  Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba
axis have been predicted to open a partial gap ("helical gap") in the energy
spectrum of noninteracting or weakly interacting one-dimensional quantum wires.
By comparing kinetic energy and Coulomb energy we show that this gap opening
typically occurs at low electron densities where the Coulomb energy dominates.
To address this strongly correlated limit, we investigate Rashba wires using
Wigner crystal theory. We find that the helical gap exists even in the limit of
strong interactions but its dependence on electron density differs
significantly from the weakly interacting case. In particular, we find that the
critical magnetic field for opening the gap becomes an oscillatory function of
electron density. This changes strongly the expected signature of the helical
gap in conductance measurements.
