Nuclear Shell Model, spin and parity

UniPhysics90

1. The problem statement, all variables and given/known data

What is the parity and possible spins predicted by the single particle shell model for the ground state of the 19K40 nucleus

(I'm most unsure about the spins)

2. Relevant equations



3. The attempt at a solution

This has 19 protons and 21 neutrons.

Odd-odd nucleus so parity is product of the parity of the shells.

Protons: 'Hole' in 1d3/2, l=2 so parity =+
Neutrons: 'Hole' in 1f7/2, l=3 so parity =-

So the parity is +*-=-

Spin of odd-odd nucleus can take values between |j1-j2| and |j1+j2| where j1 is total angular momentum of proton, and j2 is of neutron.

For proton: l=2 so j=5/2 or 3/2
Neutron: l=3 so j=7/2 or 5/2

Spin can take values of 2,3,4,5,6

Is my method for spins correct? I don't really understand what I'm doing.

Thanks