  We have undertaken a spectroscopic survey of gravitational arcs in a
carefully chosen sample of six clusters each containing a dominant brightest
cluster galaxy. We use these systems to study the relative distributions of
dark and baryonic material in the central regions. Three clusters present both
radial and tangential arcs and provide particularly strong constraints on the
mass profiles, whereas the other three display only tangential arcs and act as
a control set. We analyze stellar velocity dispersion data for the brightest
cluster galaxies in conjunction with the arc redshifts and lens models to
constrain the dark and baryonic mass profiles jointly. For the systems
containing radial arcs we find that the inner dark matter density profile is
consistent with a 3-D distribution, rho_{DM} propto r^-beta, with logarithmic
slope <beta>=0.52^{+0.05}_{-0.05} (68% CL). Similarly, we find that the
tangential arc sample gives an upper limit, beta<0.57 (99% CL). Taking the 6
clusters together, the mean dark matter distribution is quite inconsistent with
the standard Navarro, Frenk & White (1997) value, beta=1.0, at >99% confidence.
In addition, we find considerable cosmic scatter in the beta (Delta beta ~0.3)
values of the radial arc sample. We find no evidence that systems with radial
arcs preferentially yield flatter dark matter profiles as might be expected if
they were a biased subset. We discuss the validity of our 1-D mass
reconstruction method and verify its conclusions by comparing with results of a
more rigorous ray-tracing lensing code. Our results extend and strengthen the
earlier conclusions presented by Sand et al. (2002) and suggest the
relationship between dark and visible matter in the cores of clusters is more
complex than anticipated from recent simulations. (abridged)
