Pair Creation

**Figure 5:** Pair creation:a negative energy electron is excited to a positive energy state by radiation.
$\begin{figure}\centering\includegraphics[width=.6\textwidth]{hole_theory.eps} \par\end{figure}$

Pair creation is a process of two photon collision to generate $e^{\pm}$ pair, $\gamma\gamma\to e^+e^-$ . 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.

**Figure 6:** Diagrams that contribute to pair production in the EM cascade.
$\begin{figure}\centering\includegraphics[width=.6\textwidth]{pair_diagram2.eps} \par\end{figure}$

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 $2m_ec^2\simeq 1.022$ MeV, as easily imagined by FIG. 5. Equivalently, the threshold CM energy squared $s_{th}$ 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

$\begin{displaymath} {d\sigma\over d\cos\Theta}\simeq {\pi m_e^2 r_e^2 (s-4m_e^2)... ...^2}\cos\Theta\over \sqrt{s}-\sqrt{s-4m_e^2}\cos\Theta}\right]. \end{displaymath}$

(32)