Formulas

k,,p,p'
4-momenta of the initial photon, laser photon, final electron and positron.
,,,
Energies of the initial photon, laser photon, final electron and positron.

Laser intensity parameter

Laser energy parameter: .
n
Number of absorbed laser photons
x
=. (0<x<1)
u
u=1/[4x(1-x)], , ().

Maximum u for given n: .



Initial photon helicity

Laser helicity

Final electron helicity

`Detector' helicity of the final electron.

Final electron angle


The argument of the Bessel functions in the following expressions:

Total number of pair electrons per unit time summed over the positron polarization is

Sum over final electron polarization gives

These formulas can be obtained from those of by the replacement

This implies

For convenience, we have changed the sign as

For given x and n, the final momenta are given by



Here, is the azimuthal scattering angle in a head-on frame and

These vectors satisfy