4.5    THE ELECTRON DIFFRACTION

The electron verifies the Corrected De Broglie formula:

r = λ/2,  λ=h/mf(v_A)

Where m is the total mass of the conjunct: m = m₁+m₂+m₃ = 3m_j

We will see now how the explanation on how the photons exhibit the “wave-like” behaviors of diffraction applies to trains of electrons.

It is proposed that electrons can be aligned to form a train of electrons.

The problem lays on how particles of the same type of charge can be maintained together in spite of the electric repulsion. But we saw in Section 3.4 Case B, that the magnetic force is attractive and that at small enough distances it is greater than the electric repulsion. We saw also that in this case an equilibrium state at λ´ can be reached with the ultimate force F_U.

 It is proposed that a train of electrons is formed by an equilibrium state with the ultimate force on the negatrins of the extremes of the particles.

We see that there are two states of equilibrium at the same time. The equilibrium in λ/2 (between net opposite charges) is the responsible for the “wave like” behavior of the trains of electrons. It can be verified that the train of electrons present the same Huygens behavior as the photons (Section 4.2).

We have:   δ << λ/2

 Then we have the same figure as in Section 4.2 with the difference that here the negative charges are the double than the positive ones.

It can be seen in the equilibrium equation (section 3.4) that although we have double negative charges and the electric field is augmented, the magnetic field is also augmented and for the same γ we have the same λ=h/m_ef(v).

It can be observed that depending on the angle θ the trains will join at a certain large distance with different phases.

In certain angles they will join in phase what means that charges of the same sign of each train are confronted (this happens for example at θ = 0). In this case the repulsive electric force will maintain them apart and they behave separately as ordinary beams of electrons. The trains can be easily dismounted when colliding with the detector and free electrons are released.

In other angles the trains will join out of phase what means that opposite charges of each train are confronted. In this case there is an attractive force between the trains which create very compacted couple of trains.

When  sin θ = nλ/d           n=0,1,2,3,…

“constructive interference” exists and the electrons are captured by the electron detector in these angles.

When  sin θ = (n + ½)λ/d n=0,1,2,3,…

“destructive interference” exists: the two trains forms a very compacted array of a couple of trains that pass through the electron detector (between its atoms) without being detected.

The same “wave-like” behavior can be applied to the positron.