Here is a LINK to a file for the coordinates of all protons and neutrons in every element. The file is 229 kilobytes of text. The file name is nuclei_118_C.xyz .
Experiments have been consistent with the Theory of the Pyramidal Cube Shape of the Nucleus.
The journal Physical Review Letters shows the triangular atom. This triangular north pole is like in the nucleus. A second triangle of protons is on the other side for the south pole. The nucleus in not in the Letter by Trishin, et al, only the atom. White protons, dark neutrons.
"Moiré Tuning of Spin Excitations: Individual Fe Atoms..." by Sergey Trishin, Christian Lotze, Nils Bogdanoff, Felix von Oppen, and Katharina J. Franke
Phys. Rev. Lett. 127, 236801 – Published 29 November 2021
Initial Evidence
During May, 2017, the first investigation of the correctness of the Static Nucleus Theory of the Face-Armored Cubic Lattice was begun. On May 25, 2017, the structure of the iron nucleus was discovered, in theory. Iron-57 is a common isotope of iron. Fe-56 is most common. The cube of protons and neutrons (baryons) has 3x3x3 baryons. Those 27 baryons are 8 protons and 19 neutrons. The remaining 30 baryons are covering 6 faces of the cube. Each face is armored by a pyramid of 5 baryons (3 protons and 2 neutrons with symmetry). Simple logic indicates that the 27 + 30 baryons is a good candidate for the correct stucture of the Fe-57 nucleus. Symmetric allocation of protons gives 8 in the cube and 18 in the 6 pyramids, symmetrically.
To prove that Fe-57 is truely a pyramidal cube in reality, not only theory, some initial verification steps were planned.
1 Show that the 4 ferromagnetic elements all have a similar structure with two coaxial proton rings. (Fe, Co, Ni, Gd). The atomic numbers, Z, of those elements are: 26, 27, 28, 64. The key is that element Z=64 has the shape like element 26. It is unlikely for a wrong theory to get these dissimilar Z elements to have the same shape. But they do! So the theory was looking good.
2 Show that the other 114 elements have shapes that are more dissimilar to iron than are cobalt, nickel, and gadolinium.
Those two criteria were evaluated during three years and they are true!
The closest similar elements, like copper, manganese, cadmium, zirconium, germanium, and cerium all have rings of protons that have flaws, compared to Co, Ni, and Gd. For example, cadmium has rings with kinks that point toward the center of the nucleus. That flaw plausibly prevents a superconducting ring current from flowing as smoothly as in the proton rings of the 4 ferromagnetic elements. Mn has non-coaxial rings. Cu has rings that short circuit to the axial proton.
After this initial evidence was credible, other forms of evidence was justified to have the effort expended to be provided. See my 535 page book Charge distributions on the nuclei: Folmsbee, Alan Charles: 9798363495403: Amazon.com: Books
Chromium is the only antiferromagnetic element. It has a unique shape that implies antiferromagnetic properties. See the paper : July 2021 « Journal of Nuclear Physics (journal-of-nuclear-physics.com)
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More evidence
Some of the properties of the elements are implied by the structures of the nuclei.
Nitrogen nucleus, white protons and black neutrons
Nitrogen is in the photo, above. The chemical compounds that are made using nitrogen sometimes use the triple bond. The nucleus has 3 protons at the ends of a star shaped allocation. The nitrogen atom has 3 bonding electrons because of the 3 protons that are so prominent. This is evidence that this theory is the correct theory of the shape of matter. 10/31/2023
Pear shaped nuclei were found. Radon is described in this paper by many authors and Gaffney.
http://ns.ph.liv.ac.uk/~lg/papers/StudiesOfNuclearPearShapesUsingAcceleratedRadioactiveBeams_Archive.pdf
Static locations of protons and neutrons are mentioned, quote
" For certain combinations of protons and neutrons there is also the theoretical expectation that the shape of nuclei can assume octupole deformation, corresponding to reflection asymmetry or a "pear-shape" in the intrinsic frame, either dynamically (octupole vibrations) or statically (permanent octupole deformation). " Gaffney et al.
Pear shaped nuclei were found. Radon is described in this paper by many authors and Gaffney.
http://ns.ph.liv.ac.uk/~lg/papers/StudiesOfNuclearPearShapesUsingAcceleratedRadioactiveBeams_Archive.pdf
Static locations of protons and neutrons are mentioned, quote
" For certain combinations of protons and neutrons there is also the theoretical expectation that the shape of nuclei can assume octupole deformation, corresponding to reflection asymmetry or a "pear-shape" in the intrinsic frame, either dynamically (octupole vibrations) or statically (permanent octupole deformation). " Gaffney et al.
My models of barium, radon and radium nuclei have pear shapes. This is evidence that my theory matches the experiments mentioned above.
Pear shaped barium
Pear shaped radon and radium nuclei
Pear shaped barium experiment
Before I discovered the shape of the iron nucleus, other people had a blurred picture of the nucleus.
Here is an idea for a pear shaped nucleus of Barium by a researcher:
https://phys.org/news/2016-06-heavy-barium-nuclei-pear.html
This story says nuclei seem spherical but rare measurements show other shapes.
https://phys.org/news/2017-07-atomic-nucleus.html
Pear shaped mock-up of Uranium-234 and prolate Neon-22
U-234 is a foundation element. It has a smooth surface with a hexagonal arrangement of surface nucleons. That hexagonal shape is there because a cubic lattice of 27 nucleons is at its center. When U-235 is formed, a neutron is placed on the smooth surface, in the lowest available depression. The binding energy of that last neutron is less than the binding energy of most other nucleons. So during fission, that neutron is commonly set free to make a chain reaction.
Alan Folmsbee at age 62 in Wailuku, Maui, Hawaii, 2014
In 2014, I created the Gravity Volume Theory. In 2017, I discovered the theoretical shape of the iron nucleus. In 2022, I published a text file with the coordinates of all protons and neutrons in all 118 elements. More than 17,000 protons and neutrons are located in that file. See the top of this page for the link.
Simulations of the shape of the atomic nucleus
Neon nucleus gives consistent results
The next story agrees with my Periodic Table for Neon's shape :
https://phys.org/news/2012-07-atomic-nucleus-fissile-liquid-molecule.html#nRlv
That Neon paper has Schrodinger's Algebra giving the same
result as Folmsbee's Geometry. If you compare the color image on that link with the neon models here in Figures 3 and 4 you will see they have the same shape and proportions.
Figure 2, red cube baryons, (protons and neutrons), black baryons
Neon Pyramidal Cube Theory :
Evidence is found to support the theory from two sources: silicon has a shape for survival, and a second evidence is the work on the carbon nucleus by Gabor Bihari in 2017. His image of C-12 is the same shape as I predicted in 2017.
Figure: silicon with white protons and white neutrons. Its surface is a hexagonal close-pack, for survival and abundance. Alan Folmsbee September 14, 2021, Hartford, Connecticut, USA
White protons and white neutrons
Two of the most abundant elements on Earth: Fe and Si have the best armored surfaces. Notice how the hexagonal close-pack structure has no large gaps in the surfaces. That is due to the cubic core, which has large gaps between nucleons. The cube is protected against impacts, so these elements are abundant.Aluminum is also very abundant and it looks like silicon's nucleus, but with one less proton. Al-27 and Si-28 isotopes are based on the neon foundation nucleus. Oxygen is also in the top 4 abundant elements in the crust. It is smaller, so it is more robust, the way an ant is tougher in a fall than an elephant falling from the same height. Size matters.
Uranium
There are 27 baryons in the cube at the center of U 234.
There are 27 baryons difference in the fission product lobes:
See the last image on this page for isotopes from fission. Some are heavy fragments and some are light, with a distribution that has two modes.
http://www.ikp.tu-darmstadt.de/gruppen_ikp/ag_noertershaeuser/research_wn/exotic_nuclei_wn/index.en.jsp
The Uranium fission products differ by 27 as minimum because the 3x3x3 cube has
27 baryons. When element 92 breaks up, the cube stays together as part of a fragmental fission product. Some fragments have the cube, some fragments do not retain the cube. That makes two modes for fragments to use. The experimental data show two modes of fission products. Element 70 and element 80 mark near end of two distributions. They differ by about 27 nucleons in their A mass number. Cubes are tougher than some geometries on nuclei. (2/6/19 acf)
Iron is magnetic because...
Fe has 2 coaxial rings of protons.
The element with the most spectacular properties is Fe. That is why I selected Fe to explore the shape of the nucleus using glass beads. I did not design in the Two Loops of protons, I discovered the Loops after the model was assembled. I looked at the completed mock-up of the Iron nucleus and I saw the Loops that cause ferromagnetism.
Iron is magnetic because there are two loops of protons in the nucleus of its atom. Element 26 has 12 protons in one ring that is coaxial with 12 more protons in second ring.
Figure 4 : iron mock-up, green protons, white neutrons (also called baryons or nucleons)
Figure 5: 3D membrane from one iron proton to one remote electron in a second Bar Magnet
Figure 6 is discussed on my youtube video
https://www.youtube.com/watch?v=miZTTD0EPJs
All motions are clockwise, so Lenz's Law is consistent with this non-crossing law.
That puts the negative sign in Faraday's Law. Conservation of continuum.
Geometry, not Schrodinger's Algebra, has the realistic model of the nucleus.
Support for Iron Geometry that was discovered on May 25, 2017... Links :
Iron details and gravito-Maxwellian Equations for an Atom of Fe
Rules of Stacking Spheres
Iron discovery disclosure date in blogspot
Prior Art : Pyramidal Cube
Rene Hauy : expert on crystals. Photo of sketch like a nucleus with pyramids on a cube.
http://www.annales.org/archives/cofrhigeo/2001-24.jpg
pyramidal cube sketch, 1803
Also about Hauy,
https://novumveritasuniversalis.wordpress.com/2012/07/14/crystallography-part-one-orthographic-and-fischer-projections/
says
"model of a crystal structure, given by Rene Hauy in 1803, was reprinted in the Journal of Ultrastructure Research in 1958, and again in 1966 in the above mentioned textbook, titled “Elements of Organic Chemistry as Revealed By the Scientific Method” in reference to the exceptional correspondence between the early models, and the micrographs captured in the twentieth century. It is clear from Hauy’s model, that the foundational inspiration is clearly inferred by the ruling of lines which inform the building of the isometric matrix." Hauy.
Prior Art : "pyramidal cube" phrase is used in a book on minerals with a crystal lattice. It is also called a tetrahexahedron. Authors Johan Georg Heck and Spencer Fullerton Baird, "The Sciences of Chemistry, Minerology, and Geology, Illustrated with an Atlas..." rare book search.
3/3/2018 Alan Folmsbee
This cube theory explains why lithium is rare and iron is common and
why technetium is light weight and radioactive and
why cerium and iron spark when struck and
why iron is magnetic and manganese is not and
why carbon is different from all other elements and
how gravity becomes the strong nuclear force at close range to a nucleus and
why eddy currents flow near iron and
why barium is pear shaped and
why neon has that shape in that reference paper and
why gadolinium is ferromagnetic and
how neutrons help fusion be stable and
how each electron is paired to one proton and
what is a photon and
why the ratio A/Z approaches 8/3, mass number / atomic number and
why an electron is repelled by a nucleus, stable in an atom and attracted by a remote proton and
why fission splits uranium into two unequal fragments differing by a 27 baryon count: 3x3x3 and
why three jets come from a proton impacted by an electron without quarks being needed.
February 6, 2019 updated Lenz's Law replacement image, Alan C. Folmsbee
There are 27 baryons in the cube at the center of U 234.
There are 27 baryons difference in the fission product lobes:
See the last image on this page for isotopes from fission. Some are heavy fragments and some are light, with a distribution that has two modes.
http://www.ikp.tu-darmstadt.de/gruppen_ikp/ag_noertershaeuser/research_wn/exotic_nuclei_wn/index.en.jsp
The Uranium fission products differ by 27 as minimum because the 3x3x3 cube has
27 baryons. When element 92 breaks up, the cube stays together as part of a fragmental fission product. Some fragments have the cube, some fragments do not retain the cube. That makes two modes for fragments to use. The experimental data show two modes of fission products. Element 70 and element 80 mark near end of two distributions. They differ by about 27 nucleons in their A mass number. Cubes are tougher than some geometries on nuclei. (2/6/19 acf)
Iron is magnetic because...
Fe has 2 coaxial rings of protons.
The element with the most spectacular properties is Fe. That is why I selected Fe to explore the shape of the nucleus using glass beads. I did not design in the Two Loops of protons, I discovered the Loops after the model was assembled. I looked at the completed mock-up of the Iron nucleus and I saw the Loops that cause ferromagnetism.
Iron is magnetic because there are two loops of protons in the nucleus of its atom. Element 26 has 12 protons in one ring that is coaxial with 12 more protons in second ring.
Figure 4 : iron mock-up, green protons, white neutrons (also called baryons or nucleons)
Figure 5: 3D membrane from one iron proton to one remote electron in a second Bar Magnet
Figure 6 Neo-Lenz's Law : The Non-Crossing Law for paired proton electron
Figure 6 is discussed on my youtube video
https://www.youtube.com/watch?v=miZTTD0EPJs
All motions are clockwise, so Lenz's Law is consistent with this non-crossing law.
That puts the negative sign in Faraday's Law. Conservation of continuum.
Geometry, not Schrodinger's Algebra, has the realistic model of the nucleus.
Support for Iron Geometry that was discovered on May 25, 2017... Links :
Iron details and gravito-Maxwellian Equations for an Atom of Fe
Rules of Stacking Spheres
Iron discovery disclosure date in blogspot
Prior Art : Pyramidal Cube
Rene Hauy : expert on crystals. Photo of sketch like a nucleus with pyramids on a cube.
http://www.annales.org/archives/cofrhigeo/2001-24.jpg
pyramidal cube sketch, 1803
Also about Hauy,
https://novumveritasuniversalis.wordpress.com/2012/07/14/crystallography-part-one-orthographic-and-fischer-projections/
says
"model of a crystal structure, given by Rene Hauy in 1803, was reprinted in the Journal of Ultrastructure Research in 1958, and again in 1966 in the above mentioned textbook, titled “Elements of Organic Chemistry as Revealed By the Scientific Method” in reference to the exceptional correspondence between the early models, and the micrographs captured in the twentieth century. It is clear from Hauy’s model, that the foundational inspiration is clearly inferred by the ruling of lines which inform the building of the isometric matrix." Hauy.
Prior Art : "pyramidal cube" phrase is used in a book on minerals with a crystal lattice. It is also called a tetrahexahedron. Authors Johan Georg Heck and Spencer Fullerton Baird, "The Sciences of Chemistry, Minerology, and Geology, Illustrated with an Atlas..." rare book search.
3/3/2018 Alan Folmsbee
Figure 7 : iron 10 trillion X magnification on 1::1::1 crystallographic axis for the Face Armored Cubic lattice, red protons , gray neutrons
why technetium is light weight and radioactive and
why cerium and iron spark when struck and
why iron is magnetic and manganese is not and
why carbon is different from all other elements and
how gravity becomes the strong nuclear force at close range to a nucleus and
why eddy currents flow near iron and
why barium is pear shaped and
why neon has that shape in that reference paper and
why gadolinium is ferromagnetic and
how neutrons help fusion be stable and
how each electron is paired to one proton and
what is a photon and
why the ratio A/Z approaches 8/3, mass number / atomic number and
why an electron is repelled by a nucleus, stable in an atom and attracted by a remote proton and
why fission splits uranium into two unequal fragments differing by a 27 baryon count: 3x3x3 and
why three jets come from a proton impacted by an electron without quarks being needed.
February 6, 2019 updated Lenz's Law replacement image, Alan C. Folmsbee
========================================================
Begin October 23, 2021
The foundation elements are noticed in the graph of binding energy versus A, mass number.
Notice that the curve in that reference has break points for A = (57, 90, 140, 210, and 234). Those elements are iron, zirconium, cerium, polonium, and uranium. This is considered to be evidence that the pyramidal cube theory is correct. Those elements are foundation elements. That means each foundation element has a simple cubic lattice of baryons in the core and the six faces of that cube are covered by six piles of baryons. Other elements are incremental elements if they have a foundation element inside and a few neutrons and protons added on the outside. A crystallographic lattice type is proposed for the nuclear structure: the Face Armored Cubic lattice. Iron is a tetra-hexahedron. So is N and Pm.
Read my book:
There are 19 foundation elements upon which the 90 incremental elements are built. The 18 foundation elements are:
carbon, oxygen, neon, phosphorus, argon, iron,
germanium, krypton, zirconium, cadmium, xenon, cerium, hafnium,
tungsten, polonium, radon, uranium, mendelevium, and nihonium.
Large gap in cubic stack and small gap in hexagonal stack of protons and neutrons
White protons and black neutrons in neon
White neutrons and protons in silicon model
Silicon is an incremental element based on the foundation element neon. Neon has a cubic lattice of baryons visible on its surface, so large gaps are between baryons. Silicon has small gaps between baryons because its surface has a hexagonal arrangement of protons and neutrons (baryons). The red color highlights some gaps in the picture. The binding energy of a baryon added on a large gap is greater than the binding energy of a baryon added onto a small gap. The strong nuclear force is greater near a large gap, compared to near a small gap. Neon has a porous surface and silicon has a smoother surface. See the graph of the average binding energy per nucleon for the chemical elements, below.
Average binding energy per nucleon.
This figure is based on the encyclopedia Britannica.
The cube-2 foundation elements have porous surfaces. The cube-3 foundation elements have HCP smooth surfaces. That is why light elements' curve has a rising slope and the heavy elements have a falling slope in this graph of binding energies. A porous light element, has a higher binding energy for an added nucleon because it plugs up a big gap between nucleons. More plugging of gaps increases the force for the next added nucleons. For a smooth heavy foundation element, all gaps are small, so adding another nucleon reduces the average binding force for more added nucleons because the AVERAGE binding energy includes all the ones before the new added nucleons. The average force is divided among a larger number of nucleons. Therefore the average binding energy decreases as baryons are added onto heavy elements.
Pear shaped elements were visualized after experiments. Barium, radon, and radium have pear shapes. The Theory for them also is pear shaped. The function is like dart, with a tough, heavy front end and a lighter, delicate rear end. This provides survival of the nucleus during a one-sided nova blast. (Red cubic lattice of baryons (protons and neutrons). Black baryons. Two protons on the outside of the foundation, Xe, are blue.
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Carbon gives evidence supporting the theory
The sixth element has two lines of protons
Figure: from Am Phys Soc April, 2022 meeting in NYC, On Broadway.
The white protons on the right touch each other and the triangle defines a plane. That plane makes graphite have planar crystals. The graphite powder can be a slippery lubricant because the protons drive the electrons directly using lines of flux. Those lines are also called wavefunctions. This supports the law:Law : protons make lines of protons, commonly
The lines of protons make strong chemicals. Electrons are given torque and a flexible response by the line of flux. Imagine that nuclei are not weak influences on chemistry.
The black neutrons in the nuclear model make up six of eight nucleons in the cube in the core.
Each line of protons has two ends. This is consistent with the four bonds of carbon. A chain of a polymer can be flexible because bonding from protons and electrons of an atom to another atom has no complicated additional protons. The simple shape of carbon is rare among elements. For example, silicon has 4 bonds, but its extra protons get in the way of mobile bonds. Carbon has no obstacles for the wavefunction from one of four protons to one of four electrons. Silicon's wavefunction will be adjacent to an un-related proton on the nucleus of the silicon nucleus. That protruding nuclear shape makes the siliceous bonds be stiff.
The s orbital electrons are associated with the 2 inner protons. The ones in the cube. A drama goes on for the two non-valence electrons and protons. The drama is anti-salient for its stage. The two protons face off in the core, across a vacuum. Only S-shell electrons can get in that central location.
Stability research is enabled by expanding on the strucures that I defined in tables. The carbon-14 and nitrogen-14 nuclei are goals for comparison. C-14 is not stable, but its has the same shape as N-14.
Carbon is different from all other elements. It has two symmetrical lines of protons with no other protons to interfere. Where a wavefunction exits a line of three protons, no other protons are spouting a wavefunction within an octant. December 23, 2023
Evidence of the cubic nuclear core
The centers of all chemical elements have a simple cubic lattice of protons and neutrons, except the five lightest elements. The chemist, Lewis, suspected a cube, related to his octet rule. But now, a new type of evidence is understood. The bond angle in the water molecule is 104.5 degrees. That angle is evidence of a cubic geometry!
104.5 degrees = arc cosine ( -1/4 )
This angle occurs commonly in the pyramidal cube nuclear shape. But water is especially suitable to show that angle between a line of protons and another line of protons.
See the carbon page for more discussion. H2O is like H2S, hydrogen sulfide, but the bond angle is not the same (92.1 degrees). This may be due to water having a simple oxygen nucleus instead of a more complicated sulfur proton distribution that bends the bond angle. A model of the sulfur nucleus shows the 104.477 degree angle between proton lines but the H2S bond angle is 92.1 degrees.
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