Nuclear physics Pions and Parity?

[Davorak]

Nuclear physics Pions and Parity? Ignore, nevermind

Why can:
$$\pi^- + d \rightarrow n + n + \pi^0$$
not happen for pions at rest?

work so far:
$$\begin{array}<br /> {|c|c|c|c|c|c|}\hline&\pi^-&d&\rightarrow &n \ + \ n&\pi^0\\\hline{Spin}&0&1&\<br /> \rightarrow &1/2 \ 1/2&0\\\hline{J}&0&1&\rightarrow &L + \<br /> S&0\\\hline{Parity}&-1&1&\rightarrow &(-1)^{S+L+1}&-1\\\hline<br /> \end{array}$$
d is deuterium
S+L for the nuetron pair must be even since they are identical fermions
Partity egeinvalues -1 != 1
I think the Paritiy inequality is the key, but i can not make the connection with a physical law.
Any help would be nice, Thanks

Edit: never mind I figuared it out. Aditional angular momentum on the left hand side will flip parity(l=1,3,5...), making parity conserved again. Thanks anyway

 

[wais]

.

Thank you for sharing your thought process and solution. It is great to see that you were able to figure it out on your own. Keep up the good work!