Nonperturbative signatures of nonlinear Compton scattering

The probabilities of various elementary laser/photon/electron/positron interactions display in selected phase space and parameter regions typical nonperturbative dependencies such as proportional to P exp{/aE(crit)/E}, where P is a preexponential factor, E-crit denotes the critical Sauter/Schwinger field strength, and E characterizes the (laser) field strength. While the Schwinger process with a = a(S) pi and the nonlinear Breit/Wheeler process in the tunneling regime with a = a(nlBW) 4m/3 omega' (with omega' the probe photon energy and m the electron/positron mass) are famous results, we point out here that also the nonlinear Compton scattering exhibits a similar behavior when focusing on high harmonics. Using a suitable cutoff c > 0, the factor a becomes a = a(nlC) 2/3 cm/(p(0) + root p(0)(2) / m(2)). This opens the avenue toward a new signature of the boiling point of the vacuum even for field strengths E below E-crit by employing a high electron beam/energy p(0) to counter balance the large ratio E-crit/E by a small factor a to achieve E/a -> E-crit. In the weak/field regime, the cutoff facilitates a threshold leading to multiphoton signatures showing up in the total cross section at subthreshold energies.