  Nonthermal velocity distributions of radical atoms in various low-temperature
plasmas have been observed for decades. Although this nonthermality has been
attributed to the generation of energetic radicals by dissociation, the
distribution has been difficult to quantitatively understand because the
theoretical form considering collisional relaxation remains missing. Here,
based on the collision theory and experimental observations, we show that a
power-law velocity distribution is robustly formed through the collisional
energy cascade of energetic radicals. The dissociation-degree dependence of the
power-law index is also found. We propose an analytical form to represent the
distribution, which can be used for plasma-diagnostics.
