  We present explicit expressions for Rayleigh and Raman scattering
cross-sections and phase matrices of the ground $1s$ state hydrogen atom based
on the Kramers-Heisenberg dispersion formula. The Rayleigh scattering leaves
the hydrogen atom in the ground-state while the Raman scattering leaves the
hydrogen atom in either $ns$ ($n\geq2$; $s$-branch) or $nd$ ($n\geq3$;
$d$-branch) excited state, and the Raman scattering converts incident
ultraviolet (UV) photons around the Lyman resonance lines into optical-infrared
(IR) photons. We show that this Raman wavelength conversion of incident flat UV
continuum in dense hydrogen gas with a column density of $N_{\text{H}} >
10^{21}~\text{cm}^{-2}$ can produce broad emission features centred at Balmer,
Paschen, and higher-level lines, which would mimic Doppler-broadened hydrogen
lines with the velocity width of $\gtrsim 1,000~\text{km}~\text{s}^{-1}$ that
could be misinterpreted as signatures of Active Galactic Nuclei, supernovae, or
fast stellar winds. We show that the phase matrix of the Rayleigh and Raman
$s$-branch scatterings is identical to that of the Thomson scattering while the
Raman $d$-branch scattering is more isotropic, thus the Paschen and
higher-level Raman features are depolarized compared to the Balmer features due
to the flux contribution from the Raman $d$-branch. We argue that observations
of the line widths, line flux ratios, and linear polarization of multiple
optical/IR hydrogen lines are crucial to discriminate between the
Raman-scattered broad emission features and Doppler-broadened emission lines.
