The relevant parameters of the problem are the number of particles , the ratio
of the scattering length to the transverse harmonic oscillator length
and the anisotropy parameter
. For a given set of parameters we solve exactly,
using the Diffusion Monte-Carlo method (Sec. 2.3), the many-body
Schrödinger equation (2.6) for the ground state and we calculate the
energy per particle and the mean square radii of the cloud in the axial and radial
directions. Importance sampling is used through the Bijl-Jastrow trial wave function
(2.37). For the one-body term, which accounts for the external confinement,
we use a simple gaussian ansatz (2.41)
, with
and
optimized variational parameters. The two-body term
accounts
instead for the particle-particle interaction and is chosen using the same technique
employed in Ref. [GBC99] for a homogeneous system. Of course, since DMC is an
exact method, the precise choice of
is to a large extent unimportant
and the results obtained are not biased by the choice of the trial
wave function3.1.