A proton is composed of uud. Are the two up quarks paired up to cancel each other's spin or are one up quark and one down quark paired up?

I know the three quarks may only carry a small proportion of the total proton spin. But they still need to be aligned somehow.

I see the following figure on http://www.lns.mit.edu/nig/programs. It seems in most cases the two protons in He3 are paired up. Could the quarks in a nucleon work in a similar way?

enter image description here

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    $\begingroup$ On the wiki, you can find exotic baryons differing from the proton/neutron only that they have +++ spin configuration. This results a highly unstable particle with spin 3/2, decaying in the order of $10^{-20} s$ to a proton/neutron. $\endgroup$
    – peterh
    Sep 2, 2016 at 19:29
  • $\begingroup$ @peterh The Delta baryons could probably be considered as a case where the three quarks are not paired at all. That is why they have spin 3/2. $\endgroup$
    – Fan
    Sep 2, 2016 at 19:35

1 Answer 1


The wave function of a proton is $2|u\uparrow u\uparrow d\downarrow\rangle-|u\uparrow u\downarrow d\uparrow\rangle-|u\downarrow u\uparrow d\uparrow \rangle$... So the probability of having u paired up with d is 2/3, and that of having u paired up with u is 1/3.

  • $\begingroup$ Here you can get a latex tutorial to tune your formatting skills. $\endgroup$
    – peterh
    Sep 9, 2016 at 16:56

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