Total Angular Momentum in Nuclear Shell Model

1. Mar 25, 2012

mackabra

1. The problem statement, all variables and given/known data
Calculate the allowed total angular momentum quantum numbers J for 2 protons in a nuclear shell model state j = 3/2.

2. Relevant equations
J = j1 + j2 where j are the total angular momenta of each proton. Protons are spin 1/2, orbital angular momentum L is not given.

3. The attempt at a solution
Protons are identical, and therefore cannot occupy the same state. I need some clarification on the the addition of the angular momenta.
I know that for a completely filled state, J = 0. However does this come from the fact that all the mj's cancel out (mj = -j, -j+1, ... j) , and how is this related to J = j1+j2+j3+etc...?

Any help would be appreciated
Thank you
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution