We model the X-rays reprocessed by an accretion disk in a fiducial low-mass X-ray binary system with a neutron star primary. An atmosphere, or the intermediate region between the optically thick disk and a Compton-temperature corona, is photoionized by the neutron star continuum. X-ray lines from the recombination of electrons with ions dominate the atmosphere emission and should be observable with the Chandra and XMM-Newton high-resolution spectrometers. The self-consistent disk geometry agrees well with optical observations of these systems, with the atmosphere shielding the companion from the neutron star. At a critical depth range, the disk gas has one thermally unstable and two stable solutions. A clear difference between the model spectra exists between evaporating and condensing disk atmospheres. This difference should be observable in high-inclination X-ray binaries, or whenever the central continuum is blocked by absorbing material and the extended disk emission is not.
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