Neutron (n0) is an electrically neutral nuclear particle that decays into a proton (p+) and an electron (e–) that much is known. In experiments, we can directly observe neutron decay by noting proton and electron tracks on nuclear emulsion plates.
Technically, there is also a third particle involved — a neutrino — but for the sake of simplicity I am going to omit neutrinos from discussion. Instead I am going to focus on the following question: if neutron decays into a proton and an electron, is it fair to say that a neutron is composed of a proton and electron much in the same way as a hydrogen atom, but perhaps smaller?
Neutron is Not a Bound State of Proton and Electron
The correct, although not a particularly intuitive answer is ‘no’. Neutron does not contain an electron and therefore cannot be viewed as a bound state of a proton and an electron.
Why not? To answer this question, we must fall back to the definition of the electron. Electron is more than a ‘quantum of electricity’ associated with a static electric charge of -1.6 x 10-19 Coulomb. According to our quantum mechanical understanding, the electron is a particle, whose motion is governed by the Schrödinger equation. In this sense a neutron cannot be understood as a bound system of a proton and an electron because when we bind an electron to a proton we get a hydrogen atom, and all attempts to extend the Schrodinger equation to include negative or fractional quantum states (including Mills’ hydrino hypothesis) so far disagree with experiments.
So, if the ground state (n = 1) of an electron in the potential well around a proton corresponds to a hydrogen atom, what happens if we somehow force the electron closer to the proton? If there is no electron inside a neutron, how come a free neutron decays into a proton and an electron?
Electron vs. Elementary Charge
To resolve this apparent paradox, we must draw a clear distinction between the notions of ‘electron’ and ‘elementary charge’. Once again, an electron is a fermion, which means it is magnetic spin 1/2 particle that obeys Fermi statistics. Therefore motion of an electron is governed by Dirac equation, which is relativistic version of Schrodinger’s wave equation.
What these fancy words mean is that an electron is a complex entity with behavior very different from that of a simple round classical ball of static charge. When we think of electrons as balls of charge, we overlook that they are miniature vibrating magnets, which cannot be squeezed to occupy the same space when they resonate at the same frequency; this is a well-known Pauli’s exclusion principle.
The analogy with magnets is quite intuitive: magnets repel each other when we push the same poles together, but if we flip one of the magnets they attract. This analogy explains why electrons like to arrange in pairs and why additional electrons must vibrate at different frequencies when we squeeze more and more of them into the same space.
In the same time, the Standard Model of Particle Physics offers other particles that carry the same elementary charge (the charge of the electron) but have different magnetic properties (i.e. different spin) and different mass from that of an electron. Take W– boson for example. W– boson is a spin 0 particle, which means that it is non-magnetic and therefore you can ‘stack’ an unlimited number of them in the same space and have them all vibrate at the same frequency.This is how the Standard Model of Particle Physics understands the inner workings of an atomic nucleus. One can argue that this is a complicated and overly mathematical model, which may be true. But once you translate the fancy particle physics jargon into plain English it basically means this: in order to force an electron to merge with a proton to form an neutron we must deprive the electron from its magnetic properties (thus turning into into another particle, the W– boson).
Conservation of Spin
There is yet another reason why neutron is not a composite particle formed by a proton and an electron. This reason is the conservation of spin. Spin is a quantum mechanical counterpart of angular momentum that is measured in units of Planck constant ℏ, which has a dimension of angular momentum. Angular momentum is a conserved quantity in both quantum and classical mechanics. As such, if we put together an electron (spin 1/2ℏ) and a proton (also spin 1/2ℏ) we ought to get a composite particle with spin 0 (when the electron and the proton ‘spin’ in different directions) or spin 1ℏ (when the electron and the proton ‘spin’ in the same direction). Yet the spin of neutron is 1/2ℏ.
The spin of a neutron along is enough to prove that a neutron is not a bound state of an electron and a proton, simple as that.
Neutron Charge Distribution
Experiments designed to probe charge distribution inside a neutron reveal that neutron has a positive core surrounded by a shell of a negative charge – Fig. 1.
Superficially this picture is consistent with the structure of a hydrogen atom in a ground state. Yet conceptually there is no electron inside the neutron for reasons I already stated above.
Superficially this picture is consistent with the structure of a hydrogen atom in a ground state. Yet conceptually there is no electron inside the neutron for reasons I already stated above.
The confusion arises from the confounding of terms ‘electron’ and ‘elementary charge’. The two are not the same. Electron is an elementary charge that behaves a certain and very specific way. Yet there are other elementary charges in nature that behave quite differently from electrons, and this is what we find inside a neutron.
So, the high energy scattering experiments tell us that neutron does have an internal structure, yet it is incorrect to think of this structure as a bound state of an electron and a proton. Inside of a neutron we do have a system of elementary charges, and our current best attempt at understanding them involves the theory of quantum chromodynamics.
Electron Glue
While quantum chromodynamics is a very complex and mathematically intense theory, it is possible to develop a simple, intuitive understanding of the underlying physics.
Free electrons and free protons are well-studied charged particles with well-established properties (such as charge, spin, mass). We know that to form a neutron out of a proton and an electron we must ‘crush’ an electron depriving it of its magnetic properties (i.e. remove the spin 1/2 and replace it with the spin 0). A ‘crushed’ non-magnetic electron forms a kind of ‘electric glue’ that holds nucleons together in a nucleus. Quantum chromodynamics even uses a quite fitting term ‘gluon’ to describe the particles that facilitate the interaction between nucleons in a nucleus on the most fundamental level.
Here I would like to emphasize that there are no ‘fixed’ protons and ‘fixed’ neutrons inside a nucleus, and therefore it is fundamentally incorrect to view a nucleus as some sort of a fixed arrangement of protons and neutrons. This fixed / ‘crystalline’ structure approach is wrong for two reasons:
- High-energy scattering experiments involving nuclei bombarded by electrons or protons are consistent with the ‘fluid’ or continuum model of a nucleus rather than with a ‘crystalline’ or ‘composite’ structure that so many armatures like to entertain. If protons and neutrons were situated in fixed locations inside nuclei, the scattering experiments would have shown that. Yet there is no evidence for such a fixed structure.
- The protons and neutrons inside of a nucleus are one and the same – there is no difference between them as they constantly morph one into another. A proper visualization of a nucleus IMHO would be a bound system of oscillating positive charges held together by negatively charged ‘electric glue’ made out of ‘crushed’, de-magnetized electrons.
The proposed visualization is broadly consistent with quantum chromodynamics, which teaches us that protons and neutrons inside a nucleus constantly morph one into another by exchanging π-mesons, which are the carrier particles for the strong nuclear force.
The model of a nucleus is very similar to the Thomson atomic model, except that instead of electrons we have a negatively charged ‘glue’ – Fig. 2.
To me it feels like we build an essentially electrostatic well as we inject neutrons in a nucleus. Electrons lose their magnetic properties turning into static charges that merge into a continuum forming a potential well within which the positive protons are oscillating. Kind of like an atom, but in reverse.
Such visualization (Fig. 2) is an intuitive representation of the nuclear shell model.
The Insight
The above exercise comes with an important insight: we must ‘crush’ electrons or rather deprive them of their magnetic properties in order to transform them into a glue that binds nucleons together. How do we do that?
The answer is in the recipe. Suppose we take an electron beam. Quantum mechanically, an electron beam is a traveling (as opposed to standing) electron wave, the electron wave with strong magnetic properties that we must eliminate.
Now take a proton beam. A proton beam is a traveling wave of protons, which is also characterized by strong magnetic properties.
Now superimpose the two. By superimposing the two traveling matter waves perfectly, we might just cancel their magnetic fields because electrons and protons traveling in the same direction will create a mutually opposing and therefore mutually cancelling magnetic field.
Will this cancellation of the magnetic field ‘crush’ the electrons turning them into the non-magnetic W– bosons we need to form neutrons? I certainly think so.
Let me know what you think! Comment and subscribe to the blog.