  In this paper, we present the density, \rho, velocity dispersion, \sigma, and
\rho/\sigma^3 profiles of isotropic systems which have the energy distribution,
N(E)\propto[\exp(\phi_0-E)-1], derived in Paper I. This distribution, dubbed
DARKexp, is the most probable final state of a collisionless self-gravitating
system, which is relaxed in terms of particle energies, but not necessarily in
terms of angular momentum. We compare the DARKexp predictions with the results
obtained using the extended secondary infall model (ESIM). The ESIM numerical
scheme is optimally suited for the purpose because (1) it relaxes only through
energy redistribution, leaving shell/particle angular momenta unaltered, and
(2) being a shell code with radially increasing shell thickness it has very
good mass resolution in the inner halo, where the various theoretical
treatments give different predictions. The ESIM halo properties, and especially
their energy distributions, are very well fit by DARKexp, implying that the
techniques of statistical mechanics can be used to explain the structure of
relaxed self-gravitating systems.
