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3.5.6 Electrons and Protons

Given the large disparity between the energy content of an electron and a neutron, (\(8.14\ 10^{-14}\) and \(1.5053411\ 10^{-10}\) Joules, respectively), it might be expected that the structure of an electron is significantly different to that of a neutron. However, this is not the case, and it would seem that the main structural difference is that the displacement in neutron structure is negatve, (against the direction of expansion,) whereas, the displacement in electron structure is positive, (in the same direction as expansion).

For this reason, electron structure can be analysed on the basis that its core zone is an empty, spherical void (neutrino). As before, the structure outside the core zone can be visualized as a system of concentric spherical shells. The curvature of each spherical shell will depend on its radius, and the curvature of a shell at radius, \(r\), is simply, \(2/r\). Since displacement in an electron is opposite in sign to that of a neutron, energy density and displacement functions which describe electron structure are slightly different to those of a neutron.

The displacement in electron structure is positive, that is, \(N=B/r\), and hence displacement gradient is negative, that is, \(\frac{\partial N}{\partial r} = - \frac{B}{r^2}\). A mathematical expression describing energy distribution in electron strcture may be derived from that of a neutron simply by replacing, the neutron displacement gradient, \(A/r^2\), by that of an electron, \(-B/r^2\). Hence we have that
\begin{align}
neutron\ energy\ distribution\ =&\ 4\pi\ \rho_0\ R_0\ A (1- \frac{r_0^2}{r^2}) \nonumber \\
becomes\ electron\ energy\ distribution\ =&\ 4\pi\ \rho_0\ R_0\ (-B) (1- \frac{r_0^2}{r^2}) \nonumber \\
= 4\pi\ \rho_0\ R_0\ B \frac{r_0^2}{r^2} - 4\pi\ \rho_0\ R_0\ B \nonumber
\end{align}

The first term, \( (4\pi\ \rho_0\ R_0\ B \frac{r_0^2}{r^2})\) is an inverse square law 'field' which represents the electric field said to be emitted by the electron. The second term is negative, and since negative energy cannot exist, it must be discounted.

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