  Motivated by the report by Cottam et al. (2002) of iron resonance scattering
lines in the spectra of thermonuclear bursts from EXO 0748-676, we have
investigated the information about neutron star structure and the geometry of
the emission region that can be obtained by analyzing the profiles of atomic
lines formed at the surface of the star. We have calculated the detailed
profiles of such lines, taking into account the star's spin and the full
effects of special and general relativity, including light-bending and
frame-dragging. We discuss the line shapes produced by rotational Doppler
broadening and magnetic splitting of atomic lines, for the spin rates and
magnetic fields expected in neutron stars in low-mass X-ray binary systems. We
show that narrow lines are possible even for rapidly spinning stars, if the
emission region or the line of sight are close to the spin axis. For most
neutron stars in low-mass systems, magnetic splitting is too small to obscure
the effects of special and general relativity. We show that the ratio of the
star's mass to its equatorial radius can be determined to within 5% using
atomic line profiles, even if the lines are broad and skewed. This is the
precision required to constrain strongly the equation of state of neutron star
matter. We show further that if the radius and latitude of emission are known
to ~ 5-10% accuracy, then frame-dragging has a potentially detectable effect on
the profiles of atomic lines formed at the stellar surface.
