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
(92):
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 
.
1ex
The total rate for given is approximately
where
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
and reject if 
(the rate is too small).
.
.
. (Instead of q, one can also use 
.)
.
, 
.
from
is obtained by replacing x by 1-x.
