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.
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