  We present an XMM-Newton observation of A1413, a hot (kT = 6.5 keV) galaxy
cluster at z=0.143. We construct gas and temperature profiles up to ~1700 kpc,
equivalent to ~0.7 r_200. The gas distribution is well described by a beta
model in the outer regions, but is more concentrated in the inner ~250 kpc. We
introduce a new parameterisation for the inner regions, allowing a steeper gas
density distribution. The projected radial temperature profile declines
gradually towards the outer regions, by ~20% between 0.1 r_200 and 0.5 r_200,
and is well described by a polytropic model with gamma = 1.07+/-0.01. We find
that neither projection nor PSF effects change substantially the form of the
temperature profile. Assuming hydrostatic equilibrium (HE) and spherical
symmetry, we use the observed temperature profile and the new parametric form
for the gas density profile to produce the total mass distribution. The mass
profile is remarkably well fitted with the Moore et al. (1999) parameterisation
with a concentration parameter in the range expected from numerical
simulations. There are several indications that beyond a density contrast delta
\~600, the gas may no longer be in HE. There is an offset with respect to
adiabatic numerical simulations in the virialised part of the cluster, in that
the predicted mass for the cluster temperature is ~40% too high. The gas
distribution is peaked in the centre primarily as a result of the cusp in the
dark matter profile. The X-ray gas to total mass ratio rises with increasing
radius to f_gas ~ 0.2. These data strongly support the validity of the current
approach for the modelling of the dark matter collapse, but confirm that
understanding the gas specific physics is essential. (Abridged)
