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 electronís 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 Planckís 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.

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