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 andV. 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 Schrodinger equation and an approach based on perturbation theory. After a detailed analysis of the electron spectrum for (h) over bar omega(1) = 15 a. u., (h) over bar omega(2) = 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 (h) over bar omega(1) = 10 a. u., (h) over bar omega(2) = 9 a. u. Finally, we present new analytic formula, based on perturbation theory, describing SCS at threshold ((h) over bar omega(1) -(h) over bar omega(2) = 0.5 a. u.), i. e. for zero final electron energy.