  We study the superconducting transition in a two-dimensional electron gas
with strong Rashba spin-orbit coupling. We assume low electron density, such
that only the majority spin band participates in the transition. We show that
the superconducting transition follows either the Bose-Einstein condensation
(BEC), or the Bardeen-Cooper-Schrieffer (BCS) scenarios, depending on the
position of the chemical potential with respect to the bottom of the majority
band, and the strength of the Coulomb repulsion between electrons. Hence, the
BEC-BCS crossover in this system can be driven either by the change in the
chemical potential, or the distance to a gate.
