Nuclear / Particle Phys Notation quick q spin, parity,J

[binbagsss]

Homework Statement

When we use $J^{/pm}$ where $/pm$ gives the parity, some sources say $J$ is the spin and some say the total angular momentum, I'm confused !

Also in my notes we have $P=(-1)^l$, but looking on this thread: https://www.physicsforums.com/threads/quick-question-about-spin-parity-j-p-notation.455873/ it has $P=-1^{spin}$.?

Also confused with some other notation.. when we write $^{J} l_{symbol _s}$, where $J$ is the total angular momentuum, $s$ is the spin and $l_{symbol}$ is $s,p,d,f..$ corresponding to $l=0,1,2...$.

So looking at things such as $^{3}D_{1}$ I see we have $l=2, s=1, J=3$ and we know $J=(l+s)+...+$modulus of $(l-s)$*

BUT looking at $^{3}S_{1}$ we have $l=0,s=1,J=3$ . Which I'm confused how you get $J=3$ from *..

Thanks in advance..
2. Homework Equations

3. The Attempt at a Solution

 

[binbagsss]

bummp.