Quantum Electrodynamics Involving a Strong Laser Field

  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 photon emission angle is uniquely determined from n and .

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.