Finally, in Fig. 3.9, we show results for the mean square radius in the
transverse direction. The cross-over from 3D to 1D is clearly visible in the case of
, for both the HS and SS potential, and for the HS potential in the case of
and
. For the system with
and
we only see
small deviations from
for the largest
values of
. In the
, as well as in the
case
with the SS potential, the transverse density profile is well described by the
harmonic oscillator wave function and we find
over the whole range of values of
. It is worth noticing that for
the
system with SS potential, the largest deviations from
are achieved for
, corresponding to a
transverse confinement
where
is the range of the SS potential.
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