  We investigate the gravitational lensing properties of dark matter halos with
Burkert profiles. We derive an analytic expression for the lens equation and
use it to compute the magnification, impact parameter and image separations for
strong lensing. For the scaling relation that provides the best fits to
spiral-galaxy rotation curve data, Burkert halos will not produce strong
lensing, even if this scaling relation extends up to masses of galaxy clusters.
Tests of a simple model of an exponential stellar disk superimposed on a
Burkert-profile halo demonstrate that strong lensing is unlikely without an
additional concentration of mass in the galaxy center (e.g. a bulge). The fact
that most strong lenses on galactic scales are elliptical galaxies suggests
that a strong central concentration of baryons is required to produce image
splitting. This solution is less attractive for clusters of galaxies, which are
generally considered to be dark-matter dominated even at small radii. There are
three possible implications of these results: (1) dark halos may have a variety
of inner profiles (2) dark matter halos may not follow a single scaling
relation from galaxy scale up to cluster scale and/or (3) the splitting of
images (even by clusters of galaxies) may in general be due to the central
concentration of baryonic material in halos rather than dark matter.
