Saha Equation In Plasma for Muons

[STZweig]

TL;DR Summary

If I have a fully ionized hydrogen plasma and I introduce some muons into the plasma, does the Saha equation apply to the muons.

I am currently working on the determining the viability of muon-catalyzed fusion in a dense but tepid plasma and the first question pertains to the formation of muonic atoms once muons are injected into the plasma. Suppose the plasma is sufficiently dense such that pressure ionization ensures that all of the electrons are free. But since muons are much more massive than electrons, they can still form bound states. Assume the density of muons is less then that of the ions and that the ions and muons can be treated classically, can a version of the Saha equation where every parameter that would pertain to electrons is changed to pertain to the muons be applied?