We study crustal oscillations in magnetars including corrections for a finite Alfvén velocity .
Our crust model uses a new nuclear mass formula that predicts nuclear masses with an accuracy very close to that of the Finite Range Droplet Model .
This mass model for equilibrium nuclei also includes recent developments in the nuclear physics , in particular , shell corrections and an updated neutron-drip line .
We perturb our crust model to predict axial crust modes and assign them to observed giant flare quasi-periodic oscillation ( QPO ) frequencies from SGR 1806-20 .
The QPOs associated with the fundamental and first harmonic can be used to constrain magnetar masses and radii .
We use these modes and the phenomenological equations of state from Steiner et al .
to find a magnetar crust which reproduces observations of SGR 1806-20 .
We find magnetar crusts that match observations for various magnetic field strengths , entrainment of the free neutron gas in the inner crust , and crust-core transition densities .
Matching observations with a field-free model we obtain the approximate values of M = 1.35 \mathrm { M } _ { \odot } and R = 11.9 \mathrm { km } .
Matching observations using a model with the surface dipole field of SGR 1806-20 ( B = 2.4 \times 10 ^ { 15 } \mathrm { G } ) we obtain the approximate values of M = 1.25 \mathrm { M } _ { \odot } and R = 12.4 \mathrm { km } .
Without significant entrainment of the free neutron gas the magnetar requires a larger mass and radius to reproduce observations .
If the crust-core transition occurs at a lower density the magnetar requires a lower mass and a larger radius to reproduce observations .