This is from Introduction to High Energy Physics by Perkins, question 3.1
Show that the reaction π- + d → n + n + π0 cannot occur for pions at rest.
the π's are pions, the d is a deuterium, and the n's are obviously neutrons.
I started from the knowledge that the intrinsic parity of the pions are both = -1, and that the internal parity of d and n is =1.
I also know the spins to be 0 for the pions, 1 for deuterium, and 1/2 for the neutrons
The Attempt at a Solution
Our professor suggested the pions are both in s-wave configurations if they are at rest (?)
I tried following the arguments that ultimately decided the intrinsict parity of pi-, i.e.
something like this
to try to find some kind of contradiction if an extra π0 is included, however I didn't seam to get anywhere as that argument is built upon the fact that the final state consists of two identical fermions...
I've been working on this for about an hour, so I'm really just looking for any idea's on how to start this problem off or if I'm going about it the right way and I'm just missing something