**Electron-positron
Annihilation and Pair Creation.
**

**Compton
Scattering
**

**
**

**Fig.1 This bubble chamber
picture shows some electromagnetic events such as pair creation or
materialization of high energy photon into an electron-positron pair (green
tracks), the Compton effect (red tracks), the emission of electromagnetic
radiation by accelerating charges (violet tracks) (bremsstrahlung) and the
knock-on electrons or delta ray (blue tracks) **

*Electron-positron
Annihilation
*

The processes of electro-positron annihilation into photons pairs and of pair creation by photon are of interest both theoretically and experimentally.

The electron’s antiparticle, the positron, is identical in mass but has a positive charge. If an electron and positron collide, they will annihilate with the production of two gamma photons:

*Fig. 2 Part of a bubble-chamber picture from a
neutrino experiment performed at the Fermilab (found at the University of
Birmingham). A positron in flight annihilate with an electron. The photon that
is produced materializes at a certain distance, along the line of flight,
resulting a new electron-positron pair (marked with green)*

In the frame of reference related to the electron, the conservation laws are:

(2.1)

where

the momentum conservation is:

(2.2)

The energy transferred to is maximum when is emitted in the direction of the incident .

Hence:

(2.3)

and (2.4)

but and because of the zero-masses of photons.

Multiplying (2.4) by c, gives:

(2.5)

Subtracting from (2.5) and replacing it in (2.3) gives:

(2.6)

Therefore:

(2.7)

where one can calculate the total energy
and momentum of the incident
by using its kinetic energy **T**:

(2.8)

and (2.9)

*Electron-Positron
Pair Production
*

*
*

When a photon has quantum energy higher than the rest energy of an electron plus a positron, one of the ways such as a photon interacts with matter is by producing an electron-positron pair in the field of nucleus.

This process cannot take place in free space because of the conservation laws violation.

*Fig.3
Part
of a bubble chamber picture (Fermilab'15 foot Bubble Chamber', found at the
University of Birmingham). The curly line which turns to the left is an
electron. Positron looks similar but turn to the right The magnetic field is
perpendicular to the picture plan*

The rest energy of the electron is , so for photons with energies much bigger than , pair production is possible and can be a mode for the interaction of X-rays, or gamma-rays with matter.

*Compton
Scattering
*

*
*

*Fig.3 Part
of a bubble chamber picture (Fermilab'15 foot Bubble Chamber', found at the
University of Birmingham). An electron was knocked out of an atom by a high
energy photon.*

*
*

Compton scattering is related by crossing symmetry to pair annihilation:

Compton scattering

Pair annihilation

It can be seen that the electron on the left side of the Compton process can be replaced by its antiparticle, the positron, on the other side of the interaction resulting pair annihilation.

Crossing symmetry applies to all known particles, including the photon, which is its own antiparticle.

Generally, in the case of processes, the crossing symmetry relates the following interactions:

The over bar indicates the antiparticle.

In the Compton effect one can observe a shift in wavelength upon scattering of light from stationary electron. The Compton effect, discovered by Compton in 1923, provided the final confirmation of the validity of Planck’s quantum hypothesis that electromagnetic radiation came in discrete mass less packets (photons) with energy proportional to frequency.

Let a photon of frequency or wavelength scatter off an electron at an angle like in Fig.1. In collision, it transfers some energy to the electron and emerges at a shift frequency or wavelength as .

**Fig.1 Compton effect**

Conservation laws give:

(2.1)

or (2.2)

where (2.3)

and (2.4)

Plugging (2.3) and (2.4) into (2.1) and (2.2), one can derive the Compton scattering equation:

where the quantity is known as the Compton wavelength.