  We analyse four XMM-Newton observations of the neutron-star low-mass X-ray
binary EXO 0748$-$676 in quiescence. We fit the spectra with an absorbed
neutron-star atmosphere model, without the need for a high-energy (power-law)
component; with a 95 per cent confidence the power-law contributes less than 1
per cent to the total flux of the source in $0.5-10.0$ keV. The fits show
significant residuals at around 0.5 keV which can be explained by either a hot
gas component around the neutron star or a moderately broad emission line from
a residual accretion disc. The temperature of the neutron-star has decreased
significantly compared to the previous observation, from 124 eV to 105 eV, with
the cooling curve being consistent with either an exponential decay plus a
constant or a (broken) power law. The best-fitting neutron-star mass and radius
can be better constrained if we extend the fits down to the lowest possible
energy available. For an assumed distance of 7.1 kpc, the best-fitting
neutron-star mass and radius are $2.00_{-0.24}^{+0.07}~M_\odot$ and
$11.3_{-1.0}^{+1.3}$ km if we fit the spectrum over the $0.3-10$ keV range, but
$1.50_{-1.0}^{+0.4}~M_\odot$ and $12.2_{-3.6}^{+0.8}$ km if we restrict the
fits to the $0.5-10$ keV range. We finally discuss the effect of the assumed
distance to the source upon the best-fitting neutron-star mass and radius. As
systematic uncertainties in the deduced mass and radius depending on the
distance are much larger than the statistical errors, it would be disingenuous
to take these results at face value.
