  In linearised continuum elasticity, the elastic strain due to a straight
dislocation line decays as $O(r^{-1})$, where $r$ denotes the distance to the
defect core. It is shown in Ehrlacher, Ortner, Shapeev (2016) that the core
correction due to nonlinear and discrete (atomistic) effects decays like
$O(r^{-2})$.
  In the present work, we focus on screw dislocations under pure anti-plane
shear kinematics. In this setting we demonstrate that an improved decay
$O(r^{-p})$, $p > 2$, of the core correction is obtained when crystalline
symmetries are fully exploited and possibly a simple and explicit correction of
the continuum far-field prediction is made.
  This result is interesting in its own right as it demonstrates that, in some
cases, continuum elasticity gives a much better prediction of the elastic field
surrounding a dislocation than expected, and moreover has practical
implications for atomistic simulation of dislocations cores, which we discuss
as well.
