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.