Physics Research International

Volume 2015, Article ID 651361, 19 pages

http://dx.doi.org/10.1155/2015/651361

## Nuclear Polymer Explains the Stability, Instability, and Nonexistence of Nuclides

^{1}Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8020, New Zealand^{2}University of Canterbury, Christchurch 8020, New Zealand^{3}Rangiora New Life School, Rangiora 7400, New Zealand

Received 12 September 2014; Revised 16 April 2015; Accepted 30 April 2015

Academic Editor: Ali Hussain Reshak

Copyright © 2015 Dirk J. Pons et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Problem*. The explanation of nuclear properties from the strong force upwards has been elusive.* Approach*. Design methods were used to develop conceptual mechanics for the bonding arrangements between nucleons, based on the covert structures for the proton and neutron as defined by the Cordus theory, a type of nonlocal hidden-variable design with discrete fields.* Findings*. Nuclear bonding arises from the synchronous interaction between the discrete fields of the proton and neutron. This results in not one but multiple types of bond, cis- and transphasic, and assembly of chains and bridges of nucleons into a nuclear polymer. The synchronous interaction constrains the relative orientation of nucleons, and hence the nuclear polymer takes only certain spatial layouts. The stability of nuclides is entirely predicted by morphology of the nuclear polymer and the cis-/transphasic nature of the bonds. The theory successfully explains the qualitative stability characteristics of all hydrogen and helium nuclides.* Originality*. Novel contributions include the concept of a nuclear polymer and its mechanics; an explanation of the stability, instability, or nonexistence of nuclides starting from the strong/synchronous force; explanation of the role of the neutron. The theory opens a new field of mechanics by which nucleon interactions may be understood.

#### 1. Introduction

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 hidden-variable (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, “hidden-variable” 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 zero-dimensional (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. Hidden-variable 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 [1]. The hidden-variable approach is therefore consistent with the principles underlying the scientific method. However, it is an obscure approach because of the historical difficulty in finding such solutions, a difficulty which has only recently been overcome.

Hidden-variable designs come in two types: local and nonlocal. The* local* theories assume that the principle of* locality* applies. Locality means that the behavior of a particle is only affected by fields, forces, and phenomena at the point at which the particle exists, not by the values of fields or effects elsewhere. Related to this is* local realism* whereby the properties of an object preexist before the object is observed. The Bell type inequalities [2–4] preclude* local* hidden-variable solutions, which mean that 0D point particles are theoretically incapable of having internal structure. However this is unsurprising given that locality is closely aligned to QM’s premise that particles are 0D points. The many experiments with entanglement are generally interpreted as supporting superluminal causality and nonlocal behavior; that is, locality does not to apply at the foundational level. This introduces a major incongruity in that physics at the macroscopic level of continuum mechanics is otherwise believed to be local. The* nonlocal* hidden-variable theories, for example [5, 6] and more recently [7], accept that entanglement effects are real. They propose mechanisms based on physical causation to explain the phenomena.

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 Broglie-Bohm pilot-wave theory [5, 6] is one such solution, but it has not progressed beyond an explanation of the double-slit behavior of light, cannot explain other phenomena, and cannot function as an independent theory of physics generally. More recent nonlocal developments in the form of the Cordus theory [7] have much greater general applicability, that is, improved external construct validity. The present paper shows how this latter theory may be extended, in a conceptual manner, to provide a novel qualitative explanation of nuclear structure. It shows, using this Cordus nonlocal hidden-variable design, that it is possible to explain nuclear structure from the strong force, which has not previously been achieved for any theory of physics. The theory is the first to explain why any nuclide from H to Ne is stable, unstable, or nonexistent. Even the relative trends in lifetime can be qualitatively explained. The role of the neutron in nuclear bonding is elucidated, which also has not previously been achieved. The depth of explanations achieved is greater than that provided by competing theories. This has the profound implication that the next physics may be based on nonlocal hidden-variable designs rather than zero-dimensional point particles.

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.

#### 2. Existing Approaches to Nuclear Structure

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 [8]. Quantum chromodynamics proposes an explanation of the bonding of quarks inside the nucleons, by the exchange of gluon in the color force [9, 10]. It is generally believed from consideration of the density of the nucleus that the strong force has a short range, so that nucleons are only attracted to other local nucleons, not by the bulk of nucleons as a whole (which would increase the density beyond that observed). Density considerations also suggest that the force is repulsive at closer ranges, so the nucleons are unable to come too close. However, QCD does not fully explain all the characteristics of the strong force and is unable to explain how the proton and neutron bond. It thus has little to contribute to our understanding of how* multiple* nucleons might interact.

More comprehensive nuclear models are the liquid drop model [11], semiempirical mass formula (SEMF) [12], and Ivanenko’s shell model [13]. The nature of these models is to approximate nuclear characteristics with mathematical representations. They include terms to accommodate the strong and electrostatic forces. However, these theories mathematically* model*, rather than* explain*, the binding energy (BE) characteristics. They do this reasonably accurately, which might be considered a success if not for the fact that they are disconnected from any theory of the strong force. Anyway, binding energy only correlates weakly with nuclide stability. A further problem is that the models treat the neutrons and protons independently: there is an assumption that the particles are different and therefore occupy different quantum states. However, it is also apparent from observation that no nucleus exists with multiple protons and no neutrons, so evidently neutrons provide an important role within the nucleus, which is not represented in any of the existing theories. Similar problems apply to the* interacting boson model* [14, 15] which assumes that nucleons exist in pairs. However, this limits the model to nuclides where p = n, which is an overly simplistic assumption.

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 [16]; yet none of the models explains* how* the aggregation of 0D point particles creates geometric size. Deeply problematic is the disconnect between the QCD strong force and the nuclear models, as already mentioned.

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.

#### 3. Purpose and Approach

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 [7], which is a combination of a nonlocal hidden-variable design with externally propagating discrete fields. The hidden-variable approach was selected as it has shown excellent ability to solve many other complex problems in physics [17–20]. Seeking solutions in the hidden-variable sector is an unusual approach, as mainstream physics is generally dismissive of this sector. The usual objection is that local hidden-variable solutions are precluded by the Bell type inequalities [2–4]. Nonetheless, it is relevant to note that the inequalities do not preclude all* nonlocal* hidden-variable designs [21, 22]. A more serious limitation has been the inability of this sector to yield solutions, other than the de Broglie-Bohm pilot-wave theory [5, 6] which has limited applicability. That limitation has been overcome by the advent of the Cordus theory, which is a type of NLHV design. A second reason for selecting the hidden-variable sector is that the theories based on a 0D point premise have been unable to explain the nuclides, and therefore it is worth attempting other approaches. The results justify this decision by showing that it is indeed possible to explain the nuclides this way.

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 [23, 24]. The result is a conceptual theory, expressed qualitatively.

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 [25]. These discrete forces propagate into the external environment and are connected in flux lines (Cordus:* hyperfine fibril* or* hyff*) [7]. They make up the fields. The two reactive ends are joined by a fibril (hence* Cordus*) that does not interact with matter, and which instantaneously coordinates the phase of the two ends. Thus, there is an inner structure and an external system of discrete forces. This structure is called a* particule*. Within this theoretical framework, the strong force is mediated by the synchronicity of discrete forces emitted by NLHV particules [17]. Thus, the* strong force* is reconceptualized as a* synchronous interactio*n. More details about the particule idea are available elsewhere, including development of the theory to explain wave-particle duality [7], unification of the electromagnetic-gravitational and strong forces [17], explanations for antimatter and the process of annihilation [18, 24], and a theory for time [19]. The present paper applies the design method to identify how such a synchronous interaction might operate on nucleons. The result is a conceptual theory that predicts a specific type of geometric layout of nucleons in the nucleus and is called a* nuclear polymer*. The mechanics of this polymer are identified and noted as lemmas in Appendix of the supplementary material; see Supplementary Material available online at http://dx.doi.org/10.1155/2015/651361.

#### 4. Results

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.

##### 4.1. Proton and Neutron Structures

The Cordus theory for the proton is shown in Figure 1. The derivation of this structure is shown in the references and is not repeated here.