The photon scattering cross-sections of atomic hydrogen

We present a unified view of the frequency dependence of the various scattering processes involved when a neutral hydrogen atom interacts with a monochromatic, linearly-polarized photon. A computational approach is employed of the atom trapped by a finite-sized-box due to a finite basis-set expansion, which generates a set of transition matrix elements between $E<0$ eigenstates and $E>0$ pseudostates. We introduce a general computational methodology that enables the computation of the frequency-dependent dipole transition polarizability with one real and two different imaginary contributions. These dipole transition polarizabilities are related to the cross-sections of one-photon photoionization, Rayleigh, Raman, and Compton scattering. Our numerical calculations reveal individual Raman scattering cross-sections above threshold that can rapidly vanish and revive. Furthermore, our numerical Compton cross-sections do not overtly suffer from the infra-red divergence problem, and are three orders-of-magnitude higher than previous analytic-based Compton scattering cross-sections. Our total photon-hydrogen scattering cross-sections thus resolve the discrepancies between these previous calculations and those in the N.I.S.T. `FFAST' database.