  The outermost layers of some neutron stars are likely to be dominated by
hydrogen, as a result of fast gravitational settling of heavier elements. These
layers directly mediate thermal radiation from the stars, and determine the
characteristics of X-ray/EUV spectra. For a neutron star with surface
temperature $T\lo 10^6$ K and magnetic field $B\go 10^{12}$ G, various forms of
hydrogen can be present in the envelope, including atom, poly-molecules, and
condensed metal. We study the physical properties of different hydrogen phases
on the surface of a strongly magnetized neutron star for a wide range of field
strength $B$ and surface temperature $T$. Depending on the values of $B$ and
$T$, the outer envelope can be either in a nondegenerate gaseous phase or in a
degenerate metallic phase. For $T\go 10^5$ K and moderately strong magnetic
field, $B\lo 10^{13}$ G, the envelope is nondegenerate and the surface material
gradually transforms into a degenerate Coulomb plasma as density increases. For
higher field strength, $B>> 10^{13}$ G, there exists a first-order phase
transition from the nondegenerate gaseous phase to the condensed metallic
phase. The column density of saturated vapor above the metallic hydrogen
decreases rapidly as the magnetic field increases or/and temperature decreases.
Thus the thermal radiation can directly emerge from the degenerate metallic
hydrogen surface. The characteristics of surface X-ray/EUV emission for
different phases are discussed. A separate study concerning the possibility of
magnetic field induced nuclear fusion of hydrogen on the neutron star surface
is also presented.
