# Elastic and Inelastic Collisions in Particle Physics

Elastic and inelastic collisions are the subject of many high school physics homework problems. But are they useful in modern physics research?

It turns out the answer to this is a definite yes. Particle collisions or scattering (we will use thetwo terms interchangeably) is one of the most fundamental tools we use to study nature. Even when you're looking at an object, you are conducting a scattering experiment, observing how visible light photons are scattered off the object. Essentially all particle physics experiments involve studying the scattering of particles energized by accelerators or natural processes. Using a form of inelastic collisions called deep inelastic scattering, particle physicists have determined that the proton and neutron are made of more fundamental particles called quarks. The importance of this discovery, which was made at SLAC, was recognized with the 1990 Nobel prize.

To understand elastic and inelastic scattering in particle physics, let's first look at these phenomena in collisions between macroscopic (large) objects. In both elastic and inelastic scattering, the total momentum is conserved. The differences are that in elastic scattering

• The total kinetic energy of the colliding bodies is conserved, meaning that no energy is lost to other processes.
• The colliding particles remain intact.
On the other hand, in inelastic scattering
• The total kinetic energy of the colliding bodies is not conserved, meaning that energy is taken up by other processes. For example, some kinetic energy may turn into vibrations of the scattered bodies, which we experience in the form of heat or sound. Note that in order for vibrations to take place, at least one of the colliding bodies must be composed of smaller constituents, which then vibrate with respect to each other.
• As another example, one or both of the colliding particles may break up, if it is made of smaller constituents. In this case, some of the kinetic energy goes into breaking chemical bonds that hold the constituents together.
Let's look at the particle physics equivalents of these phenomena:

## Elastic particle scattering

As an example of elastic scattering in particle physics, we look at one of the most common processes that take place at SLAC's
BaBar experiment: the elastic scattering of an electron and a positron. The simulated computerized representation of the response of the detector to such an event is shown in the following pictures:

In the left picture, we are looking down the vacuum pipe in which the electron and positron beams travel. In the right picture, the electron is coming from the left and scatters downward after the collision, and the positron is coming from the right and scatters upward.

The green trapezoids indicate energy that these particles deposited into detector's calorimeter. The height of each trapezoid indicates the amount of energy detected by one of the 6580 cesium iodide crystals that make up the BaBar calorimeter. Each of the outgoing particles deposits energy in a cluster of several calorimeter crystals. To the inside of the calorimeter, you can see the ionization trails that the electron and positron left in the BaBar drift chamber.

First, let's check if these two particles really scatter elastically. The initial and final momenta and energies of the two particles are approximately:
Particle
`p = (px, py, pz)`
`E`
e- incoming
`(0.2, 0, 9.0) GeV/c`
`9.0 GeV`
e+ incoming
`(-0.1, 0, -3.1) GeV/c`
`3.1 GeV`
e- outgoing
`(-3.1, -1.1, 7.6) GeV/c`
`8.3 GeV`
e+ outgoing
`(3.1, 1.1, -1.8) GeV/c`
`3.7 GeV`

From this table, can you determine whether the collision was elastic or inelastic? What do you need to calculate in order to make this determination? After finding the answer, check the
solution.

## Inelastic particle scattering

When at least one of the colliding particles is composite - composed of smaller constituents - relative motion of the constituents can take up some of the initial energy. This is one of the processes that can take place when, for example, a high-energy particle hits an atom (a composite object) and kicks one of its orbital electrons out of its place near the atomic nucleus. This phenomenon, called ionization, is used in a wide range of particle detectors, from handheld Geiger counters to the large drift chambers used in particle physics experiments.

As in the case of macroscopic bodies, a composite particle may break up into its constituents. In this case, the initial energy is shared among the kinetic energies of all the final particles, and some of it also goes to sever the bonds that initially held the constituents together.

When the constituent particle is a hadron - generally, a particle made of quarks - its breakup results in an additional process that is unique to the quantum mechanical regime of particle physics and does not take place in collisions of macroscopic bodies: the creation of more quarks and anti-quarks. This happens because the attractive force that binds the quarks together increases roughly in proportion to the distance between them, like a spring. As the quarks fly apart and the distance between them increases to about the size of the proton (10-13cm), the energy stored in that spring is enough to create the mass of a quark-anti-quark pair. The energy cost to create this pair is, of course, E=2mc2, where m is the mass of each of the particles in the pair.

Check out our animation of what happens when a high-energy electron breaks up a proton: as the constituent u, u, and d quarks of the proton begin to fly out, two of them get sufficiently far apart and have enough energy to create a u quark and an anti-u quark, which subsequently bind to the original quarks to create a proton and a π0 meson.

When the electron is more energetic, more quark-anti-quark pairs can be created, resulting in the production of more hadrons. The following picture shows such an event, recorded by the ZEUS detector at the HERA electron-proton storage ring. The electron beam is coming in from the left of the picture and the proton beam is coming in from the right. The electron is scattered to the top left part of the picture, leaving a track in the drift chamber (marked CTD). The small yellow blob at the end of the track indicates that the electron deposited all its energy in the electromagnetic calorimeter (marked EMC). The particles created in the breakup of the proton go mostly to the bottom left, where we can see a jet containing several charged particles and energy deposited in the hadronic calorimeter. Note that the calorimeter also records the energy deposited by neutral particles (such as neutrons), which would not be detected by the drift chamber. One low energy charged particle is seen swirling to the right side of the picture.

For a great explanation of how events like this have helped us understand the structure of the proton and have led to the discovery of quarks, check out Oxford University's Inside the Proton web site.

## Just how elastic can it really get?

You know that in everyday life it's impossible to get a purely elastic collision, as there will always be some energy lost to vibration. You can choose your colliding bodies such that very little energy is lost, but it is impossible to completely eliminate energy loss. For example, a well-inflated basketball bounces very well, but it still loses some energy to heat and sound waves when it bounces.

The photons emitted in the radiative e-e+ collision usually have energies that are low compared to those of the incoming particles. Very often, they also have a very small angle with respect to one of the incoming particles. In this case, they go down into the beam type and are not detected by the detector. In other cases, these photons have a small angle with respect to one of the outgoing charged particles, with a relatively low energy. As a result, the photon and the charged particle deposit their energies in the same cluster of calorimeter crystals, making it hard or impossible to detect the photon by identifying two separate signatures in the calorimeter.

But often enough, the radiated photon is so energetic that the outgoing charged particle is left with relatively little kinetic energy, and therefore curves in the magnetic field before reaching the calorimeter. The photon is not charged and therefore does not curve, resulting in enough separation between the charged particle and the photon that they can be separately identified in the calorimeter.

The following pictures show such an event. Note how the outgoing electron is curving to the left in the left picture, making the high-energy photon easily identifiable.

Click on these pictures to see the energies of the three calorimeter clusters and the momenta determined from how the charged particles curve in the magnetic field. Note that the measured momentum of each of the charged tracks is very close to the energy the particle deposited in the calorimeter. This is a characteristic behavior of electrons and positrons, and is the main method we use to identify these particles. Read more about how we use bremsstrahlung to measure the energies of photons, electrons, and positrons.

Photons may be radiated in any event, especially if it involves light particles, such as electrons, which tend to radiate more. For example, see this deep inelastic scattering event at ZEUS.

## Things to ponder

• Remember the elastic scattering event? We said that it was elastic up to the precision of the measurement. Do you think it may have also involved a radiated photon, and that this is the reason that energy and momentum appeared not to be exactly conserved in the event? What evidence and considerations support this possibility? What can you say against it?
• At the top of this page we gave an example of a scattering experiment: simply looking at something. Can you think of other scattering experiments that we do in everyday life? What about medical applications, military applications, or air traffic control? Can you thik of additional examples? Share your thoughts in our hypernews group discussion forum.