Chadwick: Neutron = Proton + Electron

Let me backtrack the idea explored in recent posts of neutron = proton + electron, with the electron as a negative point kernel surrounded by cloud of positive charge as a proton, as a small scale analog of a  Hydrogen atom as a proton as positive point charge surrounded by a a cloud of negative charge as electron with observed change of spatial scale of about $10^5$. 

The 1935 Nobel Prize in Physics was awarded to English physicist James Chadwick for the discovery in 1932 of the neutron, described by Chadwick in his Nobel Lecture as follows:

• The idea that there might exist small particles with no electrical charge has been put forward several times. 
• Nernst, for example, suggested that a neutral particle might be formed by a negative electron and an equal positive charge.
• The first suggestion of a neutral particle with the properties of the neutron we now know, was made by Rutherford in 1920. He thought that a proton and an electron might unite in a much more intimate way than they do in the hydrogen atom, and so form a particle of no net charge and with a mass nearly the same as that of the hydrogen atom. 
• On the other hand, a structure of this kind cannot be fitted into the scheme of the quantum mechanics, in which the hydrogen atom represents the only possible combination of a proton and an electron. 
• The first real step towards the discovery of the neutron was given by a very beautiful experiment of Mme. and M. Joliot-Curie.

We here find the idea of a neutron = proton + electron, however with the caveat that such a thing does not fit with quantum mechanics. Chadwick (1891-1974) thus had to wait to the emergence of the Standard Model in the 1960s with neutron = two down quarks + one top quark, glued together by gluons.  

But maybe the idea of neutron = proton + electron was dismissed too quickly. In any case, the binding energy of an electron kernel + surrounding proton cloud is about 0.8 MeV, to be compared with the binding energy of a Hydrogen atom as a proton kernel surrounded by an electron cloud of 13.6 eV, with a change of scale of about $0.5\times 10^5$ matching the change of spatial scale between proton and electron.  

It is possible that Chadwick would have been happy to see something like this, rather than the quark mystification of the Standard Model. What about you? 

What is the Difference between a Hydrogen Atom and a Neutron?

This is a follow up of the previous post on Real Quantum Mechanics applied to atomic kernels.

A Hydrogen atom is composed of a small positive proton kernel and a surrounding large negative electron charge density cloud held together by Coulombic attraction. The binding energy is 13.6 eV. 

A neutron decays into a proton and an electron (and an antineutrino) releasing 0.78 MeV based on the rest masses of the neutron, proton and electron. We can thus view a neutron to be composed of a proton and an electron with a binding energy of 0.78 MeV,  thus with the same components as a Hydrogen atom with a binding energy of 13.6 eV, with a scale factor of about $10^5$.

Thus the same components but vastly different energies, how come? The neutron must be composed in a different way from a Hydrogen atom. The only possibility is to switch the roles between proton and electron and view a neutron to be composed of a very small electron kernel surrounded by a small proton cloud. 

A Hydrogen atom and a neutron will then be described by the same Schrödinger equation, with only a change of spatial scale with some factor $S$, and then with ground state energies also scaling with $S$.  

With an energy scale factor of $S=10^5$, we would thus expect a neutron to be about $10^5$ times smaller than a Hydrogen atom, which is confirmed by observation. 

We thus find experimental support to an idea of viewing a neutron to be composed of a very small electron kernel surrounded by a small proton cloud as an explanation of its very large binding energy compared to a Hydrogen atom. 

Nucleosynthesis into heavier elements would then start by transformation of Hydrogen=proton+electron into neutron=electron+proton under very high pressure and temperature, followed by proton+neutron synthesis. Synthesis of proton+proton into 2proton would then not be needed, and in fact is not observed. But electron+electron into 2electron seems to be needed.

Neutron as Inverted Hydrogen Atom?

Is this a proton charge density surrounded by an electron charge density. Or is it the other way around? 

The Hydrogen atom consisting of a positively charged proton and a negatively charged electron can in Real Quantum Mechanics RealQM  be mathematically modeled in terms of two spatial charge densities, $\phi (x)$ for the proton $\psi (x)$ for the electron as functions of a Euclidean space coordinate $x$, assuming $\phi$ and $\psi$ have disjoint supports (filling space) meeting at a boundary $\Gamma$ signifying that the proton and the electron do not overlap. 

The ground state of Hydrogen is then characterised as the state of minimal total energy 

• $E(\phi ,\psi ) = PE(\phi ,\psi ) + KE(\phi ,\psi)$

where

• $PE(\phi ,\psi ) = -\int\frac{\phi^2(x)\psi^2(y)}{\vert x-y\vert}dxdy$

 is mutual potential energy, and  

• $KE(\phi ,\psi )=\int\frac{1}{2m}\vert\nabla\phi (x)\vert^2dx+\int\frac{1}{2}\vert\nabla\psi (x)\vert^2dx$

 is the sum of proton and electron compression energies under the normalisation 

• $\int \phi^2(x)dx =1$ and $\int \psi^2(x)dx =1$.

Here $m\approx 1836$ is the ratio of proton to electron mass. Eigenstates of higher energies emerge as stationary points of $E(\phi ,\psi )$. Further, $\Gamma$ is a free boundary included in the minimisation with specific boundary conditions to be decided. 

A proton-electron configuration which agrees with observations is given by a proton charge density of small radius centered at $x=0$ surrounded by an electron charge density of large radius. In the limit with the proton modeled as a constant charge distribution of vanishing radius, this gives the standard Schrödinger equation for the Hydrogen atom with Hamiltonian

• $H = -\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$

in terms of the electron charge distribution $\psi (x)$ alone, with $\psi (x)\sim \exp(-\vert x\vert)$ as ground state.  

Now, a neutron is viewed to also consist of a proton and an electron, and so it is natural to ask if the above model can also describe a neutron? That would correspond to a switch of roles with now the electron at the center surrounded by a proton charge density. The compression energy would now be that of the proton resulting in a change of scale with the neutron radius about $\frac{1}{1836}$ of that of a Hydrogen atom.  

In RealQM the size of an electron, in an atom with electrons organised into shells, increases with distance to the kernel, and so electron size is variable. We may expect the same property of a proton with thus increasing size if harbouring an electron inside in the formation of a neutron. The size of a free proton  is estimated to about $10^{-15}$ meter. We compare with a Hydrogen atom of size $5\times 10^{-11}$  which with the above 1836 scaling, gives a proton size of about $10\times 10^{-15}$ when surrounding an electron in a neutron, about 10 times as big as when free.

These are speculations suggested by RealQM as a classical continuum model in terms of non-overlapping charge densities. RealQM can be seen as a form density functional theory which is different from that pioneered by Walter Kohn and Pierre Hohenberg (Nobel Prize in Physics 1998) formed by averaging in a standard multi-dimensional Schrödinger equation. 

Recall that a free neutron is unstable and decays with mean lifetime of 14 minutes into a proton, an electron and an antineutrino (but not a Hydrogen atom), while neutrons are formed in the fusion process of Hydrogen into Helium in a star like the Sun.