Now start to put together a nucleus...

A solitary neutron has a half-life of about 10.3 minutes. This instability may well be caused by instability in the outer boundary of its strong electrostatic field (other particles will have different electric field dimensions and strengths, leading to different half-lifes; this implies that there is an underlying law that determiens the stability of a particle from its electric field dimensions and strengths - like the neutron, particles will almost certainly have an electric field bounded at such a small radius they are not thought of as electrostatic). Two neutrons could theoretically bind (at least on the basis of what we have done above) but it is reasonable to suggest that they will destabilise each other much faster, leading to a very much shorter half-life for a double-neutron-no-proton nucleus, short enough for it to have no real chance of measurable existence. The nature of radioactive decay in the nucleus further suggests that neutrons can be stabilised by the presence of the proton’s extended electric field. Both protons and electrons seem to be intrinsically stable, possibly because of their spatially unlimited electric fields (however the grand unification theory suggests they should decay with a half-life of 10³² years, although this has yet to be measured at the time of writing).

This leads to a picture where a nucleus is stable (i.e. does not decay) if each neutron can couple with enough protons to stabilise their outer field boundaries.

Hence, if we can show there is attraction between a neutron and a proton, which there must be to hold a nucleus together, then it is the neutrons that hold the whole nucleus together. So we need at least enough neutrons to hold the protons in the nucleus despite the repulsive forces between the protons.

This leads to two conflicting demands...

1. There must be enough neutrons to overcome the repulsive forces between protons.
2. There must not be so many neutrons that they cannot all benefit from the stabilisation provided by the protons, or the nucleus will inherit the instability of the neutron. In the extreme this leads to a much shorter half-life in the nucleus than in a single neutron, as the neutrons destabilise each other.

Hence, too few neutrons and the nucleus flies apart because of the stress of the protons’ mutual repulsion. Too many and a neutron in the nucleus self-destructs as it becomes unstable by lack of the stabilising effect of surrounding protons, creating radioactive decay.

It is also a reasonable hypothesis that the geometry in the nucleus is stable and fixed for any isotope of any element, because if the protons and neutrons simply made up a roiling cloud of random configurations then virtually every nucleus would have a much shorter half-life as random configurations brought too many neutrons together away from sufficient protons to stabilise them.

First, consider a neutron and a proton close together - can we expect the interaction to be attractive or repulsive? It all depends on the model of the proton that we use. If we use a simple model for the proton like the positron, with a simple electric field but with the inner limit of the field being well within the 1 fm neutron radius, then the forces will always be repulsive (attractive if we use the negatively charged electron). However, although there is an overlap (and theoretically an interaction between a neutron and a proton of this model) at any separation to infinity, in practice the interaction is weak and drops off extremely rapidly from a repulsion of 1800 N at 1 fm separation to being virtually immeasurable beyond 4 fm.

The field is always repulsive (even in the region where two neutrons would attract) but the forces are very weak, and fall off much faster than the inverse of the square of the radius, so that by 20 neutron diameters these forces are virtually non-existent. This proton cannot be glued into the nucleus.

This leads us to a more complex model for the proton, of a strong neutron-like central field surrounded by a normal positron-like field that extends on to infinity. Now if the inner boundary of a a positron field is sharp then its radius could be taken as the classical radius of the electron; in fact this model gives the electron too high an inertia (see here) and the inner radius is nearer 3.75 fm. Put that against the neutron outer field radius of 1 fm and there is a gap. In fact, if both have sharp boundaries then the outer positron field will be trapped and it will bounce around the central field which will pin it. This can be seen by considering the field lines -when the outer boundary of the core penetrates the inner boundary of the positron field the fields align together, augmenting the energy increase and causing repulsion. In the image below the fields in the red area overlap leading to an increase in the energy in that region (since the vector sum of the electrostatic field strengths a and b is squared to give energy, so Energy = a² +b² +2.ab which is greater than the sum of the individual isolated fields a²+b²)... Therefore as the core field interpenetrates the positron-like field it will suffer repulsion. The core field is trapped inside the positron field, and it will take a lot of energy to knock the positron field out from the core field’s trapping.

Of course, the inner boundary of positron-like part of the field, and the outer boundary of the core field, may be graduated, so that the relationship of the core to the outer field is centred. Even so, it is likely that the relationship of the inner core to the outer field distorts under the forces inside the nucleus, with the inner core being attracted to neutrons and the outer field being repelled by other similar fields in other protons. There may of course be some underlying structure that pins these together.

If the structure of the outer field is correct then two positrons reach a maximum repulsion of about 4.1 N at about 7 fm separation. Nearer than that and the force drops off again because of the electrostatic “hole” in the centre of it. This also applies to a proton if we build it from a neutron and a positron. This means than normal electrostatic repulsion in the nucleus is never more than 4.1 N between any two protons, and then only at a separation of 7 fm. The positronic repulsion therefore seems quite weak over the short range of the nucleus. The other side of the coin is that the unit charge on the neutron core may not be that high.

The outer field positron/electron field may be a universal building block for particles, and the stronger unstable core field may be another (such fields need some generation mechanism at the boundaries that holds the electric field stable in space). An electron and a positron use the outer component only, the neutron uses the inner component only, and a proton uses both. Other particles may use yet more building blocks.

If we assume similar parameters for the proton to the neutron core, can this more complex model lead to nuclear binding? The answer is yes. Let us look at the actual Helium nucleus made up of two protons and two neutrons. In the following picture the two neutrons (outer field boundaries in blue) and the two protons (outer bound of core field in red) lie in an overlapped state...

Each neutron has full bonding at 1 fm separation to the other neutron and both protons. The protons bind to both neutrons at 1 fm separation, and to each other at 1.73 fm separation. This is a lot of binding force, and well able to overcome the repulsion between the protons’ outer positron-like fields.

In conclusion...

I have presented the simple idea of the neutron core being a positive bounded electric field. There is no requirement for a negative field surrounding it to provide neutron -neutron attraction. The proton may have similar structure at its heart, although extending it to the atomic nucleus needs more analysis on exact values for this internal field, and the gradation between the outer proton field and the inner core.

For nuclear binding to take place between protons and neutrons the proton must be a compound particle, containing a positron-like field surrounding and captured by an enclosed neutron core. Splitting these fields apart takes a significant amount of energy.