We All Have Our Say, Give And Take

We can do away with the notion of colliding atoms and think of the high energy experimental conditions as being conducive to the formation of small particles,

In the top most diagram, a small particle passes through a big particle with energy transitions $-E_{1\rightarrow n}$ and $E_{n\rightarrow 2}$ occurring, on entering the big particle and on leaving the big particle.  Both emission and absorption of energy occur in the same process.  The overall change in energy state is,

$\Delta E_{1\rightarrow 2}=E_{n\rightarrow 2}-E_{1\rightarrow n}$

but $-E_{1\rightarrow n}$ is energy emission and $E_{n\rightarrow 2}$ is energy absorption.

In the middle diagram, the small particle coalesce with the big particle and the lowest energy level attained is,

$n=n_{ large }+n_{ 1 }$

and the resulting bigger particle subsequently breaks into $n-n_2$ and $n_2$ particles where $n_2\ne n_1$.  This differ from the toppest case where $n\ne n_{ large }+n_{ 1 }$ but simply $n\gt n_1$.  The small particle passing through the big particle retains its distinctiveness because of its high momentum.  These two diagrams provide two scenarios as to what happened to the small particle inside the big particle.  In both cases a subsequent departure follows coalescence.

The third diagram shows a simple coalescence without a subsequent separation.  Only one singular energy emission occurs as $n_1\rightarrow n_{\small{large}}+1$.

All three process occur simultaneously.  Emissions form the colored background against which dark absorption lines show up in contrast.

Have a nice day.

Note:  This discussion is of all $n_1$, not just $n_1=1$.  The case of $n_1=1$ generates an absorption series given the two processes involved; changing $a_{\psi}$ and changing orbital energy level as according to Bohr model.