We consider a system of fermions in the continuum case at zero temperature,
in the strong-coupling limit of a short-range attraction when composite bosons
form as bound-fermion pairs. We examine the density dependence of the size of
the composite bosons at leading order in the density ("dilute limit"), and show
on general physical grounds that this size should decrease with increasing
density, both in three and two dimensions. We then compare with the analytic
zero-temperature mean-field solution, which indeed exhibits the size shrinking
of the composite bosons both in three and two dimensions. We argue,
nonetheless, that the two-dimensional mean-field solution is not consistent
with our general result in the "dilute limit", to the extent that mean field
treats the scattering between composite bosons in the Born approximation which
is known to break down at low energy in two dimensions.Comment: Revised version to be published on Eur. Phys. Jour. B, 7 pages, 1
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