  This is the third paper of a series of our works on the self-similar
orbit-averaged Fokker-Planck (OAFP) equation. The first paper provided an
accurate spectral solution of the equation for isotropic pre-collapse star
clusters and the second detailed the physical feature of the model. Based on
the works, the present work applies the solution to the observed structural
profiles of Galactic globular clusters. For fitting to the profiles, the most
fundamental (quasi-)stationary model, the King model, and the variants have
shown successful results while they can not apply to core-collapsing and
core-collapsed clusters at the late stage of the relaxation evolution. We
propose an energy-truncated self-similar OAFP model that can apply to clusters
at both the early and late stages of the evolution. This new model fits the
structural profiles of at least half of Galactic globular clusters while it
also applies to core-collapsed stars with resolved cores. As a main result, we
provide the completion rate of core collapse against concentration for the
clusters. Also, we show our new model can apply to the globular clusters even
in a broad range of radii (0.01$\sim$10 arcminutes). However, since our model
includes polytrope (elongated outer halo), the tidal radius of the model
becomes unrealistically large for some clusters. To avoid the issue, we also
propose an approximated form of the new model. Lastly, we report that Milky Way
globular clusters with low concentrations have the same spatial structures as
stellar polytropes and discuss whether such polytropic cluster is a reasonable
concept.
