Undergrad Difference between parallel and antiparallel spins?

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Parallel spins in nucleons occur when both nucleons have the same spin orientation, while antiparallel spins involve one nucleon spinning up and the other spinning down. Nucleons tend to pair due to the strong nuclear force, which has a spin component. The Pauli Exclusion Principle prevents two nucleons with identical spin states from occupying the same spatial state, allowing for parallel spins only in different spatial states. There is an energy difference between the two configurations, with nucleons exhibiting parallel spins being more strongly bound than those with antiparallel spins. Understanding these spin interactions is crucial for grasping the stability of atomic nuclei.
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What is the difference between parallel and antiparallel spins for a pair of nucleons?

My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, proton with neutron. When they pair their spins either:

cancel (spins pair antiparallel) pairing of a spin-up and spin-down nucleon
add (spins pair parallel) pairing of two nucleons with both spin up or both spin down

Am I understanding this correctly? - I'm thinking I might be missing something in regards to the Pauli Exclusion Principle. How can two nucleons with the same spin state pair?
 
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How can two nucleons with the same spin state pair?
They cannot.
You can have two nucleons in different (spatial) states with the same spin orientation, however.
 
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So nucleons have a strong tendency to pair due to the nuclear force, which has a spin component. When nucleons pair their spins will either be:
(Parallel) - Both spin the same way
(antiparallel) - One nucleon spin up and one spin down

Is there an energy difference between the two as well?
 
A more important question - Why are nucleons with parallel spin more strongly bound to each other than those having anti-parallel spin.
 

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