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CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: Unification of Nuclear Structure Theory Is Possible by Norman D. Cook [refresh]
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Author Norman D. Cook wrote on Sep. 28, 2009 @ 12:33 GMT
Essay Abstract

The impossibility of achieving a unified theory of nuclear structure has been the conventional wisdom in nuclear physics since the 1960s. However, already in 1937 Eugene Wigner indicated a way forward in theoretical work that eventually led to a Nobel Prize, but not directly to unification. Specifically, he showed that the symmetries of the Schrodinger equation have an intrinsic face-centered-cubic (FCC) geometry. Those symmetries provide for a fully quantum mechanical unification of the diverse models of nuclear structure theory, as indicated by the following facts: (i) The FCC lattice reproduces the properties of the liquid-drop model due to short-range nucleon-nucleon interactions (constant core density, saturation of binding energies, nuclear radii dependent on the number of nucleons, vibrational states, etc.). (ii) There is an inherent tetrahedral subgrouping of nucleons in the close-packed lattice (producing configurations of alpha clusters identical to those in the cluster models). And, most importantly, (iii) all of the quantum n-shells, and j- and m-subshells of the independent-particle model are reproduced as spherical, cylindrical and conical substructures within the FCC lattice – with, moreover, proton and neutron occupancies in each shell and subshell identical to those known from the shell model. These facts were established in the 1970s and 1980s, but the “impossibility of unification” had already achieved the status of dogma by the 1960s. Here, I present the case for viewing the lattice model as a unification of traditional nuclear structure theory – an unambiguous example of how declarations of the “impossibility” of progress can impede progress.

Author Bio

Undergraduate at Princeton University (Princeton, USA), graduate student at Tohoku University (Sendai, Japan) and Oxford University (Oxford, UK), post-doctoral research at Zurich University (Zurich, Switzerland), invited researcher at ATR (Kyoto, Japan), full professor at Department of Informatics, Kansai University (Osaka, Japan). Seventy-plus articles published in refereed science journals, four scientific monographs, most recently, Models of the Atomic Nucleus (Springer, 2006).

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Uncle Al wrote on Sep. 28, 2009 @ 20:30 GMT
FCC lattices need not be locally achiral in point group Oh . "On chirality and the universal asymmetry: reflections on image and mirror image" by Georges Henry Wagnière, 2007, p. 123. The presence of enantiomorphic planes can obtain splittings of otherwise degenerate energy levels, certainly in point groups O (not Oh) and T (not Th or Td). Transuranic "magic island of stabilty" calculations are not straightforward. Even the most sophisticated and prolonged calculations remain ambiguous. We see allied electronic effects in heavy element spin-orbit coupling where wonderfully utilitarian light element approximations are dysfunctional.

Newton is a fine approximation albeit tactily assuming lightspeed is infinite and Planck's constant is zero. They aren't - and Newton is overall wrong. The telling test of theory is not interpolation, it is extrapolation. Does Wigner's geometrization of the nuclear Schrödinger equation usefully extend beyond trivial numbers of nucleons to where other models quantitatively fail?

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Lawrence B. Crowell wrote on Oct. 3, 2009 @ 13:13 GMT
I am not a nuclear structure researcher by any means. Yet I was intrigued by you paper for a number of reasons. You appear to be working towards a phase of nuclear structure based on a lattice system. I too am working with lattice systems, in particular with quantum error correction codes associated with lattices in 4, 8, and 24 dimensions. This is an underlying structure, similar to skyrmion theory, to superstrungs. My essay at

indicates one facet of this with respect to quantum critical points.

I have a couple of questions here. The first is whether this FCC crystaline structure of nuclear matter at all involves a quantum phase transition? This would be a phase where quantum fluctuations determine the scale of ordering of a system, and act in a Euclideanized sense as the "temperature." The second question, which is hinted at in my essay with anyonic statistics, is whether this would involve the so called emergent supersymmetry discovered earlier this decades. So does your phase of nuclear matter, which I presume is more liquid drop model for a highly excited nucleus about to fission.

Thanks for your informative essay,

Cheers LC

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Terry Padden wrote on Oct. 11, 2009 @ 06:17 GMT

An excellent essay. One of the requirements was to provide an essay suitable for general readers, especially if the topic was highly specialised physics.. Your essay succeeds admirably. Congratulations.

Permit me to extract one issue from it relevant to my essay. You write how an early formulation of your work was

"dismissed as a "quasi- classical analog" of the quantum mechanical reality - a numerological "coincidence" without physical implications.". You even end the essay with another piece of "numerology"

Numerology is the raw material for the mathematics of scientific theories. Ignoring numerological co-incidences on the theory side is equivalent to ignoring empirical results on the physical side. Symmetry and Numerology are complementary. If their is any numerology in science unexplained by theory and dismissed as "co-incidence" it is symptomatic - at least - of an incomplete mathematical theory.

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N. Nath wrote on Oct. 11, 2009 @ 07:18 GMT
The essay does try to simplify the nuclear structure into a single possible theory. However, i personally feel the better approach that has been used but not yet fully exploited involves the two body, three body and multi body interactions gradually, to reproduce the structural picture that exists. The collective model that combines the concepts of Liquid drop analogy with the shell structure aspects has met with some success but not entirely. The random walk picture has also been attempted but it also remains confined . The main reason behind all such efforts is that the two body force field itself changes its nature as you start adding the nucleons and its parameterisation has not yet been successful. This route has the potential of simplicity of the conceptaul picture, but the nature of force field comes in the way.

i use to be an low energy nuclear physicist at the start of my career and i left the search early to join the material scientists/surface studies research, etc and have finally ended up as process/design patentee! What to do when nature comes in the way and the mind does not provide a right picture to us in an innovative way!

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N.D. Cook wrote on Oct. 25, 2009 @ 00:44 GMT
Thanks for the comments Uncle AI. I can respond to two of your points and, at least partially, answer your question.

Firstly, I agree that the prediction of “magic islands of stability” is not an easy task – and in fact most of the even proton numbers from 106 to 126 have been predicted at one time or another to be the location of an island of superheavies. Still, for many years,...

view entire post

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N.D. Cook wrote on Oct. 25, 2009 @ 00:46 GMT
Thanks Lawrence for your comments.

Lattice symmetries – or maybe it is the endless complexities/simplicities of solid geometry – are fascinating. Higher “dimensionality” is sometimes unavoidable to organize the multiple properties of complex systems, but I would argue that it is an unnecessary confusion to refer to “properties” as “dimensions”. It would be perhaps possible to describe people in a “higher dimensional” space of location on the surface of the Earth, profession, gender, age and who-knows-what, but what would be gained by referring to the multiple attributes of human lives as a multi-dimensional space? So, I favor the traditional view of “dimensions” as referring to the three dimensions of space and one of time, and calling the many other fundamental properties of physical objects simply “properties”.

Coming back to the unfinished business of nuclear structure theory, the phase state of nuclear matter and the densities at which phase transitions might be expected have been studied since the late 1960s – initially in the context of neutron star matter. Unfortunately, estimates of the condensation density of nuclear matter (N=Z) range from normal nuclear densities (0.17 nucleons/fm^3) to 2-fold that figure or more, and there is still no widely-accepted Equation-of-State for nuclear matter. If the lower condensation densities are accurate, then the one-to-one correspondence between the antiferromagnetic fcc lattice and many of the quantal properties of nuclei becomes of interest as a physical model. As a small group of us have been shouting since the 1970s, various physical interpretations of the lattice might be possible, but the isomorphism just can’t be ignored! I tend to favor the more radical “nuclei are lattices” interpretation, primarily because the model predicts the asymmetrical fragment masses produced in thermal fission. Using our nuclear visualization software (NVS, Windows and Mac versions available at: ~cook/NVSdownload.html), simply construct a Uranium-235 nucleus in the fcc model (using the default IPM build-up sequence or with surface nucleons shifted around to equivalent positions), and a thermal neutron, slice it along its lattice planes (repeat 10 thousand times!), and collect the statistics on the fragments that are most favored. What you get is a fairly reasonable reproduction of the experimental data. No adjustable “asymmetry parameters,” no asymmetrical “neck” connecting the fragments, no post hoc massage of the model to fit the data! That result alone suggests that the 3D fcc geometry is real for large nuclei, and not simply some sort of abstract analog of nuclear quantal symmetries.

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N.D. Cook wrote on Oct. 25, 2009 @ 00:47 GMT
Hi Terry Padden,

Many thanks for your kind comments. Some of the early criticisms of the fcc model were dismissive in a way that I too think is really missing the mark. It is specifically the “coincidence” of the lattice model symmetries and the experimental data that is the model’s strength. Using the word “numerology” is a fancy way of dismissing a theoretical model as just playing with numbers in an unconvincing way. I think that type of criticism is fair when an elaborate hypothetical construct (filled with various assumptions) ends up making only one numerical prediction, which is then used to retroactively justify the many underlying assumptions. But the fcc pattern of quantum numbers (first noticed by Wigner in the 1930s, taken seriously by Everling in the 1950s, and later developed by a dozen of us in the 1970s and 1980s) has such extensive correspondences with nuclear properties – that it seems quite unreasonable to dismiss it with the numerology label.

Anyway, I think you are entirely correct in saying that “ignoring numerological coincidences is equivalent to ignoring experimental results.” Precisely! What we are looking for is “numerological (or, less pejoratively, numerical) patterns” in the experimental data.

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N.D. Cook wrote on Oct. 25, 2009 @ 00:48 GMT
Thanks for your comments N. Nath! What I think you put your finger on is the difference between bottom-up versus top-down approaches to the study of any phenomenon. In the reductionist tradition, what we look for are fundamental principles that work for simple systems and then can be applied again and again to describe large-scale complex systems. Unfortunately, as you note, many-body effects tend to make complex systems “more than the sum of their constituents” and the top-down or whole-system approach must be pursued as well. The tension between these two approaches is real – especially in QM where there is such great precision in dealing with 2-body interactions, and where there is an understandable reluctance to abandon the hard-headed, bottom-up approach. Nevertheless, even Renaissance astronomers knew that the “3-body problem” cannot be solved as the summation of serial 2-body calculations. Higher-order interactions are real – but they need to be incorporated in a way that does not violate the principles of 2-body effects. Nuclear structure theory, dealing with systems of 2-300 nucleons, is the perfect playing field for working out the compromise between the two approaches.

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Steve Dufourny wrote on Oct. 25, 2009 @ 10:55 GMT
Hi Dear N. D. Cook ,

Personally I loved this essay and its pictures ,normal I see spheres everywhere .hihih

Tha quantization always ,and the specific number .

Good luck and best regards


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Steve Dufourny wrote on Oct. 25, 2009 @ 11:20 GMT
It could be well if you could explain me more about FCC lattices .

With what I see on the net ,the systems are correlated with the crystals on earth .Like a link with the quantum and the cosmological dimensions .Like a serie between quantum particlers ....biological and mineral molecules ....crystals ...sun....galaxy...universe.

We must insert the evolution more the specificities more the volumes and the rotations linked with the mass .The entanglement is specific .We perceive only the surface but even the surface is specific in its rotations and specificities implying rule and polarity .

In all case it exists a real taxonomy ,a real classment of spheres .The crystals aren't sufficient .It's for me a tool for ccomputing and informations with interesting properties ,but the complexity of the quantum world is more than that .It's important for the quantization to have the correct number of spheres .

Could you tell me more too about the radius electric and magnetic please ?



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NN wrote on Oct. 25, 2009 @ 12:15 GMT
Thanks, Cook for the response to my comment. i agree with your response broadly speaking. Problems lie with the way the human mind works, it develops prejudices that are difficult to remove. Thus fresh and unbiased approaches are difficult to implement. These however can certainly emerge when you least expect, as these comes out of the 'blue'.

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NN wrote on Oct. 28, 2009 @ 06:20 GMT
i wonder what is the latest about the bootstrap approach in nuclear physics? Also there was something called Bruckner's foundational approach. I am forgetful about their nomenclature now! Sorry.

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Jayakar Johnson Joseph wrote on Nov. 3, 2009 @ 09:41 GMT
Dear Norman D. Cook,

In reference with the Semi-empirical mass formula for LDP, I think the uncertainty of the masses of the observed particles may be due to the existence of cluster-mass and elementary-mass for any particle that is only an observable composite particle, the elementary cluster-matter. This formulation of particles only as composite particles, the elementary cluster-matters;...

view entire post

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Lawrence B. Crowell wrote on Nov. 3, 2009 @ 18:04 GMT
Thanks for your reply. Though I think I did not make myself clear. Earlier in this decade there was an emergent supersymmetry detected in nuclear physics. I don’t recall the details, and I tried looking this up last September when your paper appeared, but I did not find anything definitive. I was just wondering if you had any information on this and related developments. Maybe lattice structure, even in three dimensions, might have something to do with this physics.

Cheers LC

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NN wrote on Nov. 5, 2009 @ 07:25 GMT
Author is sitting pretty with the top ranking now, may be he won't find time to respond to some short postings i happen to make more recently.Nuclear Physics is taking a rough beating for the past several years and your current essay hopefully will leadit back to life it enjoyed some decades back. LHC machine may not result in much to show, as per many in this forum. I also agree with them. However, early universe upto billion yeras may be holding several secrets that may unrival the stagnancy in particle physics, in the follow up of Nuclear physics.

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Ray B Munroe wrote on Nov. 6, 2009 @ 20:50 GMT
Dear Norman,

I apologise for not reading your paper sooner. It is interesting. I have also worked with tetrahedra and FCC close-packing lattices in my book and my essay. I understand certain fundamentals of QCD as a Particle Physicist, but admitedly, it has been many years since I studied Nuclear Physics.

The "magic" numbers in Table 2 do not look so magic to me. The Number of Distinct Wavefunctions seems to be an SO(N) algebra. This is not terribly surprising to me. A tetrahedron has an SO(4)~SO(3,1) structure. And if you include the 24 nearest-neighbors of that tetrahedron, then you build an SO(8) and the beginning of an FCC close-packing lattice.

And certainly, it is not realistic to consider these lattice sites to be point particles. They have size, and that is the dimension that "inflates" the lattice. In Solid State Physics, electron clouds help to maintain regular spacing between atoms (and lattice sites). In Nuclear Physics, the nucleons themselves have size via the kinetic energy and motion of the bound quarks.

Your pictures are quite colorful!

This is a good essay. Good Luck in the contest!

Ray Munroe

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N.D. Cook wrote on Nov. 6, 2009 @ 21:34 GMT
Dear Ray,

Thanks for the comments!

The physical interpretation of the lattice symmetries remains a vexing problem. I think it is probably the same problem as the interpretation of the Schrodinger equation - a standing wave, a probabilistic description of the localization of point-particles, or what? But, so many outstanding physicists have already debated that question to a stalemate that I think it makes sense to leave that unanswered and pursue the structural implications of the lattice.

Relative to the "magic" stability of the closed electron shells, the "magicity" of the nucleon shells are rather modest. Atomic (ionic) radii show huge jumps just after every inert gas, but there is no indication of such jumps in nuclear radial values. What is apparent are small binding energy effects that - in the fcc lattice model - reflect small increases in BE/A for compact structures.



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N.D. Cook wrote on Nov. 6, 2009 @ 21:53 GMT
Hi Steve,

Thanks for your comment that “the crystals [alone] aren’t sufficient”, but “are a tool for computing information [and] interesting properties”. Absolutely! It is the internal symmetries of crystal structures that are relevant to nuclear physics, not the external appearance of Platonic solids. The FCC lattice model, that Everling, Lezuo, Dallacasa, Bobeszko and a few others of us have worked on, has been criticized – unfairly, I think – for external appearances, but it is primarily the spin and isospin regularities within the lattice that show interesting correlations with nuclear properties.



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N.D. Cook wrote on Nov. 6, 2009 @ 22:12 GMT
Hi NN,

I also will not bet any money on finding the Higgs, but the LHC machine will undoubtedly produce some interesting data that will help unravel the unsolved problem of the mass spectrum of elementary particles. I look forward to that!

But the low-energy problems of nuclear structure physics need to be sorted out at the

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N.D. Cook wrote on Nov. 6, 2009 @ 22:16 GMT
Hi NN,

(sorry, my previous post got chopped off somehow)

I also will not bet any money on finding the Higgs, but the LHC machine will undoubtedly produce some interesting data that will help unravel the unsolved problem of the mass spectrum of elementary particles. I look forward to that!

But the low-energy problems of nuclear structure physics need to be sorted out at the level of a few 100 MeV - old, unfinished business left over from the 1950s. So, I agree that the main problem is “the way the human mind works”. There’s a strong tendency to “explain away” problems and paradoxes (as “due to the Pauli Principle” or “due to the Uncertainty Principle”), rather than to actually explain what the underlying mechanism is.



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Steve Duourny wrote on Nov. 9, 2009 @ 13:46 GMT
Hello all ,

Dear Norman,

You are welcome,thanks for your answer.

You know ,I am persuaded about the velocity of spin which is directly proportional with the mass I beleive strongly.

A big velocity spinal implies a weak mass .

In this logic on the line time in an universal point of vue ,the future universal sphere don't turn .

a little if we say m v like a constant .But the evolution time and the mass increasing must be inserted in this equation .I think what all physical spheres are directly linked.If the number of a quantum entaglement is the same with our cosmologicals spheres( super groups of galaxies,SBH or clusters centers ,BH ,stars,planets moons mainly thus with 1 for the main central sphere and after a fractal with a decrease of spheres.......)all that becomes very relevant in my opinion.We can imagine after for the space(quantum spheres without rotation)which becomes mass simply by a code of activation to become mass near main centers of gravity in a cosmological point of vue .

The regularities with mass ,fields ,energy linked with these rotating quantum spheres and its specific number and entanglement .

I have some asks about the lattices between spheres which facilitates the rotation .If the evolution point of vue on this line time constant implies an effect on the space with probably gravita waves ,sphericals,thus probably too what the lattices between entangled spheres is relevant in its variability .The strong interactions in this logic are more entangled .Thus in this line of reasoning ,all quantum spheres with or without rotation thus with or without mass are in contact .But of course our perception of this evolution thus increase of mass ,increase of gravity ,decrease of space ,but increase of lattices ,is difficult due to the impossibility to see the decimals and its variability ,thus let's accept that like a constant .

An ther point important for me is the specificty of the physical spheres ,thus with a specific volume too ....the thermodynamics thus can be correlated with the rotation implying mass .The intrinsic density in the two senses increases .The pression and the universal volume can be correlated in this rationality in fact .

I am happy to see your results of this contest ,the pragmatism is so important .All causes imply effects .The mass comes from the quantum system and not from the exterior with bizare particles ,the gravity synchronizes the light in an evolution poit of vue .

Best Regards


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NN wrote on Nov. 14, 2009 @ 07:03 GMT
I agree with your rsponse of Nov., 06. Somehow, nuclear physics got abandoned a few decades back. However, its technological applications have been put into good use in many branches of sciences. We can take solace from the same, as i myself used such techniques in surface and material science analysis/ characterization.

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Michael Thomas Deans wrote on Mar. 12, 2011 @ 17:34 GMT
Dear Norman,

Embedded in my essay 'The chip in the brain' to the current contest is a shell model for nuclear structure which may interest you. Please take a look.


Michael Thomas Deans

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Vladimir F. Tamari wrote on Nov. 9, 2011 @ 12:00 GMT
Dear Norman

I am sorry I missed seeing this article until now, since I have been an enthusiastic peruser of FQXI in relation to my contribution to the "Is Reality Analog or Digital" contest. Although your analysis here is too technical for my understanding in its details, I could get the sense of it because of the beautiful illustrations, as well as your assured discussion of the state of knowledge of the nuclear structure and the lack of consensus about a unifying theory. The historical background you describe a too familiar story for physics as a whole - competing mutually inconsistent theories abound, crying out for a physically-realistic simple framework. As you know, my approach to a unified theory of physics is also geometrical, is specifically based on an FCC lattice of identical universal nodes. Your encouragement of my Beautiful Universe ideas is the most valued feedback I have had so far. In fact I intuitively feel (and hope) that an FCC lattice of elementary dipole building blocks might be the basis of the structure and characteristics of individual nucleons. The FCC model lends itself beautifully to modelling polyhedral spherical arrangements (proton, neutron) that have - as you propose - 3:2 facets (quarks?) most probably due crystal-like fracture surfaces made up of the elementary tetrahedral basis of the lattice.

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