For the nonlinear laser-electron and laser-gamma interactions, CAIN uses the subroutine package nllsr. This appendix is written for the description of the package. Some arguments of subroutines haven been modified when installed into CAIN, these are not reflected here. Also note that the notation of some variables is different.
Included items in nllsr are
)
and Breit-Wheeler scattering
(
)
with nonlinear effects with respect to the laser intensity.
The laser intensity paramater 
must not be too large
because the multiple-photon expansion is used.
When is large, the computing time and the storage requirement will be
enormous.
In both the Compton and Breit-Wheeler processes,
the laser field intensity is characterized by the parameter
where m the electron rest mass in eV/
, and a is the vector potential
(4-vector) of the laser field. When the laser is circularly polarized
completely, is a constant and is given,
in terms of the laser power density, as
where 
is the laser wavelength 
in meter,
c the velocity of light in m/s, 
,
and P the power density in Watt/m
.