Neutrons as composite particles
In our rather particular conception of the world, we think of photons, electrons, and protons – and neutrinos – as elementary particles. Elementary particles are, obviously, stable: they would not be elementary, otherwise. The difference between photons and neutrinos on the one hand, and electrons, protons, and other matter-particles on the other, is that we think all matter-particles carry charge—even if they are neutral.
Of course, to be neutral, one must combine positive and negative charge: neutral particles can, therefore, not be elementary—unless we accept the quark hypothesis, which we do not like to do (not now, at least). A neutron must, therefore, be an example of a neutral (composite) matter-particle. We know it is unstable outside of the nucleus but its longevity – as compared to other non-stable particles – is quite remarkable: it survives about 15 minutes—for other unstable particles, we usually talk about micro- or nano-seconds, or worse!
Let us explore what the neutron might be—if only to provide some kind of model for analyzing other unstable particle, perhaps. We should first note that the neutron radius is about the same as that of a proton. How do we know this? NIST only gives the rms charge radius for a proton based on the various proton radius measurements. We, therefore, only have a CODATA value for the Compton wavelength for a neutron, which is more or less the same as that for the proton. To be precise, the two values are this:
λneutron = 1.31959090581(75)10-15 m
λproton = 1.32140985539(40)×10-15 m
These values are just mechanical calculations based on the mass or energy of protons and neutrons respectively: the Compton wavelength is, effectively, calculated as λ = h/mc. However, you should, of course, not only rely on CODATA values only: you should google for experiments measuring the size of a neutron directly or indirectly to get an idea of what is going on here.
Let us look at the energies. The neutron’s energy is about 939,565,420 eV. The proton energy is about 938,272,088 eV. Hence, the difference is about 1,293,332 eV. This mass difference, combined with the fact that neutrons spontaneously decay into protons but – conversely – there is no such thing as spontaneous proton decay, confirms we are probably justified in thinking that a neutron must, somehow, combine a proton and an electron. The mass of an electron is 0.511 MeV/c2, so that is only about 40% of the energy difference, but the kinetic and binding energy could make up for the remainder.
So, yes, we will want to think of a neutron as carrying both positive and negative charge inside. These charges balance each other out (there is no net electric charge) but their respective motion still yields a small magnetic moment, which we think of as some net result from the motion of the positive and negative charge inside.
Let us now move to the next grand idea which emerges here.
Electrons as gluons?
The negative charge inside of a neutron may help to keep the nucleus together. We can, therefore, think of this charge as some kind of nuclear glue. We tentatively explored this idea in a paper: Electrons as gluons? The basic idea is this: the electromagnetic force keeps electrons close to the positively charged nucleus and we should, therefore, not exclude that a similar arrangement of positive and negative charges – but one involving some strong(er) force to explain the difference in scale – might exist within the nucleus.
Nonsense? We don’t think so. Consider this: one never finds a proton pair without one or more neutrons. The main isotope of helium (4He), for example, has a nucleus consisting of two protons and two neutrons, while a helium-3 (3He) nucleus consists of two protons and one neutron. When we find a pair of nucleons, like in deuterium (2H), this will always consist of a proton and a neutron. The idea of a negative charge acting as an in-between to keep two positive charges together is, therefore, quite logical. Think of it as the opposite of a positively charged nucleus keeping electrons together in a multi-electron atom.
Does this make sense to you? It does to me, so I’d appreciate any converging or diverging thoughts you might have on this. 🙂
 The reader should note that the Compton wavelength and, therefore, the Compton radius is inversely proportional to the mass: a more massive particle is, therefore, associated with a smaller radius. This is somewhat counterintuitive but it is what it is.
 None of the experiments (think of the Super-Kamiokande detector here) found any evidence of proton decay so far.
 The reader should note that the mass of a proton and an electron add up to less than the mass of a neutron, which is why it is only logical that a neutron should decay into a proton and an electron. Binding energies – think of Feynman’s calculations of the radius of the hydrogen atom, for example – are usually negative.
2 thoughts on “Neutrons as composite particles and electrons as gluons?”
How do you manage to understand the math so easily? I have a Ph.D. and struggle
Hi there ! Thanks for the compliment ! I think I stick to very easy math and very easy conceptual stuff – which is why I understand it easily. I am currently working on something more complicated and that takes me probably much more time than you would have to spend on it ! 🙂 JL