Ionization dynamics of a model atom exposed to a strong laser pulse andrelativistic calculation of matrix elements for two-photon transitions in hydrogen-like ions

Part I: Recent calculations of ionization rate based on the numerical solution of the time-dependent Schrödinger equation (TDSE) in configuration space gave results in disagreement with the ionization rate obtained under the strong field approximation(SFA), is to say, assuming that the ionization is by tunneling. Moreover, recent experimental results, which clearly show among other things, (a) the presence of resonant structures in the region of low energy spectrum of emitted electrons and (b) interference figures for the distribution of moments of electrons emitted cannot be explained in the context of the SFA. These findings reinforce the idea that the electrons, at least those of low energies, are emitted by another process than the tunnel effect. Under these conditions, the influence of the Coulomb potential compared to the electric field remains high even in the strong field limit. To analyze the role of the Coulomb potential, we developed a new mathematical model that goes beyond the SFA as well as the efficient numerical codes that allow obtaining relevant information on the role of atomic structure in the dynamics of ionization. Part II: Using Sturmian expansions of the Dirac-Coulomb Green's functions derived by R. Szmytkowski (J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), fully relativistic treatment) and us (quasirelativistic approach), we have derived in a rigorous way the explicit expressions of the two-photon absorption, Rayleigh and Raman scattering probability amplitudes that take into account both relativistic and retardation effects. A distinctive feature of our tensor treatment is that the expressions derived are quite general and could be applied to any multipole of the two-photon bound-bound transitions. An illustration of our method is undertaken by computing the two-photon absorption transition rates from the ground state towards the excited states of L and M shells for the lighter elements to the heavier ones. A comparison is made also with
(PHYS 3) -- UCL, 2010