What is the Relationship Between Spin and Parity in Nuclei?

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My table of nuclides has a column for Spin/Parity for the nuclides when applicable. It says it is the nuclei's total spin... yet I was under the assumption that a nucleus would have different spins depending if the proton and neutrons have various combination of up and down spins.
 
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The table gives you the spin of the lowest-energy state. All other combinations would be excited and unstable.
 
Oh yeah, your are right, I didn't think of it like that. I see what you mean, thank you.
 

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