I have one question regarding these quantum numbers. When I read through my textbook, it sometimes just says something like: "And this atoms ground state has $J^{\pi} = 0^+$ and isospin $+1$" – as an example.
Is this supposed to be measured quantities, that you just look up (I know you can do that), or is there some trick to see that, oh, that atom got this and that.
It has just been bothering me 🙂
Thanks in advance.
Best Answer
The ground state nuclear spin quantum number and parity, $J^{\pi}$ for all even-even nuclei is $0^+$. The isospin can vary, but for the ground state of even-even will probably be either 0 or 1.
The isospin quantum number, $I$, is limited to the range of $$\frac{|Z-N|}{2}\le I \le \frac{Z+N}{2}.$$
The $J$ for odd-mass-number nuclei will be a half-integer (1/2, 3/2, 5/2, etc.) and the parity depends on the shell of the extra (odd) nucleon.
The $J$ of odd-Z/odd-N nuclei are integer, but not necessarily zero, and the parity, depends on a combination of shells which contain the odd nucleons.
See this Wikipedia article to learn about the nuclear shell model.