  We investigate the effective Lande factor in semiconductor nanowires with
strong Rashba spin-orbit coupling. Using the $\mathbf{k}\cdot\mathbf{p}$ theory
and the envelope function approach we derive a conduction band Hamiltonian
where the tensor $g^*$ is explicitly related to the spin-orbit coupling
constant $\alpha_R$. Our model includes orbital effects from the Rashba
spin-orbit term, leading to a significant enhancement of the effective Lande
factor which is naturally anisotropic. For nanowires based on the low-gap, high
spin-orbit coupled material InSb, we investigate the anisotropy of the
effective Lande factor with respect to the magnetic field direction, exposing a
twofold symmetry for the bottom gate architecture. The anisotropy results from
the competition between the localization of the envelope function and the spin
polarization of the electronic state, both determined by the magnetic field
direction.
