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In this discussion,
quarks are assumed to be Dirac particles that carry one (negative) unit of
magnetic monopole. Now, in the Regular Charge-Monopole Theory (RCMT)
(click here),
monopoles are counterparts of charges. Thus, charges and monopoles
are related by duality
transformations. Hence, one expects to find a similarity between a
system of quarks characterizing a nucleon (a proton or a neutron)
and a system of electrons characterizing an atom.
This page is dedicated to
a general description of the similarity and the difference between the two
systems. The excellent success of the quantum mechanical treatment of
atomic spectroscopy justifies a comparison of the two systems.
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Differences between atomic physics and nucleons.
The elementary unit of the
electric charge is quite small and e2≈1/137.
Now, in RCMT the elementary unit of magnetic charge is a free parameter.
However, hadronic data indicate that the elementary unit of magnetic
charge is about unity. Hence, relativistic effects are
expected to be significant in
a quantum mechanical description of hadronic systems. In particular:
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The size of spin-related interactions is similar to the Coulomb-like
interactions. Hence, in nucleons, the analog of the fine-structure
split is expected to be very large.
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In atomic spectroscopy the number of particles (electrons) is a constant
of the motion (the Lamb shift is a very small perturbation). This property
does not hold for nucleons where antiquarks are measured directly.
(click here
for reading a discussion of this point.)
It follows that additional quark-antiquark pairs should be included
in a part of the terms describing the entire wave function.
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The effects mentioned in the
foregoing points indicate that much more configurations are required for
a good description of the state.
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In atomic spectroscopy there is one kind of particle - the electron.
On the other hand, today six kinds of quark flavor are known. In
particular, two kinds of quarks (called u,d) take part in
the set of three valence quarks of a nucleon.
Thus, the approximate isospin
symmetry arises. Atomic spectroscopy does not contain an
analogous phenomenon.
Similarities between atomic physics and nucleons physics.
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The overall charge of a neutral atom vanishes. Obviously, an analogous
property holds for the overall magnetic monopole of a nucleon. Indeed,
the nuclear force resembles the van der Waals force between neutral
molecules. There is no Coulomb-like attraction/repulsion between
nucleons. For this reason it is mandatory to assume that nucleons
have a core carrying three (positive) monopole units. Thus, the
overall monopole charge of the three valence quarks and of the baryonic
core vanishes. Hence, the state of a nucleon resembles a
state of a neutral atom.
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Atomic states are described by a sum of terms belonging to many
configurations. (An example of this claim can be seen in [1],
where 35 configurations
are used for describing the ground state of a two-electron atom.)
However, due to the arguments presented in 1.A-1.C above, one expects that
the number of configurations required for a description of
three valence quarks is much larger.
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Like in atomic physics, each term must have the required angular momentum
and parity. However, here one must also treat configurations having
additional quark-antiquark pairs. Thus, the additional pairs must
satisfy flavor conservation, where the members of each quark-antiquark pair
must have the same flavor.
Another problem is the structure of the baryonic core that attracts
quarks. A simple minded assumption may regard it as an elementary
point-like object. However, there are quite strong indications
supporting the idea that the baryonic core
is a more complicated system having inner closed shells of quarks.
Click here
for reading a discussion.
Obviously, if the baryonic core contains
closed shells of quarks then a calculation of the baryonic wave function
becomes an even more complicated assignment.
These principles are used in more detailed discussions of the proton,
the neutron and the Δ1232 baryon. Links to these
pages are listed below.
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The form of the proton's wave function.
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The neutron's mean-square charge radius.
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The Energy Level of the Δ1232 Baryon.
[1] A. W. Weiss, Phys. Rev. 122, 1826 (1961).
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