Spectral caustics in laser assisted Breit-Wheeler process

Electron-positron pair production by the Breit-Wheeler process embedded in a strong laser pulse is analyzed. The transverse momentum spectrum displays prominent peaks which are interpreted as caustics, the positions of which are accessible by the stationary phases. Examples are given for the superposition of an XFEL beam with an optical high-intensity laser beam. Such a configuration is available, e.g., at LCLS at present and at European XFEL in near future. It requires a counter propagating probe photon beam with high energy which can be generated by synchronized inverse Compton backscattering.