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Cambridge University Science Magazine
Why are some elements stable and others unstable? One could well say that the stability of a nucleus is beholden to the laws of thermodynamics, and that radioactivity occurs when a loosely bound nucleus becomes more tightly bound. But it isn't obvious where this binding energy should come from, as an atomic nucleus should fly apart under the mutual repulsion of the positively charged protons within it. Moreover, as has been obvious for almost a century by now, the orbiting electrons that neutralise the nuclear charge do not cling to them that tightly, as the lightness of an electron conspires with Heisenberg's uncertainty principle to keep them from approaching the nucleus that closely.

Before we can begin to understand what is going on, we must first understand quantum field theory. As it turns out, in order to accurately describe reality, we must first assume the existence of a handful of overlapping fields that each assign a few parameters to each point in space and time. These parameters interact in highly correlated ways, such that a vibration in any one field induces vibrations in the other fields at the same location, forming a mathematical construct that behaves identically to a particle. These coupled vibrations, or particles, can then travel in either direction in time, with the particles travelling backwards in time being interpreted as antimatter. Moreover, we find that identical copies of certain classes of these vibrations, termed fermions, by definition cannot approach each other infinitely closely, giving rise to what is termed the Pauli exclusion principle.

In this context, the fundamental forces of nature arise since whenever two particles approach each other sufficiently closely, their combined vibrations cause the fields in the space between them to vibrate such that these particles experience a force between them. As these shared vibrations transfer momentum, they are considered particles, or force carriers, in their own right. The best known of these is the photon, which mediates electromagnetic interactions, but we also have W and Z bosons mediating weak interactions and gluons mediating the strong force. However, with the exception of the photon, the movement of these force carriers through space sets up dependent vibrations in the surrounding fields across the entire length of their passage. This has the effect of limiting the effective range of these fields, as these nascent vibrations require energy to set up, and together these vibrations are then even more likely to encounter, or even create, another particle before they can travel very far.

This now allows us to understand the origins of the nuclear binding energy. We know that the protons and neutrons in a nucleus are sufficiently close together for their constituent quarks to experience the strong force. However, the gluons mediating the strong force interact so strongly with the fabric of spacetime that their effective range is very short, and so the bulk of these interactions can only take place between the quarks within a nucleon. Only a small proportion can involve a quark in a neighbouring nucleon, as sometimes an antiquark with appropriate properties may appear out of the maelstrom of vibrations flanking each gluon, that then creates a pion that may then travel towards and attract a quark in a neighbouring nucleon. Left unchecked, this would eventually cause all the quarks in a nucleus to fuse together into a singular blob of quark matter. However, the positively charged protons repel each other quite strongly as the photons mediating the electromagnetic interaction travel infinitely far, so each proton feels the repulsion of all other protons in the nucleus but only the attraction of neighbouring nucleons. The aforementioned Pauli exclusion principle also prevents this outcome, as any two nucleons of the same type trying to occupy the same point in space must take on different values of spin direction, angular momentum, and distribution in space. This requires each additional nucleon to be located further away from the centre of the nucleus, where they are more weakly bound, because there are fewer nucleons for them to interact with.

From this, we now gain an insight into what makes a radioactive nucleus unstable. We see that in nuclear fission and in alpha decay, these loosely bound surface protons and nucleons can spontaneously bind together and form a separate nucleus. If this nucleus happens to form sufficiently far away from the parent nucleus, electrostatic repulsion may overpower the attraction to the parent nucleus from the strong force. This seals the deal by flinging both nuclei apart at high velocity. Even if nuclear fission does not occur, a sufficiently large imbalance in protons or neutrons may result in the outlying nucleons being sufficiently loosely bound that they can just fly off. Or, these loosely bound protons and neutrons may happen to release a W or Z boson that may bump into a time travelling positron, antineutrino, or even an orbiting electron instead of a fellow nucleon, and thus a proton may become a neutron or vice versa.

Thus, we can see why certain nuclei are radioactive, and why these nuclei become progressively more unstable the heavier they get. In particular, we find that for certain numbers of protons, there is no number of neutrons that will result in a nucleus stable for long enough to remain in large enough quantities from their formation until their subsequent extraction and discovery on Earth. Thus, they must be made with nuclear fusion in a lab. This is easier said than done because not only are these highly charged nuclei harder to fuse, but they are also more unstable than they should be as the lighter nuclei from which they are made do not have enough neutrons to compensate for the increased mutual repulsion between the extra protons.

Still, for sufficiently large nuclei, the innermost nucleons may approach each other closely enough that they could undergo a phase transition into the aforementioned blob of up and down quarks. Just as an ice cube can melt, so can the quarks inside the nucleus begin to intermingle freely instead of being frozen within individual nucleons that only occasionally exchange a quark. Once formed, they would be largely immune against most forms of decay, although there would still be limits to how strongly charged they could get before electrostatic forces broke them apart or induced the emission of electrons or positrons.

However, this limit is sufficiently large and extremely unlikely to be reachable in the lab. Even if the limit is reached, it is unclear whether it could avoid decaying into smaller nuclei for long enough until the phase transition could take place. Instead, this process is theorised to happen within gravitationally bound nuclei such as neutron stars, where the lack of mutual electrostatic repulsion and the extremely long ranged gravitational force allow enough nuclei to be held together for an indefinitely long period of time. However, this also means that it is improbable that we will ever find naturally produced quark matter on Earth, as there is no conceivable process through which these star sized nuclei could be broken up into smaller pieces and find their way to us.

And thus, we find ourselves back in the present situation, where we have discovered all the elements that we have been able to find in nature, as well as a smattering of highly radioactive elements that we have been able to provably create through nuclear fusion.

Mickey Wong graduated in 2015 with a degree in Music from the University of Cambridge. Artwork by Pauline Kerekes.