  We study the stabilization of one spatial dimension in (p+1+1)-dimensional
spacetime in the presence of $p$-dimensional brane(s), a bulk cosmological
constant and the Casimir force generated by a conformally coupled scalar field.
We find general static solutions to the metric which require the fine-tuning of
the inter-brane distance and the bulk cosmological constant (leaving the two
brane tensions as free parameters) corresponding to a vanishing effective
cosmological constant and a constant radion field. Taking these solutions as a
background configuration, we perform a dimensional reduction and study the
effective theory in the case of one- and two-brane configurations. We show that
the radion field can have a positive mass squared, which corresponds to a
stabilization of the extra dimension, only for a repulsive nature of the
Casimir force. This type of solution requires the presence of a negative
tension brane. The solutions with one or two positive tension branes arising in
this theory turn out to have negative radion mass squared, and therefore are
not stable.
