  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)
