  In the vortex state of a d-wave superconductor, massless Dirac quasiparticles
are scattered from magnetic vortices via a combination of two basic mechanisms:
effective potential scattering due to the superflow swirling about the vortices
and Aharonov-Bohm scattering due to the Berry phase acquired by a quasiparticle
upon circling a vortex. In this paper, we study the superflow contribution by
calculating the differential cross section for a quasiparticle scattering from
the effective non-central potential of a single vortex. We solve the massless
Dirac equation in polar coordinates and obtain the cross section via a partial
wave analysis. We also present a more transparent Born-limit calculation and in
this approximation we provide an analytic expression for the differential cross
section. The Berry phase contribution to the quasiparticle scattering is
considered in a separate paper.
