  We construct models for strongly-magnetized neutron star atmospheres composed
of mid-Z elements (carbon, oxygen and neon) with magnetic fields
B=10^{12}-10^{13} G and effective temperatures Teff=(1-5)*10^6 K; this is done
by first addressing the physics relevant to strongly-magnetized plasmas and
calculating the equation of state and polarization-dependent opacities. We then
obtain the atmosphere structure and spectrum by solving the radiative transfer
equations in hydrostatic and radiative equilibrium. In contrast to hydrogen
opacities at the relevant temperatures, mid-Z element opacities are dominated
by numerous bound-bound and bound-free transitions. Consequently, temperature
profiles are closer to grey profiles, and photosphere densities are lower than
in the hydrogen case. Mid-Z element atmosphere spectra are significantly softer
than hydrogen atmosphere spectra and show numerous absorption lines and edges.
The atmosphere spectra depend strongly on surface composition and magnetic
field but weakly on surface gravity. Absorption lines are primarily broadened
by motional Stark effects and the (unknown) surface magnetic field
distribution. Given the multiple absorption features observed from several
isolated neutron stars, it is possible to determine, with existing X-ray data,
the surface composition, magnetic field, temperature, and gravitational
redshift; we present qualitative comparisons between our model spectra and the
neutron stars 1E1207.4-5209 and RX J1605.3+3249. Future high-resolution X-ray
missions such as Constellation-X will measure the gravitational redshift with
high accuracy by resolving narrow absorption features, and when combined with
radius measurements, it will be possible to uniquely determine the mass and
radius of isolated neutron stars. (Abridged)
