Question

How can I calculate nuclear spin for Na for example?

Answer 1

First you need to define what isotope you are talking about!

Say we have Na(Z=11, N=15). Now both N and Z are odd, so we have to "align spin, and flip L accordingly to get I".

For protons, looking up the shell model table ( https://en.wikipedia.org/wiki/Nuclear_shell_model#/media/File:Shells.png), we have our 11th proton resides at the d(5/2) shell. This means the total angular momentum for proton j is 5/2, and l=2 (d shell).

For neutrons, looking up the same table, for the 15th at the 2s(1/2) shell, so the total angular momentum for neutron j is 1/2, and l=0 (s shell).

Now for the tricky part. For proton, to get j=5/2 with l=2, we must have s=1/2. For neutron, for j=1/2 for l=0, s=1/2 as well. Adding "s with s" and "l with l" yields I=(2+0)+(1/2+1/2)=3. The parity of both shells in question is +, so the term symbol is 3+.

For Na(11, N=17), we have for proton d(5/2) and for neutron d(3.2) (look up the table as before, and go to the correct filled level, 17 neutrons is d(3/2)).

For proton, for j=5/2 when l=2 means s=1/2 as before.
For neutron, for j=3/2 when l=2 means s=-1/2.
So we "align s" meaning to say for neutron, l=-2 and s=1/2.
Adding "l with l" and "s with s" yields: (2-2)+(1/2+1/2)=1
Parity is + x + since both have even l.
Thus 1+

Hopefully these examples can help you in determining the ground state spin and parity assignment.