Spin-Spin interaction question

[DaveSmith]

According to wikipedia
http://en.wikipedia.org/wiki/Diproton
"Diprotons are not stable; this is due to spin-spin interactions in the nuclear force, and the Pauli exclusion principle, which forces the two protons to have anti-aligned spins and gives the diproton a negative binding energy."

But spin in proton and neutron is also the same (spin=1⁄2, isospin=1⁄2), and a proton and neutron stick together so why can't p-p or n-n can stick together?

 

[tom.stoer]

In pp and nn isospins are identical, therefore (due to the Pauli principle for identical particles) you only have one arrangement for spin (which results in a slightly non-bound pp or nn) whereas for np the two particles are not identical and there is no restriction for the spin (which results in an slightly unbound np which we do not consider and a bound np = the deuteron).

For nn and pp the total interaction potential (it is not a simple potential like exp(-r/a)/r but something more complicated) for the required spin and isospin orientation is slightly attractive (which can be seen in the partial wave analysis of pp and nn scattering) but not attractive enough to form a bound state. Perhaps you remember from QM that in dim=1 every attractive potential has at least one bound state but in dim=3 this need not be the case.