  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.
