Pair creation is a process of two photon collision to
generate pair,
.
This process can be understood in the hole theory proposed
by Paul Dirac in 1930 where the vacuum state
is one with all negative energy electrons
(corresponding to ) levels filled and all positive energy levels empty.
It is possible for a negative-energy electron to absorb photons
and be excited into a positive-energy state, as shown schematically
in FIG. 5. If this occurs, we observe
an electron of charge and energy and in addition a hole
in the negative-energy sea. The hole registers the absence
of an electron of charge and energy and would be interpreted
by an observer relative to the vacuum as the PRESENCE of a particle
of charge and energy ; that is the **positron**.

This process is also described in the Feynman theory of positron
where positrons are interpreted as a negative energy electron
running backward in space-time. This interpretation leads
to the famous **Feynman diagram**
as shown in FIG. 6
by which the relevant cross section can be calculated in relatively
straightforward manner.

The threshold energy of photons for pair creation
is
MeV, as easily imagined by
FIG. 5. Equivalently, the threshold CM energy squared
defined by Eq. 26
is also given by the ones considered at recoiling electron rest system
as
. The pair creation process
dominates the Compton scattering above this threshold energy.

The differential cross section can be obtained in CMS
in relatively simpler manner. Under the UHE regime we are interested
in here when we can neglect electron mass in its second order,
it is approximately given by

2002-07-18