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, __

__
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
__

__(1)____Compute and reject if (the rate is too small).____(2)____Generate a uniform random number 0<__*p*<1 and compute .__(3)____Reject if .____(4)____Generate another uniform random numbers 0<__*q*<1 and -1<*y*<1 and compute . (Instead of*q*, one can also use .)__(5)____Reject if .____(6)____Accept and compute__*x*from eq.(104) and , .__(7)____Compute the final polarization of from__

The formula for is obtained by replacing*x*by 1-*x*.__(8)____In the case of rejection, the polarization of the photon should be changed according to eq.(12):__

__
__

Thu Dec 3 17:27:26 JST 1998