  We report on numerical simulations of the intrinsic spin Hall effect in
semiconductor quantum wires as a function of the Rashba spin-orbit coupling
strength, the electron density, and the width of the wire. We find that the
strength of the spin Hall effect does not depend monotonically on these
parameters, but instead exhibits a local maximum. This behavior is explained by
considering the dispersion relation of the electrons in the wire, which is
characterized by the anticrossing of adjacent subbands. These results lead to a
simple estimate of the optimal wire width for spin Hall transport experiments,
and simulations indicate that this optimal width is independent of disorder.
The anticrossing of adjacent subbands is related to a quantum phase transition
in momentum space, and is accompanied by an enhancement of the Berry curvature
and subsequently in the magnitude of the spin Hall effect.
