  The gravitational lensing properties of cosmological halos depend upon the
mass distribution within each halo. The description of halos as nonsingular,
truncated isothermal spheres, a particular solution of the isothermal
Lane-Emden equation (suitably modified for Lambda nonzero), has proved to be a
useful approximation for the halos which form from realistic initial conditions
in a CDM universe. The nonsingular TIS model reproduces many of the
quantitative features of the N-body results for CDM halos, except in the very
center, where CDM N-body halos show density profiles which vary as rho ~
r^(-alpha), alpha>1, instead of a small flat core. Possible discrepancies
between these cuspy halo predictions of the CDM N-body simulations and
observations of the inner mass profiles of dwarf and LSB disk galaxies based
upon their rotation curves and of clusters based upon strong lensing
measurements have led to a search for other diagnostics. A description of the
lensing by TIS halos would be useful in this regard, as a self-consistent model
for CDM halos in a proper cosmological context, nonsingular but otherwise
consistent with the CDM N-body results. We derive here the basic lensing
properties of individual TIS halos. For comparison, we also consider three
singular profiles: the Navarro-Frenk-White density profile, the singular
isothermal sphere, and the Schwarzschild lens. For all profiles, we compute the
critical curves and caustics, the image separation, the magnification and
brightness ratio, the shear, the time delay, and the average shear inside the
tidal radius. This provides tools for studying the statistical properties of
lensing by TIS and other lenses in the context of a theory of cosmological
structure formation.
