Rayleigh scattering from hydrogen atoms including resonances and high photon energies

The non-relativistic cross section from Rayleigh scattering by hydrogen atoms in the ground state is calculated over a wide range of photon energies ($< 0.8$ keV). Evaluations are performed in terms of the real and imaginary components of the atomic polarizability. The sum over intermediate states that characterizes this second-order radiative process is performed using exact analytic expressions for oscillator strengths of bound and continuum states. Damping terms associated with the finite lifetimes of excited states and their splitting into two fine-structure levels ($p_{1/2}$ and $p_{3/2}$) are taken into account in resonance cross sections. Fitting formulas required for cross-section evaluation are presented for incident photon energy i) redward of the first resonance (Lyman-$\alpha_{1/2}$), ii) in the spectral region corresponding to resonances (for an arbitrary number of them), and iii) above the ionization threshold.