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 particle
s 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 proton
s and neutron
s. The nucleon
s themselves are also no point particles but consist of quarks
. The Rosenbluth formula
describes how their form factors relate to the cross section.