Unification of Nuclear Structure Theory Is Possible by Norman D. Cook

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?

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

http://www.fqxi.org/community/forum/topic/534

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

Norman.

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.

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!

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, Seaborg and colleagues have been adamant: "One fact should be emphasized from the outset: while the various theoretical predictions about the superheavy nuclei differ as to the expected half-lives and regions of stability, all theoretical predictions are in agreement: superheavy nuclei can exist. Thus, the search for superheavy nuclei remains as a unique, rigorous test of the predictive power of modern theories of the structure of nuclei." (Seaborg & Loveland, Contemporary Physics 28, 33, 1987). If "existence" means isotopes with lifetimes of a few milliseconds, then Seaborg was correct, but the actual predictions have been much more optimistic than that. For example, Moller and Nix predicted a magic island at Z=114 with a half-life of 10^14 years (Journal of Physics G20, 1681, 1994), but the empirical reality is in the millisecond range and nothing above Z=115 has been discovered or constructed. Already in 1989, in a monograph entitled Superheavy Elements (Hilger, London), K. Kumar declared this to be a "crisis of nuclear theory" because the theory that is believed to be correct and is used to calculate binding energies seems not to predict the actual situation. On the strength of theoretical "certainties," funding for such research has been abundant for decades. To be sure, many interesting things have been discovered, but the theory of the nuclear force that has motivated superheavy research appears to be incorrect, so that, after more than 40 years, is it not fair to ask what conclusion might be drawn from what Seaborg and Loveland called a "rigorous test of the predictive power of modern theories of the structure of nuclei"?

The failure of superheavy research is arguably a good example of your second comment. The independent-particle model - which remains the central paradigm of nuclear structure theory - can be used for interpolation, but extrapolating beyond the known range of stable/semistable isotopes simply doesn't work.

With regard to your question, Wigner's geometrization of the Schrodinger equation applies to all known isotopes - not just small nuclei. In other words, insofar as the IPM description of nucleon states is accurate, Wigner's geometry (the antiferromagnetic fcc lattice with isospin layering) is also accurate. (Wigner himself took it up to Molybdenum, but others have generalized the technique and shown that it precisely follows the harmonic oscillator indefinitely to the largest nuclei and beyond.) In that regard, the theorists are in agreement and experiment is supportive. The remaining question is then how should we interpret the geometry of this known pattern of nucleon build-up. With so many correspondences between the lattice and known structural properties of nuclei (radii, alpha structures, shells and subshells, etc.), it seems perverse to suggest that it is all just a huge coincidence, but if the correspondence is truly with coordinate space, then nuclear structure theory based on the Schrodinger equation needs to be reconceptualized as "standing waves" without the "orbiting" of nucleons that are so densely packed that there is virtually no empty space between nearest neighbors.

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: www.res.kutc.kansai-u.ac.jp/ ~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.

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.

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.

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

Steve

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 ...earth ...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 ?

Regards

Steve

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'.

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.

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; is to conserve energy and gravity, in that gravity is fundamental for all other forces. The mass asymmetries of the fragments produced by the thermal fission of actinides, is also determinant for the existence of cluster-mass and elementary-mass, in relevant with the elementary cluster-matters described with this.

Constant core density and saturation of binding energies of nucleons expressional by IPM have similarities with the characteristics of rotational cluster-matters comprised of elementary cluster-matters. Nucleon-nucleon interactions representational in dense liquid-drop lattice model is applicable on the synchronized opposite rotations of coherent and incoherent cluster-matters, in that fission phenomenon is described as spatial de-composition of coherent and incoherent cluster-matters in synchronized rotations as elementary cluster-matters.

Many-body problem indicates the essentiality of matrix of composite particles for the formulation of a matrix nuclear structure to be evolved from LDM and IPM on applying the quantum physics of shell model for determining correlative elements in the matrix, that are composite particles. There is incompleteness of applicability for Schrödinger equation on wavefunction for wave travel, in that speed of wave travel differ from point to point as there is no absolute vacuum in any point. Though IPM has predictability for nuclear spins, the summation of the properties of independent nucleons is not expressional for the nuclear structure adaptable for wave travel in neutrino oscillations. The tetrahedral clustering only with nucleons within the close-packed lattice may have constrains to unify wave travel and neutrino oscillation.

The coupled orbital momenta of electrons with intrinsic angular momenta of nucleons expressed in quantum mechanics of shell model is transformational and expressional as the momenta of the synchronized rotational composite particles in a matrix that are elementary cluster-matters and for this rho mesons have appropriate candidature as they have spin. The particles so far determined along with further identification of particles by experimental data may evolve generations of rho mesons that have spin and a spin matrix model of nuclear structure is probable that may evolve as atomic analogy rather than nuclear structure. By this matrix model, it may be possible to classify and to tabularize chemical elements, that may be possible in representational as generations of determinants of matrices in matrix.

With this I think; the unification of nuclear structure may be possible if we evolve a spin matrix model from trinification of rho mesons proposed by Sheldon Lee Glashow, Howard Georgi and Alvaro de Rujula; in that generations of rho mesons are representational as matrix elements. As electrons are quarks with different energy level in quantum, this spin matrix model may be the unification of atomic analogy with wave travel to describe the continuum of the universe by quantum physics, in that neutrino propagation by oscillation is expressional. Tetrahedral sub-grouping of nucleons indicates the probability of the existence of rho mesons in generations that may be in synchronized rotations in tetrahedral lattice and representational as rotating spheres, in that Gaussian probability function with trinification is determinant for rho mesons in generations.

Thereby I think that some adaptations and variations to be included in this FCC lattice model that may be representational as atomic analogy rather than nuclear structural unification and may be applicable with neutrino physics. It's a good article that provides me background to evolve this, thanking you ..

With best wishes,

Jayakar

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

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.

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

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.

Cheers

Norman

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.

Cheers,

Norman

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