Differential Cross Section

In nuclear physics, cross section is a raw data from experiment. Or more precisely differential cross section, which is some angle of the cross section, coz we cannot measure every scatter angle and the differential cross section gives us more detail on how the scattering going on.

The differential cross section (d.s.c.) is the square of the Form factor, which is the Fourier transform of the density.

d.s.c. = |F(θ)|^2 = Fourier[ ρ(r), Δp , r ]

Where the angle θ come from the momentum change. So, sometime we will see the graph is plotted against momentum change instead of angle.

On the other hand, F(θ) is the amplitude of the scatter spherical wave.

Therefore, by measuring the yield of different angle. Yield is the intensity of scattered particle. We can plot a graph of the Form factor, and then find out the density of the nuclear or particle.

However, the density is not in usual meaning, it depends on what kind of particle we are using as detector. For example, if we use electron, which is carry elected charge, than it can feel the coulomb potential by the proton and it reflected on the "density", so we can think it is kind of charge density.

Another cross section is the total cross section, which is sum over the d.s.c. in all angle. Thus, the plot always is against energy. This plot give us the spectrum of the particle, like excitation energy, different energy levels.