How to determine isospin $T$ (not just $T_z$) of a nuclear ground state I’m trying to work out the total isospin and the $z$-component of the isospin for specific elements like $^{20}O$ and $^{20}F$ in the ground state. I’ve worked out the $z$-component, as I concluded this is just
$$T_z=(1/2) (Z-N).$$
My question is how do I work out the total isospin? I had a look at the nndc and found the isospin of $^{20}O$ to be $T=2$, but how do i calculate this?
I tried adding the 8 proton (isospin 1/2) and the 12 neutron (isospin 1/2) but it’s wrong and I am unsure of how the total isospin itself is calculated.
 A: Nuclei are strongly interacting quantum many-body systems, and there is no simple algorithm (theoretically or experimentally) for assigning spin, isospin and parity. 
Experimentally, if a nucleus has isopsin $I$ then it should be a member of a multiplet of dimension $(2I+1)$. This is not trivial to check because you have to correct for the Coulomb interaction (members of the multiplet have different charge), and some members of the multiplet may be unstable or difficult to observe. There are various other ways for assigning isospin based on selection rules for decays etc. 
A simple first guide is the shell model. $^{16}O$ is a closed shell nucleus with $J=I=0$. $^{20}O$ has 4 neutrons outside the closed shell, so we would expect $I=2$. 
$^{20}F$ has 3 neutrons and a proton outside a closed shell core. This could be $I=2$ or $I=1$, but neutrons and protons like to make pairs with $(I=1,J=0)$ (this is the channel in which we find $nn$ and $pp$ superfluidity) or $(I=0,J=1)$ (the deuteron channel), so my guess would be $I=1$. 
These guesses are confirmed by nuclear data tables. 
