Polarization operator approach to electron-positron pair production in   combined laser and Coulomb fields
  The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for circular laser polarization and for the general case of elliptic polarization, which has not been treated before. Our approach allows us to obtain by analytical means the asymptotic behaviour of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic threshold of this process, the rate obeys a power law in the laser frequency with different exponents for linear and circular laser polarization. With the help of the upcoming x-ray laser sources our results could be tested experimentally. 
A. I. Milstein, C. M\"uller, K. Z. Hatsagortsyan, U. D. Jentschura,   and C. H. Keitel