Quarks and gluons in hadrons and nuclei Page: 9 of 31
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any pair is in the 3 and is antisymmetric. Note that 3 x 3 = 6 + 3. These are
RY-YR RY+YR (2)
Note well: Any Pair is Color Antisymmetric
The Pauli principle requires total antisymmetry and therefore any pair must
Symmetric in all else
("else" means "apart from color").
This is an important difference from nuclear clusters where the nucleons have
no color (hence are trivially symmetric in color!). Hence for nucleons Pauli says
Nucleons are Antisymmetric in Pairs (3)
and for quarks
Quarks are Symmetric in Pairs (4)
If we forget about color (color has taken care of the antisymmetry and won't
affect us again), then
(i) Two quarks can couple their spins as follows
S = 1: symmetric
S = 0: antisymmetric
(ii) Two u,d quarks similarly form isospin states
I = 1: symmetric
I = 0: antisymmetric
(iii) In the ground state L = 0 for all quarks; hence the orbital state is
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Close, F. E. Quarks and gluons in hadrons and nuclei, article, December 1, 1989; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1058782/m1/9/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.