OTOH, how does one know in the scattering they don’t flip each other?
Interesting question.
The short answer is that you /don't/ know a_priori ...
but you can figure it out by doing a little bit of work.
Let's start by assuming that it might flip. Then we just
need to think of a mechanism and calculate the rate.
Each atom is strongly magnetized. The electron is like
a little bar magnet. Suppose atom A flies past atom B.
Whether they collide or not, this creates a time-varying
magnetic field. Calculate the probability that this
field causes a spin flip. Fermi's golden rule.
Answer: the rate is really small.
Now suppose the atoms actually collide. This distorts
the electron cloud. This in turn affects the nucleus,
due to hyperfine interactions. Calculate the spin-flip
rate. Answer: really small.
Lather, rinse, repeat. Try any mechanism you can think
of.
If there is no mechanism that can cause an appreciable
probability of spin flip, then the spin isn't going to
flip. Spins don't flip by magic.
===========
Also: The nuclei are identical particles, so you get to
ask whether they might undergo exchange.
Again you need to come up with a /mechanism/. Quantum
mechanical exchange is not magic. It's not a mathematical
symmetry. It is a /physical/ process. There has to be
a physical pathway for one particle to hike from point A
to point B, while the other particle hikes from point B
to point A. The probability of a hydrogen nucleus
crawling outside of its electron cloud is reeeeeally
small. There's an enormous energy barrier.
My reference for all such things is
Feynman and Hibbs
_Quantum Mechanics and Path Integrals_
I found that book very difficult to read, but worth
the trouble.