  We report on the detailed modelling of the X-ray spectra of three likely
neutron stars. The neutron stars, observed with XMM-Newton are found in three
quiescent X-ray binaries in the globular clusters: omega Cen, M 13 and NGC
2808. Whether they are accreting at very low rates or radiating energy from an
accretion heated core, their X-ray spectra are expected to be those of a
hydrogen atmosphere. We use and compare publicly available hydrogen atmosphere
models, with constant and varying surface gravities to constrain the masses and
radii of the neutron stars. Thanks to the high XMM-Newton throughput, and the
accurate distances available for these clusters, using the latest science
analysis software release and calibration of the XMM-Newton EPIC cameras, we
derive the most stringent constraints on the masses and radii of the neutron
stars obtained to date from these systems. A comparison of the models indicate
that previously used hydrogen atmosphere models (assuming constant surface
gravity) tend to underestimate the mass and overestimate the radius of neutron
stars. Our data constrain the allowed equations of state to those which concern
normal nucleonic matter and one possible strange quark matter model, thus
constraining radii to be from 8 km and masses up to 2.4 M$_\odot$.
