The only di-nucleon bound state is the n-p system (the deuteron); the n-n and p-p di-nucleon bound systems are not observed in nature. This is because:
Nuclear forces are strongly spin-dependent
The deuteron is bound only in the spin-triplet \(^{3}S_{1}\) state; the spin-singlet \(^{1}S_{0}\) two-nucleon state is unbound.
For two identical nucleons (n-n or p-p) the Pauli principle forbids the symmetric spin-triplet S-wave state, leaving only the unbound singlet channel; hence no n-n or p-p bound state exists.
Charge independence alone would predict identical bound states in all three channels; the observed asymmetry between triplet and singlet channels shows a strong spin dependence of the nuclear force.
Hence, nuclear forces are strongly spin-dependent.
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