**Background**

The neutrino (also referred to as the electron neutrino) is an elementary particle that is much smaller than any subatomic particle that has been discovered thus far. It is an electrically neutral particle that is found in the weak force, nuclear reactions (such as the process in stars) and some particle collisions. The majority of neutrinos found around Earth originate from the Sun. In fact, billions of neutrinos pass through an area the size of a human fingernail each second. However, they are incredibly small, and because they are neutral and not attracted to particles, they rarely hit another particle in an atom. Thus, they can pass through the entire Earth without any collision.

A neutrino has been found to oscillate to become larger and increase mass. It can become a muon neutrino or a tau neutrino. Both of these particles are still neutral and belong to the neutrino family. The three neutrinos are also a part of the lepton family of particles, which include the electrically charged electrons (electron, muon electron and tau electron).

**The Fundamental Particle**

In energy wave theory, the neutrino is the likely candidate for the sub-particle known as the wave center, which makes it the fundamental particle that creates other particles. The Longitudinal Energy Equation makes an assumption that there is a collection of wave centers (K) in a particle. A single wave center for particles would be analogous to a single proton for elements (hydrogen).

A single wave center reflecting spherical, longitudinal waves to create standing waves would look like this:

**Neutrino – ****Standing Waves of Energy from One Wave Center**

**Calculating Neutrino Mass**

The calculation of the neutrino energy assumes spherical volume (V) and a radius (r) of one wavelength before standing waves transition to traveling waves. It also assumes that wave amplitude (A) is longitudinal from three dimensions (cubed) and it decreases with the square of the distance.

**Neutrino – Geometry **

Energy can be calculated using the following equation – the base equation for energy of any type (longitudinal or transverse). It is found in the overview section.

** Energy Wave Equation**

Using the neutrino geometry, volume (V) is replaced and amplitude (A) from the equations above.

This is simplified to the following equation and solved using the wave constants from this theory. The result is 3.83E-19 joules, or 2.39 electron-volts (**2.39 eV**). This is compared to neutrino mass ranges from the Standard Model which range potentially as high as 2.2 eV (*neutrino mass experiments are underway to continue to refine the exact mass of the neutrino*).

**Calculated Value: **3.83E-19 joules (kg m^{2}/s^{2}) or 2.39 eV

**Using the Longitudinal Energy Equation**

The complete Longitudinal Energy Equation allows additional particles with particle count (K) to have their rest energy calculated. The *Particle Energy and Interaction *paper has the details of the full derivation, but in short, each fundamental particle (neutrino) added to the core of the new particle proportionally increases amplitude (in three dimensions) and radius. Below is the calculation of the neutrino rest energy using the Longitudinal Energy Equation. For the neutrino, there is one wave center (K=1).

Using the Longitudinal Energy Equation and wave constants, the result is the same as above. 3.83E-19 joules or 2.39 eV.

## Leptons

Neutrinos are a part of the lepton family, which includes the three neutrinos and three electrons. There are similarities found between these particles when using energy wave equations.

**Oscillation and Decay**

A separate section discusses the process of oscillation and decay. Oscillation is the process of particles becoming larger and decay is particles breaking up into two or more particles. Here in this section, the process of the neutrino oscillating and why it only occurs for neutrinos is described.

Neutrino oscillations have been found in nature. The neutrino can oscillate to become a larger muon neutrino and a muon neutrino can become a tau neutrino. This occurs naturally as trillions and trillions of neutrinos arrive on Earth, from the Sun. As it was found using the Longitudinal Energy Equation, the muon neutrino has a particle count of 8 and the tau neutrino has a particle count of 20. With the exception of the electron (particle count of 10), all other known subatomic particles are much larger. The next particle count is the muon electron at 28.

It is proposed that the reason that neutrinos are found to oscillate is that the chance of 20 or less neutrinos randomly merging with sufficient kinetic energy allows them to oscillate and grow bigger.

Particles with higher particle counts (e.g. 28 or more) require high energy experiments such as particle accelerator labs to generate the kinetic energy to combine and form particles.

**Magic Numbers**

If neutrinos can oscillate up to a count of 20 (tau neutrino), then what about the other arrangements? For example, why are neutrinos with particle counts of 2, 3, 4, 5, 6 or 7 not found? The next neutrino that is found is the muon neutrino with a particle count of 8.

As described in the calculations of particles, leptons appear at the same magic numbers found in atomic elements. The numbers 2, 8, 20, 28, 50, 82, 126 are special in the atomic world because a combination of the stability of these atoms when their nucleons contain these numbers (number of protons or neutrons). The magic numbers align with the orbital shells and how electrons fit within the orbit surrounding the nucleus. Nuclear binding energy levels are found to be higher in these numbers.

**Magic Numbers in Atomic Elements**

It is proposed that leptons are slightly more stable, and hence found in nature, because of geometric configurations that are similar to protons and neutrons in the atomic nucleus. The neutrino family would be relatively stable at these proposed geometric structures (left side of the figure below). They are tetrahedral structure and symmetric, which means they may have no charge if the two tetrahedrons spin in opposite ways. This leaves the possibility of discovering a neutrino with a particle count of 2 (K=2). It would have a rest energy around 110 eV.

In the figure above, the right side contains the electron family. These may also be tetrahedral structures, but non-symmetric. Therefore, as the particle spins, it creates the transverse wave found in the magnetic force.

If particles consist of wave centers at certain geometric configurations, then leptons are made of wave centers in a nucleus with these same counts: 2, 8, 20, 28 and 50. This was found in the calculations.