RESUMO
Electron radiation and γ photon annihilation are two of the major processes in ultra intense lasers (UIL). Understanding their behavior in one coherence interval (CI) is the basis for UIL-matter interaction researches. However, most existing analytic formulae only give the average over many CIs. Present understanding of these two multi-photon processes in one CI usually assume that they emit forward and their spectra have a cutoff at the energy of the electron/γ. Such assumptions ignore the effects of involved laser photons (EILP). We deduced the formulae for these two processes in one CI with EILP included and give the conditions for the EILP to be significant. Strong EILP introduces new behaviors into these two processes in one CI, such as large angle emission and emit particles above the usually assumed cutoff. Simulations show that the EILP would be significant when laser intensity reaches 2 × 1022 W/cm2, which is within the reach of state-of-art lasers.