There is still 10-20% uncertainty on the neutron star (NS) mass-radius relation. These uncertainties could be reduced by an order of magnitude through an unambiguous measure of M/R from the surface redshift of a narrow line, greatly constraining the Equation of State for ultra-dense material. It is possible that the SXS on ASTRO-H can detect this from an accreting neutron star with low surface velocity in the line of sight i.e. either low inclination or low spin. Currently there is only one known low inclination LMXB, Ser X-1, and one known slow spin LMXB, J17480-2446 in Terzan 5. Ser X-1 is a persistent source which is always in the soft state (banana branch), where the accreting material should form a equatorial belt around the neutron star. A pole-on view should then allow the NS surface to be seen directly. A 100 ks observation should allow us to measure M/R if there are any heavy elements in the photosphere at the poles. Conversely, J17480-2446 in Terzan 5 is a transient accretion powered millisecond pulsar, where the accreting material is collimated onto the magnetic pole in the hard (island) state (L_x < 0.1 L_Edd). The hotspot where the shock illuminates the NS surface is clearly seen in this state. A 100 ks ToO observation of this (or any other similarly slow spin system) in this state, may again allow the surface redshift to be directly measured. (abstract continues)
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