 Degeneracy onset from thermal wavelength

Equating thermal de Broglie wavelength $h/\sqrt{2\pi m{k}_{B}T}$ to mean particle spacing $n^{-1/3}$ gives the displayed quantum-degeneracy scale. It is an onset estimate rather than a universal phase-transition temperature. Different typical-momentum conventions change its order-one factor; density, mass, spin degeneracy and interactions determine the detailed crossover or condensation criterion.