  We re-examine the formation of the inner Oort comet cloud while the Sun was
in its birth cluster with the aid of numerical simulations. This work is a
continuation of an earlier study (Brasser et al., 2006) with several
substantial modifications. First, the system consisting of stars, planets and
comets is treated self-consistently in our N-body simulations, rather than
approximating the stellar encounters with the outer Solar System as hyperbolic
fly-bys. Second, we have included the expulsion of the cluster gas, a feature
that was absent previously. Third, we have used several models for the initial
conditions and density profile of the cluster -- either a Hernquist or Plummer
potential -- and chose other parameters based on the latest observations of
embedded clusters from the literature. {These other parameters result in the
stars being on radial orbits and the cluster collapses.} Similar to previous
studies, in our simulations the inner Oort cloud is formed from comets being
scattered by Jupiter and Saturn and having their pericentres decoupled from the
planets by perturbations from the cluster gas and other stars. We find that all
inner Oort clouds formed in these clusters have an inner edge ranging from 100
AU to a few hundred AU, and an outer edge at over 100\,000 AU, with little
variation in these values for all clusters. All inner Oort clouds formed are
consistent with the existence of (90377) Sedna, an inner Oort cloud dwarf
planetoid, at the inner edge of the cloud: Sedna tends to be at the innermost
2% for Plummer models, while it is 5% for Hernquist models. We emphasise that
the existence of Sedna is a generic outcome. We define a `concentration radius'
for the inner Oort cloud and find that its value increases with increasing
number of stars in the cluster, ranging from 600 AU to 1500 AU for Hernquist
clusters and from 1500 AU to 4000 AU for Plummer clusters...
