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Coherent Pair Creation


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 tex2html_wrap_inline8918 is the energy of the initial photon. (tex2html_wrap_inline10468 and tex2html_wrap_inline10470 are defined in eq.(84).) The probability of the process is exponentially small (tex2html_wrap_inline10472) when tex2html_wrap_inline10474 is small.

Let us denote the energy and polarization vector of initial photon and final positron/ electron by tex2html_wrap_inline8918, tex2html_wrap_inline10478 (tex2html_wrap_inline10480), tex2html_wrap_inline7924, and tex2html_wrap_inline10484. 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 tex2html_wrap_inline10486 is defined as
tex2html_wrap_inline10296 is the modified Bessel function and tex2html_wrap_inline10298 is defined in eq.(87). Their arguments are tex2html_wrap_inline7944 defined in eq.(99). The transition rate summed over the final polarization is

Figure 9: Function tex2html_wrap_inline10494 for three values of tex2html_wrap_inline10474. The solid, dotdash and dashed curves are for tex2html_wrap_inline10498, 1, -1, respectively. The curves for tex2html_wrap_inline10498 are normalized such that tex2html_wrap_inline10504, and those for tex2html_wrap_inline10506 are drawn with the same scale as the corresponding tex2html_wrap_inline10498 curves.

The function tex2html_wrap_inline10494 is plotted in Fig.9 as a function of tex2html_wrap_inline10512.


The total rate for given tex2html_wrap_inline7924 is approximately
In order to make the spectrum function flatter, CAIN introduces the variable y (-1<y<1) instead of tex2html_wrap_inline10520 (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 tex2html_wrap_inline10530 for any tex2html_wrap_inline10532. tex2html_wrap_inline10534 is plotted in Fig.10.

Figure 10: Function tex2html_wrap_inline10534 as a function of y for three values of tex2html_wrap_inline10474 =0.3, 2, 40 and for tex2html_wrap_inline10542. The parameter tex2html_wrap_inline10474 is indicated by the line mode and tex2html_wrap_inline7246 is by crosses (no cross for tex2html_wrap_inline10498).

Now, the event generation goes as

The error of the formula (103) does not cause any inaccuracy of event generation (but causes inefficiency).

next up previous contents index
Next: Incoherent Pair Production Up: Physics and Numerical Methods Previous: Enhancement factor of the

Toshiaki Tauchi
Thu Dec 3 17:27:26 JST 1998