5.2    PAIR CREATION AND ANNIHILATION

The electron and the positron are made by three elementary particles and the photons by two then, in a pair of positron and electron creation/annihilation must be involved two photons and a third pair of elementary particles.

It is proposed that theoretically a third particle exists in a creation or annihilation processes and that it is a neutrino.

I)                   The annihilation process

In the annihilation process we have:

positron and electron with:

      masses: m_e

      Mass Energy = E_m = ½ m_ec²

      Electromagnetic Potential between them: P_EM > m_e c²

photons with:

      Total Energy = E_TOTAL = m_fc²

      masses:  m_f

neutrino with:

      small Kinetic Energy

      small mass

It must be considered that the electron and the positron are attracted by the Electric Force and repelled by the Magnetic force. They interact between themselves in a similar way as two separated rings of opposite charge. An Electro-Magnetic Potential P_EM between them exists.

The Electro-Magnetic Potential is the sum of the Electric Potential and the Magnetic Potential.

Note that the particles themselves are in an “inner” equilibrium and have also an “inner” Electro-Magnetic Potential which we call here the Mass Energy.

It is good to remember that Electro-Magnetic Potential and Mass Energy are two names for the same kind of energy stored and is applied one or another just for convenience in the notation.

It is proposed that the Electromagnetic Potential P_EM between a positron and an electron separated at a distance equal to their De Broglie λ where the annihilation process takes place is:

 P_EM = ½(m_e+ m_p)c²=  m_ec²

Just before the creation of the photons the situation can be thought as an unstable intermediate structure of six rings and, in some way not totally understood yet, one pair of positrin and negatrin becomes a neutrino delivering its Mass Energy to the two pairs of remaining rings that becomes two photons traveling in opposite directions. A quantity equal to ½(m_e+ m_p)c² = m_ec² of energy of the pair positron-electron is converted to Kinetic Energy for the photons.

We will consider the situation where the electron and the positron are at some distance and so they have a P_EM > m_ec².

The electron and the positron attract themselves. The attractive Electric Force is greater than the repulsive Magnetic Force. There’s a natural tendency for the annihilation process to take place.

The energy balance in the annihilation process can be calculated.

Initially, for the electron and the positron we have:

E_m = ½ m_ec² for each one

P_EM > m_ec² for the pair

The energy converted for the photons is

E_TOTAL = 2E_m + m_ec²= 2m_ec²

Finally, for the photons created we have:

E_m = ½ m_fc² for each one.

E_k = ½ m_fc² for each one

E_TOTAL = E_m + E_k = m_fc² + m_fc² = 2m_fc²

And a neutrino will be produced with small mass and the remaining kinetic energy just to validate the principle of conservation of energy in the process.

It must be:

2m_ec² = 2m_fc

We conclude that: m_f = m_e

The photons created have a mass equal to the mass of the electron or the positron.

They will also have the same λ.

II)   The creation process

We will consider now the symmetric process: two colliding photons and a little neutrino with just the necessary energies to produce the creation process:

 photons with energy: m_fc² =  m_ec²

neutrino with energy: E_m + E_k  = ΔE

 The energy balance in this case is also completely symmetric to the annihilation case.

Total Energy of the two photons and the neutrino:

E_TOTAL = 2m_fc² + ΔE > 2m_ec²

The energy for the electron and positron pair is:

E_TOTAL = E_m + P_EM  + E_k =  m_ec² + m_ec²+ ΔE

It´s important to observe that half of the energy of the photons is used in this creation process to create the positron and the electron but also more energy is needed for the Electromagnetic Potential P_EM and the relative Kinetic Energy that exist when they are separated apart. The other half of the energy and the neutrino energy are converted to them.

Note that this creation process needs two photons and one neutrino to be accomplished. One question arises: where the little neutrino comes from?

It is proposed that there exist an abundance of neutrinos with negligible mass and negligible Kinetic Energy everywhere in the Universe. It's one of the basic particles of the Universe like electrons and photons and they are more concentrated around every material object in the Universe attracted by the gravitational fields.

There’s another way for the creation of an electron-positron pair to take place:

In a similar process two photons with enough energy E_TOTAL = m_fc²=m_ec² each traveling together can also produce a pair if they interact simultaneously with one neutrino near an atom (momentum must be conserved).

This is the way the creation process happens in laboratory experiments where the high energy photons are emitted to collide with some atoms.

NOTE: The described processes verify the Principle of Conservation of the Angular Momentum considering all the rings. It does not conserve the currently called “spin” of the particles which is not a direct measure of the Angular Momentum (see Section 4.10).