Arc Statistics with Realistic Cluster Potentials. I. Method and First Results

{}From the lensing properties of a numerically simulated cluster, from the statistical properties of the giant arcs produced by the cluster, and from comparing the cluster properties derived both from lensing and from the X-ray properties of the intracluster gas, we conclude (1) that clusters may be significantly more efficient for lensing than estimated from their velocity dispersion on the basis of iso- thermal-sphere models, (2) that the discrepancy between cluster core radii derived from lensing and from their X-ray surface brightness may be understood assuming that the intracluster gas was expelled from the cluster galaxies when the dark `body' of the cluster had already formed, and (3) that clusters may be efficient in producing giant arcs even if they have extended cores and a fairly shallow sur- face-density profile. This may mean that arcs may be much easier to produce, and therefore more abundant, than previously estimated.