  We give exact results for the emission spectra of both nonlinear
Breit-Wheeler pair production and nonlinear Compton scattering in
ultra-intense, ultra-short duration plane wave backgrounds, modelled as
delta-function pulses. This includes closed form expressions for total
scattering probabilities. We show explicitly that these probabilities do not
exhibit the power-law scaling with intensity associated with the conjectured
breakdown of (Furry picture) perturbation theory, instead scaling
logarithmically in the high-intensity limit.
