The random number generation using the acception-rejection method is applicable when the distribution function is everywhere finite and is most efficient when the function is flat.
Since the function is infinite at ,
the following variable y is introduced in
CAIN instead of the photon energy fraction x in order to make the
distribution function finite and relatively flat.
The number of photons during a time interval in the
photon energy range (y,y+dy) is then given by
The function is less than or equal to unity for any and y. It is plotted in Fig.7.
Figure 7: Function for various values of . Unpolarized case only.
The photon generation in CAIN proceeds in the following way.
Figure 8: The acception probability in the step (6) as a function of . The solid line is the unpolarized case The dot-dash and dotted lines are polarized cases with = 1 and -1, respectively.