experiment was done by

Rutherford, and I will attempt to use it to illustrate what the form factor means. Rutherford looked at the collision of

alpha particles with gold atoms. From the angular distribution of the scattered alphas he was able to deduce that gold atoms (and all others as well) consist of mainly empty space, and all the mass is concentrated in a small, hard

nucleus.
He did the math and calculated the so called

Rutherford cross section. He was right only by accident because he didn't take into account relativistic or quantum effects, but nevertheless his formula is valid for

spin-less, pointlike targets.

It turns out that the

cross section in a more general case can be expressed as the Rutherford cross section (with small modifications, see

Mott cross section) times a function F(Q^2) called the

*form factor*, where Q is the momentum transferred in the collision. This function is the

Fourier transform of the charge distribution of the target. In Rutherford's case F was a constant and as such did not distort his calculation. This is consistent with his idea of a pointlike nucleus - it gives a

delta function as charge distribution and the Fourier transform of a delta function is constant.

However, nowadays we have access to higher energy probes, and thus can do measurements with higher momentum transfers. Therefore we know that F is constant only for small values of Q^2, and nuclei are not points but have a substructure, namely

protons and

neutrons. The

nucleons themselves are also no point particles but consist of

quarks. The

Rosenbluth formula describes how their form factors relate to the cross section.