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**INTRODUCTION:**

Simplistic theories of charged atomic particles represent the particles as point charges and point masses. Nuclei are represented as having incident particle kinetic energy dependent absorption and scattering cross sections. In reality every particle has a spacial distribution of both charge and energy. The geometry of the charge distribution and the motion of the charge is such that the net force on the charge is zero. A particle's spacial energy distribution may extend to infinity but its total energy is finite. Its net charge is quantized.

The material contained on this web page involves application of spheromak theory to atomic particles. A charged atomic particle consists of an electro-magnetic spheromak containing a confined photon. A spheromak is an electromagnetic structure analogous to a glazed doughnut. The shape is toroidal. Inside the doughnut glaze the magnetic field is toroidal. Outside the doughnut glaze the magnetic field is poloidal. Charge motion (current) follows a complex closed spiral path within the glaze layer. The net charge is quantized. The current path has a uniform net charge per unit length.

The spheromak gives a charged particle most of its static electro-magnetic field properties, including its natural frequency. A radiation photon confined within the inside region of the spheromak gives the particle most its inertial mass.

**HISTORY:**

During the period February 2016 to to August 2018 Charles Rhodes showed that the existence of elementary charged particles such as electrons and protons with quantum charges is in part due to formation of electromagnetic spheromaks. Electromagnetic spheromaks have energy associated with their electric and magnetic fields. Note that a real charged particle also has a confined photon which together with the spheromak meets all the experimentally measured particle parameters.

A spheromak can be described in terms of a quantum charge string moving at the speed of light along the string axis which is a closed path containing Np poloidal turns and Nt toroidal turns. These integers together with the speed of light C, the permiability of free space Muo, the quantum charge Q and the geometric constant Pi precisely define the Planck constant h. The integer Np and Nt values also set the magnetic properties of quantum charged particle spheromaks. The spheromak dimension Ro determines the spheromak frequency Fh and the amount of static electromagnetic field energy Ett contained in the spheromak.

Quantum charged particles have an electro-magnetic field energy component Ett that obeys:

Ett = h F

where:

h = Planck constant

and

F = natural frequency of the particle at energy Ett.

Spheromaks have quantized poloidal and toroidal magnetic fluxes. For a particular poloidal magnetic flux direction there are two equally possible toroidal flux directions. Much of quantum mechanics rests on the structure and behavior of electro-magnetic spheromaks.

Chemical binding is largely due to far field interactions between spheromaks. The "weak" nuclear force is believed to be due to near field interactions between spheromaks. The apparent "strong" nuclear force is believed to be due to fracturing or merging of spheromaks.

**CHARGED PARTICLE EXISTENCE:**

A charged atomic particle, such as an electron or proton, is a nearly localized packet of energy with a static spheromak energy component Ett which obeys:

Ett = h Fh.

The spheromak structure contains energy in the static electric and magnetic fields due to circulating quantized electric charge that continuously moves along a closed spiral path at the speed of light. The charge motion causes local toroidal and poloidal magnetic fields. The charge causes an external radial electric field. In the case of a simple spheromak the closed charge motion path traces out a toroidal shaped surface referred to as the spheromak wall. The resulting static electric and magnetic fields have an energy density and are stable in time and relative position. Integrating the field energy density over all space gives the spheromak's static field contribution to the particle's rest potential energy. In its normal minimum energy state (ground state) the spheromak does not radiate photons. Hence a spheromak's energy is normally stable. The static field energy content of a spheromak is inversely proportional to the spheromak's linear size.

Real particles also contain inside their spheromak walls confined photons which account for most of the particle rest mass energy.

**SPHEROMAK WALL POSITION:**

The circulating charge forms a charge and current sheet known as the spheromak wall. The position of the spheromak wall in space relative to the center of the spheromak is stable if at every point on this wall the total field energy density on one side of the wall is equal to the total field energy density on the other side of the wall and if at every point on the wall the position of the wall corresponds to a spheromak total energy minimum . These conditions define the physical shape of the spheromak wall and hence the closed spiral charge path.

**PHOTON ABSORPTION AND EMISSION:**

If a particle changes energy by absorption or emission of a photon it shifts from its initial spheromak state to a new spheromak state. In order for the particle's static field energy to increase the natural circulation frequency Fh of the spheromak must increase implying that either the linear dimensions of the spheromak must decrease or the number of spheromak spiral turns must decrease. The ratio:

(change in spheromak field energy Ett) / (change in circulation frequency Fh) = h

at the spheromaks stable operating point is known as the Planck constant.

The Planck constant is a function of other physical constants including: quantum charge Q, speed of light C and permiability of free space Muo and the inverse Fine Structure constant (1 / Alpha). The inverse fine structure constant is a function of the number of charge path poloidal spiral turns Np and the number of charge path toroidal spiral turns Nt.

**NUCLEAR MAGNETIC RESONANCE:**

The potential energy of a charged particle spheromak located in an externally applied magnetic field is dependent upon the orientation of the spheromak's axis of symmetry with respect to the axis of the applied magnetic field. A change in the orientation of the spheromak axis of symmetry with respect to the magnetic field axis is accompanied by emission or absorption of a photon. The frequency of that photon is proportional to the external magnetic field strength and the spheromak magnetic moment.

This phenomena is variously known as electron magnetic resonance (EMR) and nuclear magnetic resonance (NMR). Hydrogen NMR has immense importance in biomedical magnetic imaging. However, NMR has limited general application because in heavier nuclei the magnetic moments of different nucleons tend to cancel each other.

The experimentally measured magnetic moments of some particles are:

PARTICLE | MAGNETIC MOMENT (X 10^-27 J / T) | SPIN QUANTUM NUMBER |
---|---|---|

Electron | -9284.764 | 1 / 2 |

Proton | 14.106067 | 1 / 2 |

Neutron | -9.66236 | 1 / 2 |

H-2 | 4.3307346 | 1 |

H-3 | 15.046094 | 1 / 2 |

He-3 | -10.746174 | 1 / 2 |

He-4 | 0.0 | 0 |

**ELECTRON MAGNETIC RESONANCE:**

The electrons in a material exist in a wide range of local magnetic fields due to both nuclei and other electrons. Hence in many materials electrons absorb and emit photons over wide frequency bands. The lack of sharp frequency dependent resonances makes electron magnetic resonance (EMR) a relatively little used technique. However, broad band emission of photons by thermally energized electrons is an important source of thermal radiation.

**PARTICLE SIZE AND PARTICLE REST MASS:**

The derivation of the Planck constant on this web site is independent of the spheromak nominal radius Ro and hence is independent of the total spheromak electromagnetic energy Ett.

If:

Rs = outside radius of spheromak wall with respect to the spheromak axis of symmetry;

Rc = inside radius of spheromak wall with respect to the spheromak axis of symmetry;

then the Planck constant effectively sets the parameter So where:

So^2 = (Rs / Rc)

but does not directly establish:

Ro = (Rc So) = (Rs / So)

Thus the Planck constant is the same for different energy particles such as electrons and protons that have the same quantum charge magnitude.

Work with Josephson junctions in superconducting materials indicates the existence of a magnetic flux quantum of:

Phio = h / (2 Q)

= 2.0678337 X 10^-15 Weber.

This magnetic flux quantum is an observed change in magnetic flux due to gross movement of a single electron and hence is itself much larger than the underlying magnetic flux quantum. To pursue this theory we develop on this web site accurate expressions for both the quantum spheromak poloidal magnetic flux and the quantum spheromak toroidal magnetic flux.

At this time, this author does not know the underlying mechanism of charge quantization. The magnetic flux quantization is simply a result of charge quantization and the laws of electrodynamics.

**SPHEROMAK INTERACTIONS:**

Charged particles that are separated by long distances interact via their overlapping electric fields. The change in total energy due to the change in field overlap causes acceleration of the entire particle mass. However, when the distance between particles is small the situation becomes more complicated.
The interaction due to overlap of the particle magnetic fields becomes important. At even closer distances particles may merge and in the process emit gamma photons. In addition some particle potential energy may convert into particle kinetic energy.

**SPHEROMAK THEORY APPLICATION:**

The electromagnetic behavior of isolated quantum charged particles can be described by using spheromaks. The behaviour of ionized gases forming a toroidal shaped plasma can also be described by spheromaks.

**ELECTRONS, PROTONS, NEUTRONS, DEUTERONS, POSITRONS AND ANTI-PROTONS:**

In our local universe energy is primarily concentrated in the rest mass of stable particles known as electrons and protons and semi-stable particles known as neutrons. Neutrons may be stable in an atomic nucleus but in free space soon spontaneously decay into electrons, protons and neutrinos.

The net charge on a proton is 1.60217657 X 10^-19 coulombs.

The net charge on an electron is - 1.60217657 X 10^-19 coulombs.

The net charge on a neutron is zero.

The rest mass of a proton in free space is 1.67262178 X 10^-27 kg.

The rest mass of an electron in free space is 9.10938291 X 10^-31 kg.

The rest mass of a neutron in free space is slightly more than the combined rest masses of a proton plus an electron.

The rest mass of a deuteron in free space is slightly less than the combined rest masses of a neutron plus a proton.

There are corresponding charged particles known as anti-electrons (positrons) and anti-protons.

A positron has the same mass as an electron but opposite charge.

An anti-proton has the same mass as a proton but opposite charge.

These anti-particles are rare in our local universe. Positrons are usually observed as a result of conversion of a > 1 MeV gamma photon into an energetic electron-positron pair. In some nuclear decays the energy release is sufficient to produce an energetic electron-positron pair. The positron is emitted while the net charge on the nucleus decreases by addition of one electron charge. That electron is absorbed by a proton and converts that proton into a neutron.

Note that neutrons rely on the electric fields from adjacent protons for long term stability. Absent such external electric fields free neutrons spontaneously decay with a half life of about 10 minutes.

Spin is a charged particle parameter which is related to the direction of the spheromak poloidal magnetic field with respect to the the direction of an external magnetic field. For a specific poloidal magnetic field direction there are two possible toroidal magnetic field directions. In an atomic nucleus the nucleons tend to pair up so that their net external poloidal magnetic fields cancel. Similarly, in an atom the electrons tend to pair up so that their net external poloidal magnetic fields cancel. Field cancellation reduces the aggregate total energy and thus creates a mutual potential energy well. The combined electric and magnetic interactions between spheromaks in an atomic nucleus or in a solid creates numerous closely spaced energy states.

**MAGNETIC STATES:**

A free electron is generally indistinguishable from every other similarly oriented free electron except via its toroidal field orientation with respect to its axial field.

A free proton is generally indistinguishable from every other similarly oriented free proton except via its toroidal field orientation with respect to its axial field.

A free positron is generally indistinguishable from every other similarly oriented free positron except via its toroidal field orientation with respect to its axial field.

A free anti-proton is generally indistinguishable from every other similarly oriented free anti-proton except via its toroidal field orientation with respect to its axial field.

**PAIR PRODUCTION AND ANNIHILATION:**

Under circumstances of a high gamma photon concentration and a low particle concentration a high energy photon can convert into an electron-positron pair. In circumstances of a high charged particle concentration and a low gamma photon concentration an electron and a positron can annihilate each other to form photons. Under circumstances of a very high energy gamma photon concentration and a low particle concentration a very high energy gamma photon can convert into a proton-anti-proton pair. Under circumstances of a low gamma photon concentration and a high particle concentration a proton and an anti-proton will annhilate each other to form a new gamma photon. There is an equilibrium between radiation energy density and particle concentration at which the rate of pair production equals the rate of pair annihilation. At this equilibrium the photons and the particles are said to be at the same temperature.

Our local universe has evolved to the point that, except in the cores of stars, the concentration of high energy gamma photons that can produce particle-anti-particle pairs is very low and the concentration of anti-particles is very low, so that particle generation and annihilation are no longer significant processes. However, cosmologists believe that the universe evolved from an initial high gamma photon concentration known as the "big bang". The high energy gamma photons formed charged particles. The charged particles then formed neutral hydrogen. The high concentration of free charged particles immediately prior to hydrogen formation prevents astronomers observing earlier events.

**CHARGE HOSE:**

A Charge hose is a mathematical construct that quantitatively explains experimentally observed atomic particle and plasma spheromak phenomena.

A quantum charged particle in a spheromak can be mathematically modelled as a long thin filament of circulating charge referred to herein as "charge hose". The charge hose coils to form a toroidal shaped charge and current sheet known as a spheromak wall. The two hose ends are connected together to form a closed spiral path with length **Lh**. The charge hose forms the geometric divider wall of a stable electro-magnetic configuration known as a spheromak.

**CHARACTERISTIC FREQUENCY:**

If C = speed of light, then the time required for the quantum charge to propagate around the closed charge hose path of length **Lh** gives the charged particle at rest a characteristic frequency **Fh** where:

**Fh = C / Lh**

Note that if the moving charge is composed of opposite charges moving in opposite directions the individual charge motion can be less than the speed of light whereas the apparent current flows at the speed of light.

For a given charge the smaller a spheromak is the more energy that it contains and the higher is its characteristic frequency **Fh**. If the spheromak's energy changes due to photon capture or photon emission while the spheromak's net charge remains constant there is a corresponding change in spheromak size and hence there is a corresponding change in the spheromak's characteristic frequency **Fh**. The photon emitted or absorbed by the spheromak must reflect both the change in energy and the change in the charged particle natural frequency. The proportionality constant between the change in energy and the change in frequency Fh is known as the Planck constant **h**.

Note that the emitted or absorbed photon frequency Fp is approximately equal to the beat frequency difference between the initial particle natural frequency **Fha** and the final particle natural frequency **Fhb**. Thus:

Fp = |Fhb - Fha|

Note that during this configuration change a small amount of energy may be converted into kinetic energy related to particle recoil momentum.

**ENERGY STABILITY:**

As long as charge is uniformly distributed along the length of the charge hose and moves at a uniform axial velocity C along the charge hose, and as long as the charge hose coil is geometrically and dimensionally stable, there is no change in the spacial distribution of charge with time and hence there is no change in field geometry or field energy. Hence there is no emitted or absorbed electro-magnetic radiation and the particle is stable.

**DISCRETE SOLUTIONS:**

There is a further aspect of charge hose that is important in quantum mechanics. In order for the particle to be stable over time each turn of the charge hose of length **Lp** around the charge hose coil's main axis of symmetry must be the same length and geometry as every other similar such turn. Likewise each turn of length **Lt** around the toroidal axis must be the same length and geometry as every other similar such turn. The number of poloidal turns **Np** and the number of toroidal turns **Nt** must both be exact integers. The poloidal and toroidal directions are mutually orthogonal. Hence:

**Lh^2 = (Np Lp)^2 + (Nt Lt)^2**

**NEUTRON STRUCTURE:**

Consider two charged particles, one inside the other, with opposite static charges, sharing a common axis of symmetry. The result is a seemingly neutral particle with a net external magnetic moment. This is the assumed structure of neutrons and anti-neutrons.

The electric field between the inner particle and the outer particle contains part of the neutron rest mass energy. Much of the rest mass energy is in confined photons that circulates within the spheromak walls.

**NEUTRAL ASSEMBLY:**

Consider two particles, one inside the other, sharing common major axes and with opposite net static charges. The positive particle has much more energy than the negative particle and hence fits inside the core of the negative particle. If these opposite charges are identical the result is an assembly with no net charge known as an atom.

The electric field between the inner particle and the outer particle contains part of the assembly rest mass energy.

**NUCLEAR PARTICLE BINDING:**

A proton can magnetically bind to 0, 1 or 2 neutrons to form hydrogen, deuterium and tritium nuclei. A tritium nucleus is unstable and absent intense gamma ray radiation will spontaneously decay into a He-3 nucleus. A particularly stable combination is two protons plus two neutrons forming a He-4 nucleus. The He-4 nucleus has no net magnetic moment, indicating that its constituant particles are positioned such that all the individual magnetic moments cancel.

**CHARGED PARTICLE MODEL:**

The following structure summarizes my understanding of the physical properties of simple charged particles.

Each free charged particle contains a spheromak. Each spheromak can be viewed as a quantum of charge that is uniformly distributed along a closed spiral path. The net charge motion along this spiral path is at speed of light C. The period required for the charge quantum to cycle around the closed path length Lh has a corresponding frequency Fh which gives the charged particle spheromak a characteristic frequency. The spheromaks' electric and magnetic field energies contribute to the particle's rest mass energy.

For a spheromak the closed spiral charge path forms a toroidal shaped charge and current sheet known as the spheromak wall. Inside the spheromak wall the magnetic field is purely toroidal. Outside the spheromak wall the magnetic field is poloidal. Due to the closed spiral current path geometry the charge per unit area on the spheromak wall varies with the radius from the toroid's main axis of symmetry. This configuration forms a stable spheromak. Outside the spheromak wall the total energy density **U** takes the form:

**U = Uo [Ro^2 / (Ro^2 + R^2 + H^2)]^2**

where:

**Uo** = a single spheromak peak energy density;

**Ro** = a characteristic radius from the spheromak's main axis of symetry which determines the spheromak's contained energy;

**R** = radius of a point from the spheromak's main axis of symmetry;

**H** = distance of a point from the spheromak's equitorial plane.

Define:

**Rc** = inner radius of spheromak wall on the spheromak equatorial plane

**Rs** = outside radius of spheromak wall on the spheromak equatorial plane.

Inside the spheromak wall, where the radial electric field and the toroidal magnetic field are proportional to (1 / R), for:

**Rc < R < Rs**

the static field energy density is given by:

**Ut = Uto [Ro / R]^2**

Note that **U** is the sum of the static electric field energy density plus the static magnetic field energy density and that for spheromak stability the expressions for **U** inside and outside the spheromak wall must be equal everywhere on the spheromak wall.

Thus at R = Rc, H = 0:

U = Uo [Ro^2 / ((Ro)^2 + Rc^2)]^2 = Uto [Ro / Rc]^2

and at R = Rs, H = 0:

U = Uo [Ro^2 / ((Ro)^2 + Rs^2)]^2 = Uto[Ro / Rs]^2

Thus equating the expressions for Uto gives:

[Ro Rc / ((Ro)^2 + Rc^2)]^2 = [Ro Rs / (Ro^2 + Rs^2)]^2

or

[Ro Rc / (Ro^2 + Rc^2)] = [Ro Rs / (Ro^2 + Rs^2)]

or

(Ro^2 + Rs^2) Rc = (Ro^2 + Rc^2) Rs

or

Rs Rc (Rs - Rc) = (Ro)^2 (Rs - Rc)

or

**Rs Rc = Ro^2**

The spheromak shape factor So is defined by:

So^2 = (Rs / Rc)

Note that for **(R^2 + H^2) >> Ro^2** the dependence of **U** on radial distance is the same as for a theoretical point charge.

Spheromaks tend to emit photons until they reach their stable low energy state.

As shown on other web pages on this web site this spheromak mathematical model accurately predicts the Planck constant and appears to explain the experimentally observed parameters of particle charge, particle magnetic moment. The spheromak wall confines a photon to the spheromak. The confined photon contains most of the particle rest mass.

**ATOMIC PARTICLE SPHEROMAK:**

The charge on an atomic particle spheromak is quantized. The mechanism of this charge quantization is not known. The net charge circulates at the speed of light. The circulating charge exhibits no inertial mass. The characteristic frequency Fh of an atomic particle spheromak is:

Fh = C / Lh

where:

C = speed of light

and

Lh = charge hose length

= [(Np Lp)^2 + (Nt Lt)^2]^0.5

where:

Lt = toroidal turn length

Lp = toroidal magnetic path length at R = Rf

Nt = number of toroidal turns in length Lh

The characteristic frequency Fh of an atomic particle is given by:

**Fh = C / Lh**

= C / [(Np Lp)^2 + (Nt Lt)^2]^0.5

Due to spheromak geometry:

Lp = Pi (Rs + Rc)

and

Lt = Pi (Rs - Rc)

and

Ro / Rc = So = Rs / Ro

Thus:

**Fh** = C / [(Np Lp)^2 + (Nt Lt)^2]^0.5

= C / [(Np Pi (Rs + Rc))^2 + (Nt Pi (Rs - Rc))^2]^0.5

or

** Fh = C / {Pi Ro [[(Np (Rs + Rc))^2 / (Ro)^2] + [(Nt (Rs - Rc))^2 / (Ro)^2]]^0.5}**

Hence:

**(1 / Ro)**

= {Pi Fh / C) [[(Np (Rs + Rc))^2 / (Ro)^2] + [(Nt (Rs - Rc))^2 / (Ro)^2]]^0.5} (Fh / C)

= {Pi Fh / C) [[(Np Rc (So^2 + 1))^2 / (Ro)^2] + [(Nt Rc (So^2 - 1))^2 / (Ro)^2]]^0.5}

= {Pi Fh / C) [[(Np (1 / So) (So^2 + 1))^2] + [(Nt (1 / So) (So^2 - 1))^2]]^0.5}

= Qs C / [(Np Lp)^2 + (Nt Lt)^2]^0.5

= Qs C / {Pi Ro [[(Np (Rs + Rc))^2 / (Ro)^2] + [(Nt (Rs - Rc))^2 / (Ro)^2]]^0.5}

**TOTAL ISOLATED SPHEROMAK ENERGY:**

As shown on the web page titled SPHEROMAK ENERGY the total energy of an isolated spheromak is given by:

**Ett = (Ett / Efs) Uo Pi^2 Ro^3**

where:

Efs = Uo Ro^3 Pi^2

and

(Ett / Efs) ~ 0.95 at So^2 = 4.0

**CHARGE HOSE SUMMARY:**

A charge hose is characterized by a net charge **Qs**, an axial current **Ih** and a frequency **Fh**. The net charge gives the particle an external electric field. The charge hose current:

**Ih = (Qs C / Lh)**

gives the charged particle an external poloidal magnetic field and an internal toroidal magnetic field. Changing the symmetry axis orientation with respect to an externally applied magnetic field causes the particle to absorb or emit photons. Linear motion of the particle with respect to an external observer gives the particle linear momentum. The linear momentum is primarily the momentum of the confined photon which has a characteristic wavelength Lamda. Interaction of neighboring spheromaks converts potential energy into kinetic energy.

**DEFINITIONS:**

Define:

**Nnh** = number of negative charge quanta forming the charge hose;

**Nph** = number of positive charge quanta forming the charge hose;

**Lh** = length of charge hose;

**Vn** = negative charge axial velocity through the charge hose;

**Vp** = positive charge axial velocity through charge hose;

**Qp** = one quantum of positive charge

**Qn** = one quantum of negative charge

**Q** = net charge on a proton

**QUARK BEHAVIOR:**

Under the standard model protons are believed to be composed of quarks.

Under quark theory:

Qs = (Qp Nph + Qn Nnh)

For a proton:

Qp = (2 / 3) Q

Nph = 2

Qn = - (1 / 3) Q

Nnh = 1

giving:

(Qp Nph + Qn Nnh) = [(2 Q / 3) (2)] + [(- Q / 3) (1)]

= Q = Qs

**STATIC CHARGE:**

A spheromak must have static charges such that the net static charge for an electron is - Q and the net static charge for a proton is + Q.

If the spheromak static charges conform to quark theory (Standard Model) then for a proton there are two positively charged quarks each with static charge:

+ (2 / 3) Q

and one negatively charged quark with static charge:

(- 1 / 3) Q.

If the spheromak static charges conform to quark theory
(Standard Model) for a neutron then there must be one quark with static charge:

(+ 2 / 3) Q

and two quarks each with static charge:

(- 1 / 3) Q.

In quark theory on decay a neutron emits a -ve portion that forms a free electron and most of the remainder becomes a proton. Note according to quark theory the emission of an electron with a charge of - Q causes a quark with a charge of:

(+ 2 Q / 3)

to change into a quark with a charge of:

(- Q / 3).

This author favors the particle structure theory developed on the web page titled: CONFINED PHOTONS which does not involve assignment of fractional quantum charges.

**ATOMIC PARTICLES:**

Spheromak like structures account for the existence of stable elementary charged particles. In these particles net charge moves along a closed spiral path at the speed of light C and adopts a shape of a spheromak. A small part of the rest mass of each atomic particle comes from the energy contained within its spheromak's static electric and magnetic fields. Most of the particle rest mass is contained within the confined photon that circulates inside the spheromak wall. The externally observed quantum charge units behave as though they are themselves composed of opposite but unequal sub-quantum charges known as quarks. However, the quarks have never been observed in isolation an may only be mathematical constructs.

**NUCLEAR BINDING:**

The elementary stable charged particles are electrons and protons. A proton can provide stability to up to two adjacent neutrons. Stable atomic nuclei appear to be coupled collections of H-1, H-2, H-3, He-3 and He-4 nuclei. This structure is experimentally observed via the net nuclear magnetic moment.

At very short ranges the magnetic field energy density of a spheromak exceeds the electric field energy density. A neutron's magnetic moment is similar to a proton's magnetic moment. Hence adjacent protons and neutrons in appropriate ratios can magnetically couple together.

Binding mechanisms seem to account for the experimentally observed changes in nuclear magnetic moment and nuclear structure stability depending on the numbers of protons and neutrons in the observed atomic nuclei. Large nuclear binding energies are achieved by changes in the confined photon configuration.

**DEFINITIONS:**

Nne = number of equivalent electron charges in an atomic nucleus;

Nnp = number of equivalent positron charges in an atomic nucleus;

Nip = number of equivalent proton charges in an atomic nucleus;

Nie = number of equivalent anti-proton charges in an atomic nucleus

Thus:

Number of protons in a nucleus = (Nip - Nne)

Number of neutrons in a nucleus = Nne

**NATURAL RADIO ISOTOPE DECAY:**

An atomic nucleus consists of an assembly of charged particles. Atomic nuclei are only stable at certain proton to neutron ratios. If a nucleus can readily change into a similar assembly with a lower energy by emission of an electron, positron or alpha particle (He-4 nucleus) and/or a photon this change may spontaneously occur. Such a change is known as radio active decay. The time required for half of the nuclei of a particular isotope to spontaneously decay is known as that isotope's half life. The half life is a function of the isotopes binding potential well.

The range of possible decay paths is constrained by the requirement for compliance with the laws of conservation of energy, conservation of momentum and conservation of charge in any nuclear decay.

A decrease in nuclear energy occurs making the nucleus more stable when emission of an electron decrements the number of neutrons Nne and increments the number of protons (Nip - Nne).

A decrease in nuclear energy occurs making the nucleus more stable when there is electron-positron pair production immediately followed by positron emission and absorption of the remaining electron which decrements the number of protons (Nip - Nne) and increments the number of neutrons Nne.

**ELECTRON AND POSITRON:**

The total spheromak static field energy is the sum of the external electric field energy outside the spheromak wall, the internal electric field energy inside the spheromak wall, the poloidal magnetic field energy outside the spheromak wall and the toroidal magnetic field energy inside the spheromak wall.

The poloidal circulation of charge around a spheromaks main axis of symmetry gives a spheromak its external magnetic moment. Since the toroidal charge motion has two direction possibilities with respect to a particular poloidal magnetic field direction, a spheromak aligned to an external magnetic field has one of two possible states which are of equal energy.

In some materials application of a strong external magnetic field can partially align the electron poloidal magnetic fields causing a phenomena known as Electron Spin Resonance (ESR). ESR has limited general application because in many materials the electron magnetic moments cancel each other.

**PROTON:**

The Standard Model claims that a proton (and other nucleons) are composed of three quarks, two of which each have charge:

**(2 Q / 3)**

and one with charge:

**(- Q / 3)**.

However, all long lived real particles have integral charges, so this assignment of fractional charges to quarks may be just a mathematical construct.

As shown on the web page titled CONFINED PHOTONS each proton has three states and the superposition of the three states has charge Q.

Note that isolated quarks have never been experimentally observed. However, they exist as mathematical constructs which explain the existance of known nuclear particles.

The electromagnetic field structure of a proton is believed to be similar to that of an electron but smaller in size.

**ELEMENTARY PARTICLES:**

Elementary particles including electrons, protons and neutrons contain spheromaks. Typically the confined photons provide most of the particle rest mass and the outer spheromak provides most of the particle magnetic moment.

Note that for electrons and protons part of the energy that is internally contained in a neutron is contained in the external electric fields of electrons and protons.

**BOUND NEUTRON:**

A neutron bound within an atomic nucleus has zero net charge and may or may not be stable, depending on its nearest neighbours. A neutron within a stable atomic nucleus can be viewed as consisting of a proton plus an electron plus some additional energy and opposed spin.

**FREE NEUTRON:**

Outside of an atomic nucleus a free neutron is unstable. A free neutron (a neutron outside an atomic nucleus) has zero net charge and thermal neutrons have an apparent half life of about 11 minutes. A free neutron contains slightly more energy than the sum of the energies of its main components, a proton and an electron. The neutron mass and neutron decay characteristics suggest that a neutron consists of a proton charge plus an electron charge plus a small amount of additional energy. On neutron decay the extra energy forms a neutrino which conveys spin but no charge and which only rarely interacts with charged particle matter.

A free neutron has no net external electric field, which absence prevents normal electric field based spheromak wall stability. Charge hose current appears to account for the neutrons external magnetic field. However, outside of an atomic nucleus a free neutron is unstable.

I suspect that a free neutron is a an unstable structure including a positive spheromak (proton) and a negative spheromak (electron) sharing the same symmetry axis. The proton spheromak is much smaller and including its confined photon provides most of the particle mass. The electron is larger and provides most of the particle magnetic moment. This structure lacks a stabilizing external electric field and hence is potentially unstable in free space. This structure can potentially be stable in a nucleus where other nearby particles provide external stabilizing electric and magnetic fields.

**NUCLEAR BINDING:**

Weak nuclear particle binding appears to involve spheromak to spheromak magnetic binding. Strong nuclear particle binding involves a change in the confined photon configuration.

**ATOMIC NUCLEUS:**

An atomic nucleus can be viewed as being an assembly of protons, neutrons and He-4 nuclei that are trapped within a mutual potential energy well. The mutual potential energy well is deep and is stable only at certain values of the number of protons and the number of neutrons. The depth of the potential energy well is characterized by its negative binding energy. When a nucleus absorbs or emits energy it usually does so via stable or nearly stable particles such as photons, electrons, positrons, protons, neutrons or alpha particles (He-4 nuclei).

**Pb-207:**

An example of a stable nucleus is a lead-207 where:

**Nip = 2 X 207 = 414**

**Nnp = 207**

and from the atomic number:

**Nne = 207 - 82 = 125**

For Pb-207:

**(Nnp / Nne) = 207 / 125 = 1.656**

It has been experimentally observed that atomic nuclei with:

**(Nnp / Nne) < 1.66**

are unstable and hence are radio active (eg uranium, plutonium, etc).

It has further been experimentally observed that atomic nuclei with:

**(Nnp / Nne) > 2.0**

are likewise radioactive (eg beryllium-7, boron-8, carbon-9,carbon-10, carbon-11, etc.)

There is only a relatively small range of **(Nnp / Nne)** values that result in highly stable atomic nuclei.

**SEMI-STABLE ATOMIC PARTICLE ASSEMBLIES:**

There are about 1000 well documented semi-stable elementary particle assemblies that are known as atomic nuclei. Many of these assemblies are unstable and hence exhibit natural radio activity.

then the nucleus tends to decay by electron emission which decrements

If:

**(Nnp / Nne) > stable value**

and if:

**Nnp < 207**

then the nucleus tends to decay by electron-positron pair production immediately followed by positron emission which together increment **Nne** and hence decrements (Nip - Nne).

If:

**Nnp > 207**

then the nucleus tends to decay by alpha particle (helium-4 nucleus) emission which decrements **Nnp** by 4 and decrements **Nne** by 2, followed by electron emission(s).

Some nuclei are meta-stable energy states that spontaneously absorb or emit small amounts of energy by photon absorption/emission with no change in either **Nnp** or **Nne**.

**NUCLEAR FORCES:**

The above work suggests that so called nuclear forces are the result of overlapping electric and magnetic fields between adjacent elementary particles (weak nuclear force) and due to changes in the configuration of confined photons (strong nuclear force).

There are a large number of short lived particles (semi-stable energy states) that can be formed via high energy collisions between nuclei. However, these particles are short lived and have limited impact on the real world and hence are outside the scope of this web site.

This web page last updated December 8, 2018.

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