# Parity of the decaying particle

1. Dec 20, 2013

### rbwang1225

1. The problem statement, all variables and given/known data
A particle of spin 3/2 decays into a nucleon and pion.
Show how the angular distribution in the final state (with spin not measured) can be used to determine the parity of the decaying particle.

2. Relevant equations
The parity of a nucleon and a pion is 1 and -1,respectively.
The spin of a nucleon and a pion is 1/2 and 0,respectively.

3. The attempt at a solution
The total spin of the nucleon and pion is 1/2.
Then I stuck here...since total spin 1/2 can not form a spin 3/2 particle?
I know it must somewhere went wrong.
Any advice would be very appreciated!

2. Dec 21, 2013

### vela

Staff Emeritus
Total angular momentum is conserved, not spin. You have to take into account the orbital angular momentum of the final state.

3. Dec 21, 2013

### rbwang1225

The final state has total spin 1/2, so the orbital angular momentum of the final state is 1?
And thus the parity of the decaying particle is 1*(-1)*(-1)=1?
I am not very sure why final state has orbital angular momentum.
When discussing the hydrogen atom, we think of the electron of the hydrogen is in a central potential which gives the contribution of angular momentum.
Does the orbital angular momentum of the final state come from the same argument?

4. Dec 21, 2013

### vela

Staff Emeritus
You also have to consider the case where $l=2$ because combining it with spin-1/2, you can get a state with $j=3/2$.

I guess calling it orbital angular momentum is a bit misleading. It's the angular momentum due to the spatial dependence of the wave function of the final state.