  We present a new method to measure the radius-to-mass ratio (R/M) of weakly
magnetic, disc-accreting neutron stars by exploiting the occultation of parts
of the inner disc by the star itself. This occultation imprints characteristic
features on the X-ray line profile that are unique and are expected to be
present in low mass X-ray binary systems seen under inclinations higher than
~65 degrees. We analyse a NuSTAR observation of a good candidate system, 4U
1636-53, and find that X-ray spectra from current instrumentation are unlikely
to single out the occultation features owing to insufficient signal-to-noise.
Based on an extensive set of simulations we show that large-area X-ray
detectors of the future generation could measure R/M to ~2{\div}3% precision
over a range of inclinations. Such is the precision in radius determination
required to derive tight constraints on the equation of state of ultradense
matter and it represents the goal that other methods too aim to achieve in the
future.
