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(It is recommended that readers read the following introduction
before reading this page:
click here.
The following short note
linked herein contains one paragraph proving that QCD has
been constructed on the basis of an erroneous argument.
click here.
The following article explains why the ground state of the
Δ++,
Δ- and Ω-
baryons can be explained by ordinary quantum
mechanical laws and without using the color variable.
click here.
In the following lines
it is shown how the regular charge-monopole theory discussed
in this site can explain the rather low energy level of the
Δ1232
baryons. Towards this end, the general analogy with atomic spectroscopy
is used together with the large quantum of the elementary
unit of the magnetic monopole charge.
The Δ 1232 baryon is an even parity state
with a total angular momentum J=3/2 and an isospin I=3/2. The
I=3/2 is completely symmetric. Therefore the spatial + spin
part of the quarks' wave function must be completely antisymmetric.
Hence, the symmetry of its quantum mechanical state is analogous
to that of an atom/ion having 3 electrons.
In atomic spectroscopy, quantum mechanics explains Hund's rule.
This rule states that a symmetric spin state of electrons (and a
completely antisymmetric state of the spatial part of the wave
function) takes a lower energy level, relative to other states
of the same configuration. The reason for the validity of Hund's rule is
that in a completely antisymmetric spatial state, the exchange
integral increases the binding energy of the system. An
analogous effect is seen in the energy levels of the He atom,
where the binding energy of a triplet state is greater than
that of the corresponding singlet state.
For a presentation of the He atomic energy levels,
Click here.
The system of three quarks attracted by the baryonic core is
analogous but spin dependent interactions are much stronger.*
Thus, considering the rather high value of the
magnetic monopole quantum g (where g2 is probably two
orders of
magnitude larger then e2 ≈ 1/137), one expects that
the value of the exchange integral is quite large.
Now let us examine a term of the full wave function
of the Δ1232 baryon, where all
the three valence quarks are in an s-wave and their radial
excitation is 0,1,2, respectively. The spins of the
three quarks are parallel (and symmetric). The radial excitations
increase the energy of the state, but each of the three
pairs of quarks yields an
exchange integral of the completely antisymmetric
spatial part of the wave function. Here each of these exchange
integrals decreases the energy of the state. Therefore, it is not
unreasonable to find that the lowest energy level of the
Δ baryons is around 1232 MeV.
In principle, one may increase the Hilbert space and use a basis
containing more than one configuration. For reading an example
containing some functions in a jj coupling scheme
Click here.
*Here the jj coupling may be better than the LS coupling.
However, this point does not destroy the qualitative
arguments presented here.
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