When the laser field is strong, the simple formulas
of Compton/Breit-Wheeler can nolonger be used. The laser strength is
characterized by the parameter

where is the laser wavelength in meter,
*m* the electron rest mass in eV/,
*c* the velocity of light in m/s, ,
and *P* the power density in Watt/m.
When , the simple formas are enough but as becomes large,
the probability of absorbing more than one photon in the laser field
cannot be ignored. When ,
the constant-field approximation becomes good.
If , the expansion in terms of the number of absorbed photons, *n*,
shows good convergence. The expansion takes a relatively simple form
when the laser is circularly polarized by 100%. The present version
accepts such case only.

In the case of the nonlinear Compton process
,
the number of emitted photons per unit time
can be expanded in the form

*E*,- Energy of the initial electron and final photon.
- ,
- Helicity of the initial electron and laser (, ).
- ,
- `Detector helicity' of the final electron and photon.
- Maximum photon energy when
*n*laser photons are absorbed:

- Laser energy parameter: . (: laser photon energy)
- Functions involving Bessel functions. See Sec.A.1 for the definition.

The formula for the nonlinear Breit-Wheeler process
can be written in a similar form.
The total number of pair electrons per unit time summed over the positron
polarization is

- ,
*E* - Energy of the initial photon and final electron.
- ,
- Initial photon helicity and `detector helicity' of the final electron.
- Laser energy parameter: (: laser photon energy).
- Minimum energy of the final electron for given
*n*:

- Functions involving Bessel functions. See Sec.A.2 for the definition.

When NPH is specified in LASERQED command,
the above formulas are used with the terms upto *n*=NPH.
See Sec.A for the algorithm of the event generation.

Thu Dec 3 17:27:26 JST 1998