Structure of radiative corrections in a strong constant crossed field

In the preceding paper [A. A. Mironov, S. Meuren, and A. M. Fedotov, Phys. Rev. D 102, 053005 (2020)] we have demonstrated a feasible resummation of the bubble-chain corrections to the electron elastic scattering amplitude in a strong constant crossed electromagnetic field. Here we present a calculation of a more general contribution to the off-shell electron mass operator in a constant crossed field with an exact photon propagator in a loop. Using such an approximated mass operator, we also obtain a corrected electron propagator and elastic scattering amplitude. The results are expressed in the form of expansion over y-matrix structures with scalar coefficients depending on the electron virtuality and the quantum dynamical parameter. By asymptotic analysis we identify the dominant contribution in the strong field limit. All the calculations were made by means of the original open-access computer-algebraic scripts. Our findings can be applied to a consistent study of the Dyson-Schwinger equations in strong-field QED.