  We investigate theoretically the combined effects of the electron-electron
and the Rashba spin-orbit interactions on two electrons confined in
quasi-one-dimensional AlInSb-based double quantum dots. We calculate the
two-electron wave functions and explore the interplay between these two
interactions on the energy levels and the spin of the states. The energy
spectrum as a function of an applied magnetic field shows crossings and
anticrossings between triplet and singlet states, associated with level mixing
induced by the spin-orbit coupling. We find that the fields at which these
crossings occur can be naturally controlled by the interdot barrier width,
which controls the exchange integral in the structure.
