Globular cluster star density as a function of distance from the center

The usual thing is a King model.

There are indeed free parameters. These are the central density, the "core radius" and a tidal truncation radius.

The background and rationale for these models is given in the link. They provide a pretty good representation of the surface density of globular clusters (or indeed open clusters). They require a numerical scheme to "deproject" from the plane of the sky to 3D.

If you find the nitty-gritty of Abel integrals too tricky in the deprojection, then you could always approximate with a Plummer model. This is analytically and computationally easier to deal with, but lacks a bit of physical realism. Central density and a characteristic radius are free parameters here.