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RULES of the QUARK-LATTICE MODEL

The model presented here is based on basic rules. After defining these rules, these rules will be used to demonstrate how nuclei can be constructed. For concreteness, models of nuclei have been built and illustrated using zome constructs (available at www.zometool.com).

Short version of rules

Rule 1: The Nature of Nucleons. Quarks are confined within their respective nucleons.
Rule 2: Color Force/Strong Force. Nucleons are bound by the strong force and quarks are confined by color.
Rule 3: Exclusion Principle. Nucleons are Fermions, that are subject to the Pauli Exclusion Principle.
Rule 4: Nearest Neighbors.
Rule 5: Electric Forces. Alignment of nucleons within a nucleus is controlled by electric bonds acting between the quarks of adjacent nucleons, the nearest neighbors.
Rule 6: Spin. Quarks are Fermions, spin is subject to the Pauli Exclusion Principle (PEP).
Rule 7: Magnetic Forces. Alignments of nucleons within a nucleus are controlled by magnetic forces acting between the quarks of adjacent nucleons, their nearest neighbors.
Rule 8: Tightest Binding. Any given system of particles in its ground state trends to the tightest bonding configuration, or the lowest energy state.
Rule 9: Balance. Mechanical balance is essential for nuclear stability.
Rule 10: Symmetry. Within the constraints of the previous rules, a given nucleus trends toward a ground state that minimizes its volume by means of various symmetry constraints.
Rule 11: Hexagonal Lattice. Nuclear stages occur in groupings of six protons and six plus �N� neutrons where �N� may be zero, two, four, six, or eight, an even number.
Rule 12: Minimum Volume. The volume of the nucleus is always a minimum.
Rule 13: Limiting Size. The size limit of large nuclei is reached when the net repulsive forces, positive charge and centrifugal force, equal or exceed the net attractive forces.
Rule 14: Excited Nuclei. Excited states of nuclei can be created when one or more of the nucleons changes positions on the nuclear lattice structure.
Rule 15: Radioactive Nuclei. Radioactive decay occurs when a more tightly bound configuration may be reached if one of the quarks within a nucleon switches and that nucleon moves to a more tightly bound position or state.

Expanded version of the rules

A. Rule 1: The Nature of Nucleons. Quarks are confined within their respective nucleons as follows:

a. Two up quarks (u, charge +2/3 e) and one down quark (d, charge -1/3 e) form a proton with net charge +e.
b. Two down quarks and one up quark form a neutron. The neutron has a net overall charge of zero. A neutron nonetheless has a magnetic moment and spin just as if it were a spinning charge.
c. The magnetic moment of the neutron is the result of the three constituent quarks.
d. Three objects like the constituent quarks of nucleons, when bound together form a triangle and define a plane. Thus, the shape of a nucleon can be described as a triangular ovoid.

B. Rule 2: Color Force/Strong Force. Nucleons are bound by the strong force and quarks are confined by color.

a. Binding of quarks within the nucleons is the result of color confinement mediated by gluons.

i. High-energy electron scattering experiments have revealed a complex structure within excited or high energy protons and neutrons.
ii. However, in the low-energy or ground state within nuclei, viewed from the outside, nucleons would look like triangular ovoids forming a plane.

b. Binding between nucleons within a nucleus is primarily by the strong nuclear force. The strong force is very short range, attractive, and acts essentially only between adjacent nucleons.

C. Rule 3: Exclusion Principle. Nucleons are Fermions, that are subject to the Pauli Exclusion Principle.

a. This keeps protons and neutrons from collapsing.
b. The exclusion principle keeps the nucleus from collapsing.
c. It also leads to restrictions on the spin of otherwise identical particle parameters within a nucleus.

D. Rule 4: Nearest Neighbors.

a. Protons always bond with neutrons

i. The two up quarks in the proton bond with the two down quarks in the neutron.
ii. The down quark in the proton binds with the up quark in the neutron.

b. Neutrons always bond to protons.

i. The two down quarks in the neutron bond with the two up quarks in the proton.
ii. The up quark in the neutron binds with the down quark in the proton.

c. Protons never bind to protons and neutrons never bind to neutrons.
d. Protons are always nearest neighbors to neutrons and vice versa.

E. Rule 5: Electric Forces. Alignment of nucleons within a nucleus is controlled by electric bonds acting between the quarks of adjacent nucleons, the nearest neighbors.

a. The electric forces are subject to the law of superposition being both attractive and repulsive.
b. The electric forces act over longer distances than the strong force and can affect the overall nuclear structure.
c. Opposite electrical charges attract.

i. In adjacent nucleons, up quarks with a +2/3 electric charge, bind only with down quarks with a -1/3 electric charge.
ii. This rule does not hold within individual nucleons.

d. Like electrical charges repel.

i. In adjacent nucleons up quarks, +2/3 electrical charge, will not bind with up quarks, +2/3 electrical charge, in adjacent nucleons.
ii. In adjacent nucleons down quarks, -1/3 electrical charge, will not bind with down quarks, -1/3 electrical charge, in adjacent nucleons.
iii. This rule does not hold within individual nucleons.

F. Rule 6: Spin. Quarks are Fermions, spin is subject to the Pauli Exclusion Principle (PEP).

a. The Exclusion Principle restricts spin for otherwise identical particles within a nucleus.

i. Each proton and neutron by itself has a spin of one-half.
ii. The spin of nucleons, protons and neutrons, represents the combined spins of their three constituent quarks.
iii. In the proton PEP dictates that the two up quarks spin in opposite directions which cancel each other, thus the spin of the down quark provides the one-half spin of the proton.
iv. In the neutron PEP dictates that the two down quarks spin in opposite directions which cancel each other, thus the spin of the up quark provides the one-half spin of the neutron.

b. Spin takes on the lowest possible value while maintaining the hexagonal lattice structure.

G. Rule 7: Magnetic Forces. Alignments of nucleons within a nucleus are controlled by magnetic forces acting between the quarks of adjacent nucleons, their nearest neighbors.

a. The magnetic forces are subject to the law of superposition being both attractive and repulsive.

i. In a proton the two up quarks have opposite spin offsetting their magnetic fields leaving the magnetic field of the down quark.
ii. In a neutron the two down quarks have opposite spin offsetting their magnetic fields leaving the magnetic field of the up quark.

b. The magnetic force is the only non-central force, it is a dipole, and hence the only force capable of exerting torque.
c. The magnetic forces act over longer distances than the strong force and can affect the overall nuclear structure.
d. Opposite magnetic poles attract, and contribute to lattice bonding.
e. Like magnetic poles repel, and adjust the type of bond (see tri-bond and bi-bond under rule 8 below).

Forces to this point are central, acting as if concentrated at the center of effective size or mass. The first seven rules are direct or absolute for the lattice structure of the nucleus. The following rules adjust or fine tune the nuclear lattice structure.

H. Rule 8: Tightest Binding. Any given system of particles in its ground state trends to the tightest bonding configuration, or the lowest energy state.

a. In terms of the model presented here, the tightest bonds are generally represented by the configuration with the maximum number of bonds between adjacent nucleons (protons and neutrons).

i. In the models, black balls or nodes represent the up quarks, white balls or nodes represent the down quarks.
ii. For the protons, two black nodes and one white node are connected by three supershort, B0s, blue struts (Zometool designations).
iii. For the neutrons two white nodes and one black node are connected by three supershort, B0s, white struts.
iv. Short white, R1s, green,G1s, red, R1s, and yellow, Y1s, struts represent the combination of strong, electric, and magnetic forces acting between quarks that are confined in nearest-neighbor nucleons, which bind protons and neutrons to each other.

b. The quark bonds between protons and neutrons occur as two classes.

i. Quark bonds between nucleons always involve oppositely charged quarks, up quarks always bond with down quarks.
ii. Class 1 the stacked or tri-bond forms when the three quarks of a proton align with the three quarks of a neutron.
iii. Class 2 the side or bi-bond forms when two quarks in a proton align with two quarks in a neutron.
iv. When the electric and magnetic field couple, the tri-bond is stronger than the bi-bond.
v. When the spins of the nucleons are opposed, one or three quarks magnetic dipoles in the tri-bond are repulsive.

1. In one state the tri-bond has three attractive electric bonds and three repulsive magnetic bonds. In these conditions the bi-bond that is stronger than the tri-bond.
2. In the other state only the odd quarks, the down quark in the proton and the up quark in the neutron, have an attractive electric bond and repulsive magnetic bond. In this condition the tri-bond will flip over to form a bi-bond.

I. Rule 9: Balance. Mechanical balance is essential for nuclear stability.

a. Loosely connected nucleons have a greater tendency to become detached as the result of any imbalance in nuclear rotation.
b. The degree of imbalance would have an effect on the stability of a nucleus and would relate to the half life for radioactive decay.
c. Balance and imbalance are functions of symmetry and lead to the next rule.

J. Rule 10: Symmetry. Within the constraints of the previous rules, a given nucleus trends toward a ground state that minimizes its volume by means of various symmetry constraints.

a. For nuclei heavier than carbon 12 symmetry exists through the center point of the nucleus or the nuclear center of mass.

i. The nucleus deviates from symmetry by no more than one nucleon.

b. In larger nuclei, symmetry around the central axis becomes increasingly important.

K. Rule 11: Hexagonal Lattice. Nuclear stages occur in groupings of six protons and six plus �N� neutrons where �N� may be zero, two, four, six, or eight, an even number.

L. Rule 12: Minimum Volume. The volume of the nucleus is always a minimum.

a. The primal shape of the nucleus is spherical ranging between oblate and prolate.

i. When the lattice structure grows along the core the shape of the nucleus becomes more prolate.
ii. When the lattice expands around the center the nucleus becomes more oblate.

b. The frame of the nucleus is a hexagonal cylindrical construct.

M. Rule 13: Limiting Size. The size limit of large nuclei is reached when the net repulsive forces, positive charge and centrifugal force, equal or exceed the net attractive forces.

a. The competition between spinning-off of extra particles via centrifugal effect, electric and magnetic repulsion or attraction and strong force determines this limit.
b. For protons the maximum bonding limit is based on a balance between.

i. The strong force, electrical and magnetic on the attraction side balanced against centrifugal force and the overall positive charge of the protons on the repulsive side.
ii. Beyond that balance point no additional protons can form any viable bond with neutrons.

c. For neutrons the maximum bonding limit is based on balance and available attachment points with protons.

i. The strong force, electrical and magnetic on the attraction side balanced against centrifugal force and available bonding positions with protons.
ii. Beyond that arrangement no additional neutrons can form a viable bond with protons.
iii. Neutrons cap columnar structures in the lattice. Thus, columns contain one more neutron than the number of protons in that vertical structure within the hexagonal lattice.

N. Rule 14: Excited Nuclei. Excited states of nuclei can be created when one or more of the nucleons changes positions on the nuclear lattice structure.

a. A nucleon is moved via an external excitation from ground-state configuration to a state where the nucleon is shifted to a less stable position within the structure.

i. Rearrangement of nucleons resulting in fewer bonds.
ii. Slight imbalances caused by decrease in over all symmetry and balance.
iii. Or both would be indicative of an excited nucleus.

O. Rule 15: Radioactive Nuclei. Radioactive decay occurs when a more tightly bound configuration may be reached if one of the quarks within a nucleon switches and that nucleon moves to a more tightly bound position or state.

a. A nucleon can move to an improved balanced configuration when a neutron becomes a proton via a down quark switching to an up quark, by ejecting an electron and an antineutrino.
b. A proton becomes a neutron via an up quark switching to a down quark by ejecting a positron and a neutrino or by capturing a K-shell electron and emitting a neutrino.
c. Radioactive decay can also occur when an imbalance in the structure results in a particle being tossed off as the nucleus spins.