Show the following reaction cannot occur (from introductory high energy course)

[enjoi668]

Homework Statement

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.

Homework Equations

Conservation laws

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

http://quantummechanics.ucsd.edu/ph130a/130_notes/node323.html

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 ideas on how to start this problem off or if I'm going about it the right way and I'm just missing something

 

[vela]

I have the third edition of Perkins. I hated that book.

Your approach is probably the right one. I haven't worked it out, but I think you're on the right track. In my copy of Perkins, there's a section on pion parity, section 3.3.1, which has a similar analysis to the one you linked to. You can look at the final state as the neutron pair, taken as a whole, plus the pion. When you do that, how does that affect the parity of the final state?