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An Extended Cluster Model of the Nucleus

31 July 2004     STRUCTURE    | abstract |          full text (45 K)            20 pages including 7 tables
31 July 2008    INTERACTION    | abstract |          full text (344 K)            12 pages including 6 figures & 1 table

A discrete theory of nuclear structure and the NN interaction
An ab initio re-analysis of the nucleon, in a space and time discrete framework, leads to a radical theory of the nucleus. The theory consists of two main elements—structure and the NN interaction. Structure arises from an extension of the cluster concept of the nucleus and the NN interaction is a natural consequence of the discrete model of sub-atomic particles applied to the nucleon.


The NN interaction explains: 
    • particle-stablility of pn, pnn, ppn and ppnn 
    • ß-instability of pnn 
    • unbound nn and pp 
All in the low energy sector. 

How protons and neutrons are bound together in atomic nuclei has remained a challenge for 75 years. There is no agreed single mechanism which can bind nucleons in a manner which is fully consistent with all, or even most, nuclear phenomena. Nuclear properties do not emerge naturally from any model of nuclear structure. Nuclear theory lacks an all embracing underlying principle. The neutron was discovered by James Chadwick in 1932. Prior to that, it was known that around half the nuclear particles carried positive electric charge. There were either some electrons in the nucleus which cancelled out the charge of some protons or the nucleus contained particles that had approximately the same mass as the proton but carried no charge. The discovery of the neutron simplified the picture of the nucleus by excluding the electron but highlighted another problem which is still with us—what holds one neutron and one proton together in the deuterium nucleus? It was soon realized that the neutron, when isolated from the nucleus, underwent beta decay; the products of which were a proton and an electron. Shortly after Chadwick’s discovery, Heisenberg proposed that the neutron might exchange an electron with the proton and thus bind the two. That theory was soon abandoned because it was realized that the strength of such a bond, which had to be electromagnetic, was far too weak to explain the strength of nuclear binding. 

In 1935, just just three years after the discovery of the neutron, Hideki Yukawa proposed that protons and neutrons were bound in the nucleus by the exchange of mesons. That theory remains a central plank in nuclear theory. It was soon realized that not all nuclear phenomena could be accounted for by meson exchange and it was later augmented by the new theory of quarks and gluons. Nuclear binding, as it is currently understood, relies primarily on the strong nuclear force which was originally proposed as the gluon-mediated bond between quarks, which are so strongly bound that they cannot escape and are never found free of protons and neutrons. The theory of quarks and gluons was concerned with what happens inside individual nucleons. It had nothing to do with what happened between them. In the theory, each proton and neutron is composed of three quarks which are permanently locked together by their gluons. This is referred to as quark confinement. Gluon leakage and meson exchange are both used in an effort to satisfy the observations that nuclei are bound by a mixture of long range and short range forces. This is the hybrid quark model in which the short range force is due to quark exchange, a long range bond due to one pion exchange and medium range force due to two pion exchange. Unlike the quark confinement bond and the electromagnetic bond which each have just one boson type, the gluon and photon respectively, Nature seemingly did not know how to construct the binding force for nuclei using one boson—she could not manage with less than two! The theory does not explain why isolated protons and neutrons have not been observed to leak gluons or emit mesons. And how nucleons knows when to leak a gluon or emit a meson that causes the bond between them is not a part of the theory. Individual isolated protons and neutrons do not seem to do anything that could explain how they bind as the deuteron. In short, philosophical problems abound for the theory that quarks and gluons bind multiple nucleons in individual nuclei. The theory of the inheritance of order deals with this issue in detail and an alternative nuclear binding process falls out of the discrete analysis. The interaction  depends upon special relativity and the rules of standard quantum mechanics and only works in a fully discrete spacetime framework in which observers have no role. It is used to explain the facts of the nuclei of deuterium, tritium, 3He and 4He. When the process is applied to those four nuclei, considered as clusters, its further application to heavier nuclei evolves to become an expanded evolution of the theory. The rules which apply to the M<5 light nuclei evolve among all the larger atoms. The analysis of that process in terms of a model of nuclear structure, shows that it extends to all the isotopes of the natural elements. 

The Extended Cluster Model (ECM)

By contrast with utilitarian motives for model development, (e.g. the liquid drop model to explain heavy nuclear fission, and the shell model to explain the nuclear magic numbers) ECM arose from an enquiry into what principles were instantiated by neutron capture among the isotopes of hydrogen and helium. It was not developed in order to explain any particular nuclear behaviour or observations, but rather to discover deeper underlying principles. Nevertheless the value of a model depends upon its consistency with phenomena which relate to its subject.

The ECM distributes the the nucleons of the nucleus of each natural element into a definite number of from one to three of four clusters according to two rules. The clusters are the deuteron, the triton, 3He and the alpha. The underlying feature is discrete, reactive collectivity; the addition or removal of a nucleon changes the global structure. There are no incomplete structures analogous to partially filled shells. The model is consistent with the concept that individual nucleons bind to form just those four clusters. And that the clusters then bind each other in the formation of all the M>4 nuclides of the whole nuclear landscape. When those four light nuclei are considered as building blocks of the larger nuclei, which behave according to the two distribution rules, several unsuspected correlations with light nuclear phenomena emerge. 

Model correlations
•The cluster structure of the one and two neutron halo nuclei explains the phenomena they exhibit 
•The nuclear beta-decay potential correlates exactly with structure 
•The series of isotopes for each element is defined by the model to be Z+1<A<3Z 
•The onset of the neutron emission decay mode for ten of the twelve lightest elements coincides with the high mass limit of their isotope series 
•The three islands of particle stability beyond the neutron drip line of F, Ne and Na are interpreted to be a tetraneutron bound to the high mass limit isotope of those elements. 

Cluster model predictions
Inherent in the cluster model are numerous testable predictions. The most obvious of which arises from the unique set of the two-, three- and four-nucleon clusters that make up each of the nuclides for the whole landscape of the naturally occuring elements. According to the model there are 8,556 nuclides, each with its own unique structural arrangement of from one to three of the four clusters. Nucleons are arranged into clusters according to definite rules.

Tests of the theory
• Each of the 8,556 predicted structures, at unspecified resonance energies, constitutes a testable model prediction. In recent experimental work by the U.S. Navy (5) the energetic carbon breakup reaction 12C(n, n´)3a was observed. The triple alpha structure for12C confirms themodel structure.

• According to the model, the recently observed islands of stability beyond the neutron drip line of fluorine, neon and sodium (1,2,3) are interpreted to be a single tetraneutron (4) coupled to the nucleus of the highest mass isotope for those elements. 
If observations of stable bound neutrons are to be made outside the laboratory, intuition suggests that small astrophysical bodies, such as comets, may be the places to look. Space probes that induce physical interactions between stable atomic matter and the nucleus of a comet containing a high proportion of polyneutrons can be expected to produce observable phenomena well in excess of those resulting from a simple collision between a metal projectile and a comet core consisting of gas, dust and water ice.

The first mission to impact a comet (Comet Tempel 1) which has a solar orbit of 5.5 yrs was the subject of the first attempt to investigate the interior of a comet nucleus. A 370 kg copper projectile impacted Comet Tempel 1 at 10.25 km/sec on 4 July 2005. The impact was a test of the model that comet nuclei contains material a great deal more reactive than gas, dust and water ice. The unexpectedly large explosion on Comet Tempel 1, followed by increasing brightness of the impact site for several days is more consistent with a highly energetic interaction among nucleons of the copper projectile and perhaps bound neutrons rather than with gas, dust and water ice.

It is also of interest that Comet Hyakutake, discovered in early 1996, was observed by the German ROSAT satellite in March 1996 to be emitting repeated bursts of X-rays three orders of magnitude in excess of expected levels. The anomalous high energy radiation, detected over 15 million km from the comet, cannot be explained by gas, dust and water ice. Since that surprise observation, similar energetic emissions from several other comets have been observed. Perhaps collections of gas, dust and water ice in the near vacuum of deep space and all but the absence of gravity behave according to different laws than those that prevail terrestially.

The theory, devised to explain cometary X-ray emission, is called charge exchange. It postulates a solar source of high energy ions that impact the nuclei of atoms that make up comets. The exchange of electrons among the ions and atoms emits bursts of X-rays. The theory does not explain why the same process is not observed to produce X-rays from the Moon or Mercury or other much larger solar system objects without atmospheres - or indeed, our own Earth. It also fails to explain the irregular output of comet X-rays.

The concept of pure neutrons is not new. Stable neutron clusters were first proposed by Gamow in 1946. Later he adopted the name ‘ylem’, introduced by Alper in 1948, to name “the primordial substance, from which the elements were formed”. The concept of polyneutrons, to explain heavy isotope nucleosynthesis, was introduced by Mayer and Teller at the 1948 Solvay conference. Perhaps comets hold the key to those 60 year old concepts, since abandoned because the nuclear theories of the day were unable to accommodate them.



Some Correlations Between Light Nuclear Phenomena and an Extended Nuclear Cluster Model


The problem of modelling nuclear structure is analyzed by extending the alpha cluster model to include the three-body mirror nuclei and the deuteron. It is possible to arrange all the nucleons of any nuclide into a set of from one to three of the four cluster types according to two principles, which are: (1) bound nucleons tend to form the alpha cluster and (2) nucleon excess is conserved by the Structure chart three-body mirror clusters. In this analysis, each excess neutron forms a triton and each proton-rich, odd-neutron nuclide forms one 3He. Within the series of isotopes for each element nuclear structure is discrete and reactive; the addition or removal of a single neutron changes its set of constituent clusters. The mass range of the isotopes of any element is defined by the model to be Z+1<A<3Z. The model correlates structure with a number of light nuclear phenomena, including the beta-decay potential and the neutron emission decay mode. The recently observed islands of particle stability beyond the neutron drip-line of fluorine, neon and sodium are analyzed as the highest mass isotope of each of those elements coupled to four neutrons, which is interpreted as the bound analogue of the recently reported free tetraneutron. PACS Nos.:  21.60.Gx; 21.10.Gv; 23.60.+e; 25.10.+s; 27.30.+t. 

Key words

Nuclear structure; discrete; cluster; light nuclear correlations.
© Physics Essays 2005

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On the W-boson NN interaction and the Extended Cluster Model of the Nucleus         

The problem of the nuclear interaction is analyzed ab initio, using a physical model of low-energy nuclear phenomena rather than the usual approach of mathematical theory and nuclear parameters. The interaction model is an extension of the fully discrete model of the electron, derived from the Dirac equation. Here we show that a nuclear bond, mediated by the W? boson, evolves naturally in a discrete physical model of the nucleon, in a framework of direct interparticle action. The new model naturally accounts for the uniquely stable two-, three- and four-body bound states, the abolition of free neutron ßdecay by the deuteron bond, 3H and 3He particle-stability and 3H ß-instability. The model is qualitative and radical. Its value lies in its congruence with light nuclear phenomena in the low-energy regime.

Key words
NN interaction; physical model; W-boson; ß-decay; discrete spacetime; nuclear clusters.

Copyright (2009) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Phys. Essays 22, 104 (2009) and may be found here

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A consequence of the cluster model is an essential distinction between 2-, 3- and 4-body clusters of nucleons, which are the bound hydrogen and helium isotopes, and nuclear structure which is composed of sets of clusters which form the M>4 bound nuclei. Individual clusters are typified by their discrete, reactive collectivity. This aspect of the theory suggests a connection between low energy nuclear reactions, associated with anomalous heat production, and in-vacuum, sub-barrier neutron transfers. The connection is developed in: Apeiron, 13:1, 1 (2006). 


Low Energy Nuclear Reactions and Sub-Barrier Neutron Transfers

The problem of anomalous heat production by hydrogenated metals is analysed in the light of deep sub-barrier nucleon transfer reactions. Consideration of the phenomena of condensed matter low energy nuclear reactions and in-vacuum few-body nuclear transfer reactions suggests that LENRs could be due to interactions among the isotopes of hydrogen and certain metals. It is postulated that hydrogen isotope infused heat-producing metals are analogous with in-vacuum ion beam plus metal target systems. It is argued that deep subbarrier, positive Q-value, nucleon transfers among hydrogen and helium isotopes and certain medium and heavy mass metals should occur under condensed matter conditions. It is concluded that several low energy nuclear reaction phenomena cannot yet be excluded as signatures of deep sub-barrier fewnucleon transfers between the nuclei of solvent metals and their dissolved gases. The need for new nuclear models is adumbrated. 

© 2006 Roy Keys Inc. — http://redshift.vif.com  

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Three imperatives distribute the nucleons of every A>4 nuclide among from one to three of the four clusters according to the following rules:

•First, if there are sufficient protons, each excess neutron forms a triton cluster. (Excess means additional to N=Z.)
•Second, remaining pairs of neutrons (not excess to protons) form alphas.
•Third, if there is a residual neutron, following alpha formation, it forms a deuteron if one proton remains, or a 3He if two or more remain.
•Any nucleons which this procedure has not included in a cluster are passengers and do not contribute to nuclear structure. Included among these are the halo nuclides.

1. Y.S. Lutostansky, M.V. Zverev and I.V. Panov. Nuclei Far from Stability: Proc. 5th Int. Conf. 288 (Am. Inst. of Phys., New York 1988).
2. H. Sakarui, et. al., Phys. Lett. B 448 180 (1999).
3. Y.S. Lutostansky, et. al., Part.Nucl. Letters 115 86 (2002).
4. F.M. Marqués, et. al., Phys. Rev. C 65 044006 (2002)
5. P.A. Mosier-Boss, et. al., Naturwissenschaften 96 135 (2009)

Comments and questions are welcome to pjf@it.net.au
© Peter Fimmel 2002-2012

Last page update 01/09/2012