Pion decaying to two neutrons demonstrates odd parity

[Gene Naden]

Does anyone have a reference to a good explanation of this experiment. I am looking at https://quantummechanics.ucsd.edu/ph130a/130_notes/node323.html

I am unable to comprehend the reasoning by which it determines the parity of the two neutrons in the final state. Particularly when it says the requirement of F-D statistics restricts the spin and angular momentum of the final state.

 

[mfb]

That is not a pion decaying to two neutrons. It is the reaction of a pion hitting a deuteron.

 

[Gene Naden]

Yes, I gave the wrong reaction. Thank you for correcting me.

The reference says the allowed two-neutron final states are, because they are identical fermions,
1s0
3p0,1,2
1d2
3f2,3,4

I looked up the spectroscopic notation. It says 1s0 is a singlet state, L=1, with J=0. So how can it be antisymmetric?

 

[mfb]

It does not react to 1s0. Only 3p1 is possible, as explained in the website you linked.