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

- Compton scattering () and Breit-Wheeler scattering () with nonlinear effects with respect to the laser intensity.
- The laser is circularly polarized. Longitidinal polarization of all the particles except that of the final electron of Compton scattering is included.

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.

Thu Dec 3 17:27:26 JST 1998