Pop And Shine

This is the case where after a collision, a particle of high energy state $n\gt1$ is created, that transit to the lowest energy state, $n=1$,

with the emission of a photon.  This allows for radiations, in addition to particle creation, in the process of particle decomposition.

At this point there seems to be no simple formulation for,

$\require{AMScd}$
$$\begin{CD}       f@>{\text{collision Xform}}>>f_0+f_1+f_2+... \end{CD}$$

Good night