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# Scattering

Scattering occurs when we fire a projectile at a target.  The projectile will be 'scattered' from it or could remain unscattered, i.e. its direction of motion is altered by the target.   By measuring the numbers of particles which scatter by different amounts we can work out much about the structure of the target.  There are two kinds of scattering elastic and inelastic.  For scattering it is easiest if the projectile is a fundamental particle (so can be considered as a point without any structure, such as the electron) so that the effects of any size is not there to complicate results and we are only observing the target (say a proton).

## Elastic scattering

In an elastic collision the incident and target particles remain intact (like billiard balls).  No energy is lost (to other processes) and the projectile's kinetic energy is shared between itself and the target after the collision, momentum is of course always conserved.  If the target is point-like then elastic scattering is the only possibility.  If the target has size then the scattering may still be an elastic process, however the formula for it will altered slightly, depending on the momentum imparted to the target particle (by a factor called the form factor).

## Inelastic scattering

In inelastic scattering part of the kinetic energy of the incident particle is lost inside the target giving rise to some internal processes and only a fraction of it goes into moving the whole target. For example if you take a spherical container and then fire a small ball onto it the collision could be considered to be elastic (in an ideal world). If you were then to fill it with some marbles and then fire another ball at it some of the kinetic energy would go into moving the ball, but a fraction would also move around the marbles inside. In this sense we can say that inelastic scattering will occur if the target consists of smaller components. One other difference between inelastic and elastic scattering is that with elastic scattering the target will not change form, whereas with inelastic scattering the target can break up into new forms.  A proton may make hadrons (particles built from quarks) by inelastic collisions. We now see that if we can show that the target (say a proton) scatters inelastically then we can presume that there must be some internal process occuring, which should not happen if the particle is fundamental, because this suggests there is something smaller inside to cause this process. This is just what happened at SLAC  with deep inelastic scattering, by probing the nucleon it was found to scatter inelastically, just as though there were smaller particles inside.

## Scattering as an exchange process

These interaction (scattering) processes are in general mediated by the electromagnetic force, meaning that it is really an exchange process between the incident electron and the target.  This is an electromagnetic interaction and the mediator (the particle which is exchanged between the two interacting ones and produces the force, in this case for electromagnetic it's the photon).

Take for example a particle of initial momentum p which interacts and scatters from the target with a new momentum p'.  The difference is q = p-p'   which is the momentum transferred to the target.  It is found that in elastic scattering the cross-section of scattering falls as q2 increases.  If we are able to work out what the form factor is (by seeing how the scattering is reduced from its value for a point particle), then we can get an idea of how the charge is distributed inside the target (in fact the form factor is the fourier transform of the charge distribution).