The internal structural relationships of the atomic nucleus are poorly understood. Although quantum chromodynamics (QCD) offers an explanation of intranucleon bonding in terms of color force, the internucleon bonding via the residual strong force is poorly understood. Neither how binding energy arises nor why the neutrons are necessary at all is clear. Models, such as binding energy, represent the empirical value of nuclide properties but do not explain nuclide stability. All these approaches have their place but are fragmentary and lack integration. None of the theories or models, singly or collectively, is able to explain nuclear properties from the strong interaction upwards. And it has not been possible to explain, from first principles, why any nuclide is stable, unstable, or nonexistent.
This paper contributes to solving this problem. It develops a conceptual framework for a solution on the basis of a proposed new physics at the foundational level. More specifically, the paper takes an existing but unusual conjectured design for the structure of particles at the fundamental level, namely, the nonlocal hiddenvariable (NLHV) design of the Cordus theory, and from that develops a conceptual theory for the arrangement of the atomic nucleus. The theory at the foundational level is based on the geometric internal structures of particles, and consequently the nuclear theory that emerges is also a geometric one, as opposed to a mathematical formalism.
In this context, “hiddenvariable” refers to the proposition that particles have internal structure. In contrast, classical mechanics and relativity are based on continuum mechanics, and quantum mechanics (QM) is based on the presumption of zerodimensional (0D) points. In QM, particles have properties such as charge, spin (orientation), and mass, but these are deemed intrinsic variables of a mathematical rather than physical origin. Hiddenvariable theories assert that particles have internal structures that give rise to the externally evident properties. Such theories are therefore premised in physical realism: if an observable property exists, then there must be an underlying physical mechanism that causes it [
Hiddenvariable designs come in two types: local and nonlocal. The
There are no grounds, neither of physical realism nor of mathematical disproof, that disallow NLHV theories as a class. This is not contentious. However, nonlocal theories have their own difficulties in that they have been hard to discover, with only a few viable candidates. The de BroglieBohm pilotwave theory [
This paper sets out the underlying assumptions of this theory, describes its mechanics, and applies these to the nuclides of hydrogen and helium. Other works extend this further, to include all the nuclides up to and including neon.
The interaction between nucleons is not known with confidence. Consequently, a direct computation of the Schrödinger equation is not feasible for anything but the simplest atoms [
More comprehensive nuclear models are the liquid drop model [
Another problem that none of the models overcomes is how the nucleus is held together. The liquid drop and SEMF treat the nucleons as point particles uniformly distributed in a volume. The models require there some bonding between nucleons but do not identify the mechanism. Furthermore, the repulsive nature of the strong force at short range is excluded from the nuclear models. A related problem is how the volume of the nucleus arises. The models can provide a mathematical fit to the empirical data for charge radii [
These theories attempt to solve the quantitative part of the problem, because that is amenable to the mathematical modeling method, but this is not the real problem. The real need is to differentiate stable from unstable nuclides, but none of these theories is able to do this. Logically consistent physics should be able to explain how the strong force causes nuclear structure, but this has not been achieved. No existing theory, or collection of theories, can explain the mechanisms whereby the strong interaction causes nuclear structures. A core unresolved problem in nuclear theory is how protons and neutrons interact. Inspection of the empirical evidence in the table of nuclides shows that the assumption of independence of the nucleon particles cannot be valid. The stability is not determined simply by quantity of nucleons, as if protons and neutrons contributed equally. The magic number approach does not generalize to explain the table of nuclides as a whole. Instead, stability of a nuclide is an unknown function of the number of both protons and neutrons. Also the evidence clearly shows that neutrons play an essential role in stability, though the trends are complex and the underlying mechanics are unknown. There is a need to find better theories describing how protons and neutrons interact, before the nuclides can be understood.
The purpose of this paper was to develop a systematic theory to explain the relationships between nucleons and how this results in the stability characteristics of the nuclides. The particular objective was to explain the stability, instability, and nonexistence states of the nuclides.
The approach started with a specific design for matter. This was the covert structure defined by the Cordus theory [
The method was conceptual, that is, a Gedankenexperiment, using the design method. This was applied to infer the structural arrangements between the nucleons that would be sufficient to provide the observed behavior of the nuclides. The design was also required to maintain logical internal consistency, that is, not to contravene the other parts of the theory. Necessary assumptions were recorded as lemmas. This design method is described more fully elsewhere [
The Cordus theory is built on the proposition that all particles have internal structures and emit discrete forces. More specifically, particles are proposed to comprise two reactive ends some distance apart, with the reactive ends energized in turn at a frequency (the de Broglie frequency), at which time they emit discrete forces [
First, the predicted structures of the proton and neutron are described. A logical consequence of the theory is that such structures will form bonds with the synchronous interaction (strong force). Surprisingly, multiple types of bonds are predicted, which are termed cisphasic and transphasic for reasons which will become obvious. This is a radical departure from all 0D point based theories and models. It leads to a conceptual breakthrough in the form of a predicted spatial arrangement of the nucleons. These principles are then used to determine the designs for the hydrogen and helium nuclides, and these are shown to have excellent fit to the two isotope series.
The Cordus theory for the proton is shown in Figure
The predicted NLHV and discrete field structures of the proton. One of these axes has an extra pair of discrete forces, giving four discrete forces in total but still a net charge of +1. (1) HEDs accept multiple discrete forces. (2) Proton has two extra discrete forces, but these balance each other. (3) Hand is identical to that of electron, but emission direction is reserved (charge). (4) Type of reactive end: oscillating. One reactive end energizing and the other deenergizing one (180° outofphase). (5) Span is inversely proportional to frequency (and mass). So proton span is much smaller than electron’s. (6) Some flexibility about location of the extra discrete forces may be possible. (i) Axis is overloaded with discrete forces. (ii) Two discrete forces. (iii) Each discrete force carries a +1/3 electrical charge and so overall +1 charge.
The HED notation is a Cordus symbolic representation of the distribution of the discrete forces in the threeemission directions and is a unique signature for the type of particule [
The Cordus theory for the neutron is shown in Figure
Predicted structure of the neutron. The HED arrangements provide a neutral pair of discrete forces, comprising a positive and negative force, on two of the emission directions. The overall charge is thus neutral. It is believed that the pairs may shift to other axes as necessary. (1) Two opposed discrete fields in the HED and hence neutral charge. (2) Only two HEDs contain discrete fields pairs. (3) Anticipate that discrete fields may dynamically relocate to other HEDs when required by bonding. (i) Arrangement of discrete fields is flexible in neutron: pairs may shift to
These predicted covert structures for the proton and neutron are plausible and are not precluded by the Belltype inequalities or any other theory. The proton and neutron structures may look exotic, but that is only because the dominant way of thinking about particles is as 0D points. They are not inconsistent with other theories of physics, that also have their intrinsic variables or hidden dimensions. A coarser level representation is obtained when the span is reduced to zero, and this corresponds to the 0D point approximation of QM. The number of parameters needed to describe a Cordus particule is consistent with the number of dimensions in some string/M theories.
Note that in this theory each particule has two ends, and there is a span, that is, a physical distance between the two reactive ends. This means that particules and their assemblies (described below) have physical size; there is no singularity as with QM. Also the particule energizes its reactive ends sequentially, at its frequency, and the reactive ends are not both simultaneously in the same state. Hence a phase exists, with further implications for bonding (described below). The concept of particules having physical size (span), phase, and spatially orientated discrete emissions is core to this theory and permits a revolution in the understanding of the nucleus.
The Cordus theory proposes that the strong force arises from the synchronization of discrete forces between the reactive ends of different particules [
The next step in the creation of a nuclear model is to find a candidate set of principles for the assembly of protons and neutrons using this synchronous interaction. Consider two particules that are in a coherent assembly, that is, have a common magnitude of frequency, and share a common location for at least
Cisphasic bonding (denoted by #) occurs where reactive ends from two or more particules are colocated and are
By
Cisphasic assembly of proton and neutron (p # n), showing the processes and how the two particules complement each other’s discrete force emissions. In Figure (a) we have the following. (1) Proton. This is the energizing side. (2) We present this interaction as the neutron doing all the adjustment, though both are involved. (3) Neutron needs to be in a suitable state regarding orientation, frequency, and phase. (4) Particules respond to each other’s discrete forces as they come closer. (5) If the state is unsuitable, then the neutron may be repulsed. In Figure (b) we have the following. (1) Neutron rearranges active HEDS to match (both particules may do this). (2) The frequencies of the two particules are pulled into synchronicity. The original individual frequencies would be slightly different, due to the different type of particule (rest mass) and energy. In Figure (c1) we have the following. (1) The particules merge to form a new assembly structure. (2) Each HED now has 2 positive discrete forces (inwards) and one negative (outwards), that is, x11.1 configuration. The total charge is still +1. (3) The subcomponents lose their individuality and become a new assembly, in this case a pn. (4) This is a closed assembly. In Figure (c2) we have the following. (1) The neutron is able to rearrange its active HEDs to align with the new planes presented by the proton. (2) This is a right angle. (3) For this structure to be stable these open ends, they will need to be joined together, if necessary by other neutrons and protons. The quality of these other joints determines the overall stability of the assembly.
The cisphasic behavior results in the merging of the reactive ends into a new assembly characterised by high bonding forces and the subcomponents losing much of their individual identity. The outcome is a new assembly, in this case a pn deuteron, for which the Cordus HED notation is
The proposed mechanics are set out in the supplementary material. Note that the output HEDs are balanced regarding discrete forces: the assembled reactive end has two inward discrete forces and one outward,
There are two subtypes of this interaction: parallel and series. In parallel assemblies, each particule joins to the other at
The transphasic joint (denoted by “×”) also involves colocation of the reactive ends of two particules and synchronous frequency, but the difference is that the reactive ends are at
Transphasic joint (p × p): the joining of two particules, two protons in this case, with opposite phase allows them to share the same space. Although illustrated with two protons, this type of bond is available to any pair of like particules, including neutronneutron and electronelectron. Parallel and series arrangements are available. In Figure (a) we have the following. (1) Proton 1, energizing at this location. (2) Proton 2 is deenergizing, outofphase. In Figure (b1) we have the following. (1) The structure is shown closed, but open structures (closed by other chains) are permissible. (2) The need to preserve the same reenergizing locations means that the energy systems of participating particules are coupled together. They can redistribute incoming energy between them and hence also entanglement. (3) Reactive ends from the two protons share the same location, but only one is energizing at any one time. (4) The interaction provides a level of bonding, because the reenergizing locales are protected from outside interference. (5) However, the relationship is one of mutual association, and the particules retain their individual identity. In Figure (b2) we have the following. (1) Two protons with a transphasic assembly. (2) The three axes (HEDs) are not filled equally, so this is unstable. (3) For these structures to be stable, the open ends need to be joined together, by other neutrons or protons. (4) Two neutrons with a transphasic assembly.
The Cordus theory for transphasic joints permits neutrons to be joined in extended closed chains. The same transphasic relationship applies to pairs of electrons, thereby explaining electronpairing, the Pauli exclusion principle, and Cooper pairs. A series transphasic relationship of a skin of electrons explains superconductors.
The above principles are proposed to be applicable to
Viability of the different proton and neutron combinations.
Cisphasic # (reactive ends in phase)  Transphasic × (reactive ends out of phase) 


Two protons 



Two neutrons 


Proton joined to neutron 

Thus, cisphasic bonds only apply to protontoneutron joints and the transphasic to bonds between like particules. Thus, it is proposed that the synchronous interaction, when applied to the nucleons, permits the joint types shown in Table
Summary of the cis and transphasic joint types and their application to parallel and series assembly structures.
Assembly 
Cisphasic (inphase) #  Transphasic (outofphase) × 

Parallel 




Series 


Importantly, this shows that multiple different types of bonds may exist between nucleons. In contrast, all extant nuclear theories and models assume only one type of strong force and assume that the strong and electrostatic forces apply at the same time. The Cordus theory makes a major departure by proposing multiple types of bonds under the synchronous interaction. A logical consequence is that nucleons form into elaborate assembly chains in the form of a
A logical consequence of the threedimensional layout of the discrete forces and the handedness thereof [
Cubic structures tend to arise from the bonding of protons and neutrons into a nuclear chain. The diagram shows exploded and assembly views. In Figure (a) we have the following. (1) Proton p1. (2) This figure represents a threedimensional cube, not a hexagon. (3) n3. (4) Discrete forces shown solid for energizing side and dashed for deenergizing. (5) p3. (6) n2. (7) Note that all the joints in this particular structure are CISPHASIC. (8) Proton p2. (9) Discrete forces shown solid for energizing side and dashed for deenergizing. This corresponds to phase. (10) Neutron n1. (11) Note that same phase of these two reactive ends from proton and neutron and hence CISPHASIC. In Figure (b) we have the following. (1) p1. (2) n3. (3) Note that at each joint the discrete forces complement each other. There is the same number of discrete forces in each of the three directions. (4) p3. (5) n2. (6) p2. (7) n1. In Figure (c) we have the following. (1) p1. (2) n3. (3) p3. (4) n2. (5) p2. (6) n1.
Exploded assembly of three protons (p) and three neutrons (n)
Assembly of three protons (p) and three neutrons (n), for example, _{3}Li_{3}
Simplified assembly diagram for the same structure
Reduced notation
At each joint, the proton and neutron complement each other’s emission of discrete forces; that is there is a synchronous interaction. Specifically, there are three discrete forces in each direction at these junctions, which gives a balanced loading across the three emission directions. Due to the orthogonality of the discrete forces underlying the synchronous bonds, the assembly of multiple particules intrinsically follows a cubic structure. Thus, the nuclear polymer follows a locus around the edges of a set of connected threedimensional
The nuclear polymer consists, in the first place, of protons and neutrons in series. However, the theory logically permits bridges to form across the polymer. The theory for these bridges is shown in Figure
Neutron crossbridges are anticipated to occur within the nuclear polymer. These result in accumulation of discrete forces at the common node. In Figure (a) we have the following. (1) The proton and neutrons each have their own arrangements of discrete forces. We presume these may be configured, something like this. (2) HEDs: three orthogonal hyperfinefibril emission directions. In Figure (b) we have the following. (1) Particules also have an emission sequence across the HEDs which also creates the matterantimatter species differentiation. By synchronization, we do not mean that particules emit all their discrete forces at once. Instead assembled particules need to synchronize their emissions into these sequences. One conjectured assembly locus of energization is shown here. (2) By synchronizing emissions of discrete forces (strong force), the particule gains more complete HEDs and hence greater stability. This is particularly important for the neutrons, which otherwise have incomplete HEDs (hence decay when isolated). (3) The assembly locus of energization is also proposed as the mechanism for the generations of matter, but the causality is incompletely understood. In Figure (c) we have the following. (1) The locus of energization pulls the reactive ends together and holds them there while the synchronization remains. This causes one reactive end from each particule to colocate in an assembly. (2) The other reactive end is free to make other arrangements, for example, bonds—even of a different type—with another particule. These other arrangements propagate their effects superluminally to the assembled reactive end. Thus, some perturbation of ANY part of the assembly or its periphery affects the whole. It is therefore important, if stability is to be achieved, that the entire extended assembly is stable. (3) The sum of the discrete forces in HED notation from the proton perspective is
The theory allows both proton and neutron bridges but predicts that certain configurations will be nonviable. See the lemmas in Appendix
To sum up the development so far, the theory proposes that the proton and neutron are linear structures (have length), bond in a variety of ways, and form polymers with linear and bridge components, with the polymer being wrapped along the edges of interconnected cubes. The network is primarily a closed loop of nucleons: there are no free reactive ends. The exceptions are certain light elements that have so few nucleons as not to be able to wrap completely around a cube, where open structures are permitted, terminated by protons [
With these concepts in place, the next idea in the Gedanken experiment is introduced: the morphology of the
With models in place for the cis and transapplications of the strong force, there are sufficient basic concepts to identify the layout of the nuclear polymer for simple nuclides.
Hydrogen _{1}H_{0} is simply the proton as already shown. It is proposed that the _{1}H_{1} deuteron is a closed (parallel) cisphasic assembly of one proton and one neutron. The _{1}H_{n} nuclides of hydrogen are expansions of the polymer by insertion of neutrons with transphasic bonds. The predicted nuclear polymers are shown in Figure
Internal structure of the nuclides of hydrogen, as proposed by the Cordus theory. In Figure (b) we have the following. (1)
This theory explains the stability trends in these nuclides.
The stability of _{1}H_{1} can be explained by the cisphasic protontoneutron bond.
Likewise, the long life of _{1}H_{2} is attributed to its cisphasic bonds and its instability to the structure lacking orthogonality.
The poor viability of all the higher nuclides is explained by their transphasic neutron chains.
The theory also explains why the series stops where it does, at _{1}H_{6}. This is because there is a neat morphological boundary at _{1}H_{6} such that the next longer polymers do not have access to a suitable layout.
Explanations of the helium nuclides are given in Figure
Internal structure of the nuclides of helium, as proposed by the Cordus theory. In Figure (a) we have the following. (1) Prohibited: two cisphasic protons do not give complete HEDs. (2) Cisphasic bonds are possible in principle but are nonviable without at least one neutron per cube. In Figure (b) we have the following: (1)
The helium nuclides are a strange series, because of abrupt changes and reversal in viability. This has historically been a difficult, even impossible, area for other theories. It is so problematic that some theories omit the light elements altogether. The Cordus theory has no such difficulties. It successfully explains the trends in stability. The explanation is entirely morphological and is based on the principle that certain combination of protons and neutrons cannot find a suitable shape and therefore cannot exist (except fleetingly). Hence, the difficult questions, which have troubled many other theories, can now be answered.
The concepts that have been presented here are a radical departure at the fundamental level and have profound implications for the directions taken by fundamental physics in the future. Almost all the ideas that have been presented in this paper are unorthodox, and conventional physics may need some time to evaluate their validity and digest the implications. To assist such an appraisal, a summary of the conceptual framework is shown in the system model of Figure
System overview of the causes of bonding between protons and neutrons in the nucleus. The diagram summarizes the main features of the Cordus design of the proton: this is a nonlocal hiddenvariable solution and it proposes that the proton has internal structures as well as a particular signature to the discrete forces (discrete fields) that it emits, likewise the neutron. The rest of the diagram identifies the two different types of synchronous (strong) bond being proposed here, namely, the cisphasic and transphasic states.
This paper provides new mechanics for the nuclides, one totally unlike any other theory. This provides a revolutionary new explanation of nuclear mechanics. The mechanics have been developed from first principles and then applied to the hydrogen and helium nuclides. They successfully explain why each nuclide is stable, unstable, or nonexistent. This is a breakthrough as this depth of explanation has not previously been achieved. The same mechanics also successfully explain the stability trends of all the nuclides up to and including Ne [
The first contribution is the conceptual one of building a more nuanced concept for the strong force generally (Cordus: synchronous interaction). A radically different idea has been proposed for the strong interaction at the quark level and the strong nuclear force. Conventionally, the strong nuclear force overcomes the electrostatic repulsion of protons. In contrast, the Cordus theory proposes that the electromagneticgravitational (EMG) forces, for example, electrostatic forces between nucleons, are
The second contribution is showing how the proton and neutron may be bonded. This has not previously been achieved. Existing theories like the shell and liquid drop models require but do not explain this, and so does QCD, which though it has a solution for the bonding of quarks via gluons, which does not explicitly explain the bonding between nucleons. The present work identifies an advantage to the proton in being bonded to a neutron, when otherwise there would seem no reason for such a bond. That advantage is the preferential alignment of discrete forces in three orthogonal directions. The neutrons are necessary because they provide a set of discrete forces that are complementary to those of the proton. The stable bonding within the nucleus occurs because of this synchronous compatibility and is proposed to have nothing to do with electrostatic charge per se. Thus, the Cordus theory predicts, in a major departure from conventional models of the nucleus, that the protons in stable nuclei are bound through neutrons, which are essential intermediaries, and that nuclear bonding involves synchronous interactions rather than charge per se. In contrast, other theories model the protons as being bound directly together or alternatively in an amorphous collection (liquid drop) or as shells. This difference may be testable and falsifiable. The Cordus theory predicts that protontoproton bonds may be either cisphasic or transphasic. This should be testable, given that the Cordus concept of frequency phase corresponds to the QM concept of spin, which in principle is measurable. The cisphasic bonds are predicted to be more stable than the transphasic.
A third contribution is the introduction of the concept of
A fourth contribution is the provision of candidate descriptive physical models for the proton, neutron, deuteron, and several simple nuclide assemblies thereof. The Cordus theory predicts that the proton and neutron have specific internal structures and specific signatures for the emission of discrete forces. This may be falsifiable. An associated contribution is the prediction of the internal structure of the hydrogen and helium nuclides and an explanation of their stability trends. The Cordus theory explains qualitatively why the stability worsens with increased neutron count. It also explains the discontinuities in stability, for example, why _{2}He_{5} is so much less stable than its neighboring isotopes. The limits of the series, why they stop where they do, are also explained. Another important explanation is why _{2}He_{1} should be stable, as the only stable nuclide with p > n. No other theory can explain all these effects, and most of the theories, for example, liquid drop and QCD, cannot explain any of these. So the contribution is an improved explanation for the H and He nuclides.
A final contribution is methodological, in that the work demonstrates (a) the vitality and relevance of nonlocal hiddenvariable theories, which otherwise have been rejected without proper consideration, and (b) the value in using a system design approach for concept development. The resulting Cordus theory provides new insights and fresh ideas towards an old problem. This has otherwise not been achieved with other hiddenvariable solutions, for example, de BroglieBohm.
The explanations of the Cordus theory are consistent with empirical evidence of how matter behaves under the strong force, so the theory has
The points of difference of the Cordus theory arise from several conceptual attributes that are radically different to any other theory of physics including QM and QCD.
The first is the proposition that the nucleons have geometric span. Hence, the Cordus theory rejects the zerodimensional point construct of QM. It is the 0D point thinking and the resulting singularities that frame the orthodox paradigm into the excessively limiting idea that the nuclear bonding force is repulsive at short range, strong at middle range, and weak at long range. This odd set of properties is a consequence of the premise and does not need to be a physical reality. The Cordus theory proposes that it is better to consider the nuclear bonding force as a synchronous interaction. The Cordus particule idea provides physical interpretations for superposition, entanglement, spin, frequency, phase, orientation angles (e.g., polarity), and parity violation which are otherwise indefinable in QM. Thus, quantum mechanics (QM) is reinterpreted as a solution of averages, applicable only to coherent bodies where the size of the particles can be neglected and otherwise not applicable at both the subatomic and macroscopic scales.
The second is that the two ends of a particule energize and deenergize in sequence, at a frequency. Consequently the whole particule is not in a single state. This is consistent with the QM concept of geometric superposition. In QM, this is attributed to a fundamental stochastic variability, but the Cordus theory rejects QM’s interpretation as a simplistic and coarse approximation to a deeper deterministic causality. Furthermore, the Cordus theory outright rejects the QM idea that a particle can be in a temporal superposition.
The third unique feature of the Cordus theory is its concept for the strong force. This is reformulated as a synchronous interaction between discrete forces [
Unique to this theory is the concept that bonds between nucleons may take two forms: cis and transphasic [
Consequently this theory predicts that there are several ways, not only one as in the orthodox theories, for how protons and neutrons may bond. Having multiple interactions also provides a means to differentiate between
The Cordus theory is currently mostly a conceptual work. It does not calculate the binding forces, lifetimes, or the charge radii. So it is not a complete description of every feature of the strong force. This is a limitation but hardly a fatal one as neither does any other theory give quantitative predictions from first principles for all these variables (except by parameterfitting and tuning).
There are two other features which might seem limitations of this theory, but they are not. The fact that this is a nonlocal hiddenvariable design is not a limitation. It is only
The Cordus nuclear theory has potentially farreaching and deep implications for the future direction of fundamental physics. It demonstrates that a hiddenvariable design has better explanatory power than other theories and models based on the 0D point premise. Given this and that it subsumes quantum mechanics, the implication is that the next deeper level of physics is better described by hiddenvariable designs than quantum mechanics. The consequences are wideranging, in that a large number of physical phenomena can be described with the Cordus mechanics. The implications for future research are therefore vast. The theory has the potential to touch every area of fundamental physics and transform the conceptual foundations on which many theories are built, thereby requiring reformulation of those theories to accommodate covert structures.
Regarding the nuclides specifically, opportunities for further work lie in several directions. One is to develop a mathematical formulism for the synchronous interaction (including its directional, discrete, and phasic attributes), quantify the parameters, and evaluate the robustness of the resulting model against empirical data. There is also a need to develop a mathematical representation of the nuclear polymer and the filling of cubic structures. This would be helpful in exploring the heavier nuclides. Another opportunity is to further develop the concept and see whether the theory can explain additional nuclides. There is a need, at present unfulfilled by quantum theory, QCD, nuclear models, or string/M theory, to explain why any given nuclide is stable or unstable. There are also a large number of deviations in the trends that need explaining. Why are more neutrons required for stability in heavier nuclides; that is, why does the trend deviate from p = n? Why are some nuclides (e.g., _{4}Be_{4}) unexpectedly unstable? Why are the margins of nonexistence (drip lines) jagged? Why do some elements have only one stable nuclide, whereas others have multiple ones? No existing theory can do any of this, so it is a formidable challenge. There are many other nuclides to explain, with odd trends apparent even within one isotope series and hence much opportunity for future work and theorybuilding. Another opportunity for research is to model binding energy and charge radii. A complete theory of the nucleus will also need to explain the decay process itself and the weak interactions (beta plus and minus decay and electron capture), and the Cordus theory has already made progress in this area [
Being able to sketch out a coherent causality starting from the fundamental level, via the nucleus, and onwards to qualitative explanations for stability of the nuclides is a significant accomplishment. It gives reason to be optimistic that another breakthrough may be achievable, the creation of a consistent theory that spans fundamental physics and chemistry. Chemical interactions are primarily mediated by the electrons between interacting atoms. Consequently, future work could be focused on integrating the electrons into the nuclear polymer theory and explaining electron valance.
The purpose of this paper was to develop a systematic theory to explain the relationships between nucleons and thereby explain the stability, instability, and nonexistence states of the nuclides. This has been achieved in a Gedankenexperiment. The work reconceptualizes the basic principles of the bonding of protons and neutrons, using inferences from the Cordus theory for the synchronous interaction (strong force). The resulting theory predicts that protons and neutrons may form different types of bonds, with different stability. Specifically, the synchronous interaction assembles particules in and outofphase (cis and transphasic resp.) and into open or closed chains. The theory identifies the role of the neutrons in nuclear bonding. The protons in stable nuclei are bound through neutrons, which are essential intermediaries. Nuclear bonding therefore involves synchronous interactions rather than charge per se. In contrast, other theories model the protons as being bound directly together or alternatively in an amorphous collection (liquid drop) or as shells. The theory predicts that the assembly structures involve a
This theory opens up a new field of mechanics, offers a different conceptual framework for the nucleus, and advances the understanding of nuclear physics. It is a different concept to other theories and exceeds them in ability to explain stability trends for the nuclides. That it has been possible to achieve this from the hiddenvariable sector, when no quantum theory has answered these questions, shows that serious consideration must now be given to the likelihood that particules may have internal structure after all. If so, the theory has the potential to revolutionize fundamental physics of the nucleus.
The authors declare that there is no conflict of interests regarding the publication of this paper. Neither was the research conducted with personal financial benefit from any third party funding body, nor did any such body influence the execution of the work.
Dirk J. Pons, Arion D. Pons, and Aiden J. Pons developed the conceptual foundation and the theory and critically evaluated the logical consistency thereof. All authors contributed to the writing of the paper. Dirk J. Pons created the drawings.