When a high energy photon goes through a strong transverse field,
it can create a real electron-positron pair. This process is known
as `coherent pair creation' and is characterized by the parameter
where is the energy of the initial photon. ( and are defined in eq.(84).) The probability of the process is exponentially small () when is small.
Let us denote the energy and polarization vector of initial photon
and final positron/ electron by
, (), , and .
The transition rate is obtained by the following replacement in the formula
Ignoring the terms related to the polarization correlation between the final electron and positron, we obtain
where is defined as
is the modified Bessel function and is defined in eq.(87). Their arguments are defined in eq.(99). The transition rate summed over the final polarization is
Figure 9: Function for three values of . The solid, dotdash and dashed curves are for , 1, -1, respectively. The curves for are normalized such that , and those for are drawn with the same scale as the corresponding curves.
The function is plotted in Fig.9 as a function of .
The total rate for given is approximately
In order to make the spectrum function flatter, CAIN introduces the variable y (-1<y<1) instead of (0<x<1):
The spectrum function with respect to y then becomes
where y/2 is used because the range of y is 2. The constant
is chosen so that for any . is plotted in Fig.10.
Figure 10: Function as a function of y for three values of =0.3, 2, 40 and for . The parameter is indicated by the line mode and is by crosses (no cross for ).
Now, the event generation goes as