  One and two-electron systems confined in a single and coupled quantum dots
defined within a nanowire with a finite radius are studied in the context of
spin-orbit coupling effects. Anisotropy of the spin-orbit interaction is
discussed in terms of the system geometry and orientation of the external
magnetic field vector. We find that there are easy and hard spin polarization
axes and in the quantum dot with strong lateral confinement electron spin
becomes well defined in spite of the presence of spin-orbit coupling. We
present an analytical solution for the one-dimensional limit and study its
validity for nanowires of finite radii by comparing the results with a full
three-dimensional calculation. The results are also confronted with the recent
measurements of the effective Lande factor and avoided crossing width
anisotropy in InSb nanowire quantum dots [S. Nadj-Perge et al., Phys. Rev.
Lett. 108, 166801 (2012)].
