# Quantum mechanics problem

1. Mar 24, 2010

### eoghan

1. The problem statement, all variables and given/known data
A particle (a) of spin 3/2 disintegrates into two particles (b) of spin 1/2 and (c) of spin 0. We are in the center of mass of particle (a). We don't know anything about (a) intrinsic parity, but we know that (b) and (c) have both even parity. If the parity is conserved, what values can the final orbital angular momentum take?

3. The attempt at a solution
The final total angular momentum must be equal to the initial one, so $$J^f=J^i^3/2$$.
Let L be the final total orbital angular momentum and S be the total final spin momentum. Then S=1/2.
L can take on only integer positive values, i.e. L=0,1,2,3,...
if L=0 then $$J^f=1/2$$
if L=1 then $$J^f=1/2, 3/2$$
if L=2 then $$J^f=3/2, 5/2$$
if L=3 then $$J^f=5/2, 7/2$$
and so on.

The only possible values of L are L=1 and L=2 because only for these values I can have J=3/2.
The parity is conserved, hence:
P(a)=P(b)*P(c)*(-)^L
where P() is the intrinsic parity.
So if (a) has positive parity, then L=2, if (a) has odd parity then L=1.

Well.... that is what I've done, but i'd like to know if it's right. Could you please check it out? Thanks!

N.B. I'm not english and I have some problem in translating physics matter .. so if I've written something wrong or incomprehensible, please let me know and I'll try to explain it better