Quarks and gluons in hadrons and nuclei Page: 11 of 31
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A very beautiful demonstration of symmetry at work is the magnetic moment of
two similar sets of systems of three, viz.
(N ;P up/ uN = -3/ 2
and the nuclei
H3 ; He3
He/ uH = -2/3.
The Pauli principle for nucleons requires He4 to have no magnetic moment:
ip(He4; P pN+N* = 0.
He3 = He4 - N
H3 a He4- P
uHe3 _ UN
To get at this
He3 = ppn: pp
S = 0.
result in a way that will bring best comparison with the
example, let's study the He3 directly.
are flavor symmetric; hence, spin antisymmetric; i.e.,
[He3]+ (pp), n
and so the pp do not contribute to its magnetic moment. The magnetic moment (up
to mass scale factors) is
uHe3 = 0 + uN. (1
uH=0 + up. (1
Now let's study the nucleons in an analogous manner.
The proton contains u,u flavor symmetric and color antisymmetric; thus the
spin of the "like" pair is symmetric (S = 1) in contrast to the nuclear example
where this pair had S = 0. Thus coupling spin 1 and spin 1/2 together, the
Here’s what’s next.
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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/m1/11/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.