M. Dondera

Above-threshold ionization of hydrogen and hydrogen-like ions by X-ray pulses

We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium Fokker-Planck equation has proposed in the literature, in which the associated curvature represents internal geometry. We present the fluctuation of the gauge field can be decomposed into three parts. We further show that if we define the Fisher information matrix by using a covariant derivative then it gives correlation of the flux components but it is not gauge invariant.This paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A2 and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L2-integrable B-spline functions for the radial coordinate and spherical harmonics Ylm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c2)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 − 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B4+. Perturbative and TDSE calculations are compared.

Stimulated Compton scattering of soft X-ray radiation by hydrogen

We extend our previous studies of stimulated Compton scattering (SCS) of X-ray [H. Bachau, M. Dondera and V. Florescu, Phys. Rev. Lett. 2014, 112, 073001 and M. Dondera and V. Florescu, H. Bachau Phys. Rev. A 2014, 90, 033423] to the case of soft X-ray domain. We consider the ionization of the hydrogen atom interacting with a coherent superposition of two pulses in the frequency range of few hundreds of eV’s. We use the two theoretical approaches developed in previous works, i.e. the resolution of the time dependent Schrödinger equation and an approach based on perturbation theory. After a detailed analysis of the electron spectrum for 15 a.u., 14 a.u., we mainly focus on SCS. We present photoelectron energy distributions, ionization rates and angular distributions at various relative directions of propagation of the pulses. SCS angular distributions are also shown for 10 a.u., 9 a.u. Finally, we present new analytic formula, based on perturbation theory, describing SCS at threshold ( a.u.), i.e. for zero final electron energy.