text: When the incoming field is very intense , the interaction of the electron with the electromagnetic field is completely equivalent to the interaction of the electron with multiple photons, with no need of explicitly quantize the electromagnetic field of the incoming low-energy radiation. While the interaction with the radiation field, i.e. the emitted photon, is treated with perturbation theory: the probability of photon emission is evaluated considering the transition between the states of the electron in presence of the electromagnetic field. This problem has been solved primarily in the case in which electric and magnetic fields are orthogonal and equal in magnitude (crossed field); in particular, the case of a plane electromagnetic wave has been considered. Crossed fields represent in good approximation many existing fields so the found solution can be considered quite general. The spectrum of non-linear inverse Compton scattering, obtained with this approach and valid for  and  , is:
  where the parameter , is now defined as:A related quantity is the rate of photon emission:<math display="block">
  \dfrac{dN}{dt}=\dfrac{\sqrt{3}}{2\pi}\dfrac{q^2 m c}{\hbar^2 }\dfrac{\chi}{\gamma} \int_0^{\chi}\dfrac{F(\chi,\eta)}{\eta}d\eta 
   no photons can be produced. This rate of photon emission depends explicitly on electron quantum parameter and on the Lorentz factor for the electron.