# How are the spins of three quarks in a nucleon aligned?

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?

• 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. Sep 2, 2016 at 19:29
• @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.
– Fan
Sep 2, 2016 at 19:35

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.