Rules of Nuclear Geometry

Copyright 1997 by Arnold J. Barzydlo

1. Strings tend to close into loops on the surface of a nuclear shell.
2. Any surface string must pass through at least three quarks before closing on itself.
3. A three string intersection is an Up quark.
4. A four string intersection is a Down quark.
5. An Up quark with a Pinned Vector Boson (P.V.B.) emulates a Down quark.
6. At least one string in a quark intersection must be in opposition to others.
7. Protons and Neutrons do not reside in the same nuclear shell.
8. Sinusoidal strings are permitted, but there may be as yet unknown restrictions.
9. A proton shell has two Up and one Down quark for every proton in it.
10. A neutron shell has two Down quarks and one Up quark for every neutron in it.
11. A radical string pinned between quarks in adjacent nuclear shells may become a hybridized orbital from distortion of the radical string.
12. Pre-quarks (intersections of only two strings) are prohibited on a stable nuclear surface.

13. (Tentative): Nuclear Strings are probably prohibited from making sharp turns. Although at least one of the models given in this site has a trapezoidal string, I doubt that these abrupt changes in direction are permitted on the nuclear surface. Then again, very little is known about the nature of the quark intersection.

Of the rules, the one I check least frequently is number 6. Some of my models may therefore be in violation of this rule, as I have not pointed the string vectors on them to check. By "opposition" I really mean that there must be some sort of collisional process going on at the quark intersection. If three strings all have their vectors pointed the same way in the intersection, there is no collision anomally, they'll just tend to pass on through each other. It only gets interesting where they crash into each other.

Rule number 8, concerning sinusoidal strings, is vague. There is a strong tendency for the strings to form flat loops in the nucleus, and I strongly feel that the nucleus will not generate sinusoidal strings unless it must have them to produce the correct quark charge distribution for compatibility with nearby shells. Sinusoidal strings represent a severe complication to nuclear geometry, opening up the possibility of wildly exotic sinusoidal solutions, and could vastly increase the number of valid solution sets for the shells. They are more difficult to mensurate, without specific rules governing their amplitude, the particles containing them must have their loop values set on a sliding scale dependent on the length of the sinusoidal string, which may wander between physical amplitude limits imposed by the specific shell geometry.

Rule number 11 is there as a reminder for chemists that the radical strings which participate in chemical bonds can be greatly influenced by nuclear structure, and hybridized orbitals can be significant clues to finding the correct shell structures for nuclei which posess them. Hybridized orbitals of this nature should be abundant in metals, hybridization permits "daisy-chain" bonds utilizing a single interstitial electron between nuclei. Less electrons used in bonding nuclei together frees more electrons for conduction. Electrons which are not pinned to a bonding string are attracted to the nucleus through electrostatic forces alone, which should require far less energy to dissociate from the nucleus than electrons which are pinned to bonding strings.

There used to be more rules, but on discovering the solutions for P5 (boron), I found that some of the rules were in error, so I eliminated them. It took me over 15 years to winnow the rules down, but I was unable to find solution sets until I eliminated some of the inflexibility of the initial assumptions. One of which was that the quarks had to be equidistant on the surface of the nuclear shell... it worked for P1, N1, P2, and N2, so I falsely assumed the higher shells would follow this rule. It took over a dozen years to kill that idea, but once I did, the solutions just came out of the woodwork.

You'll probably notice the empirical laws are a very economical mix. (Nature, ya gotta love her.) I am not responsible for all of the laws given, some of them are common knowlege. I'm responsible for 1-6, 8, 11, and 12 in case you're wondering. Actually, an amateur chemistry buff and friend of mine, Wayne Portwine, gave us rule #1...

Flashback: The time was 1979, USAF, CA., in the ground station with Airman Wayne Portwine and myself on duty. I had preliminary quark models on paper, they were intersecting field lines (magnetic lines of force, what I called energy strings in the "old days," and the source of my inspiration), but they were just flat drawings which attempted to link three quarks by intersecting strings. It was an early proton model, I believe it was mostly open curved lines at that time, a triangle of quarks formed from intersecting lines... I knew some lines had to lie outside the nucleus to account for magnetic lines of force, and I was pretty sure the electron had a string attatched to it. I told Wayne that when I tried to imagine the world like this, all I got was an incredibly tangled mass of magnetic lines, and it was giving me headaches. Wayne took a look at my drawing, studied it for about five seconds, and said, "Why don't you try looping your field lines like in a benzene ring molecule?" I took the drawing back from him and looked at it. For the first time I noticed that my model was two-dimensional, reflecting the surface I was using to describe it. If I formed them into rings as Wayne suggested, the model would be three-dimensional. When I saw Wayne the next day, I was pretty excited. There's a couple of very important lessons I learned:
1) The background spatial definition of a system of geometry imposes physical limits and conditions on the geometry.
2) Working in two dimensions leads to thinking in two dimensions.

Shell Stacking Rules

05JUL97 Please examine the boron hydrides notes for an example of shell-stacking in action, as well as some additional information on some unexpected flexibility in the stacking method.

There are no concrete rules to shell stacking... well, there probably are, but I do not have the tools necessary to determine what those rules are. All I can give you is a couple of suggestions. People with computers able to stack and analyze quark distributions and string vectors will have to advance most of the shell stacking rules. Some of these rules should be determined before moving on to solution sets for sodium on up, as I think multiple shell stacking may begin with period III elements.

My tentative observations of the inert gas solution for H4 seem to indicate that inert gases have no P.V.B.'s. In the case of H4, every quark in the inner shell has the opposite quark lying directly above it in the outer shell, resulting in a very high degree of cancellation to localized charge currents (gives it a homogeneous charge field. See Complementary Shells.) I have long suspected that the combined absence of P.V.B.'s and a complementary shell structure would be a distinguishing feature reserved only for the inert gases. I may have been premature in that assessment... The Polar Star shells of P6-30PB and N6-30P are complementary, they also lack P.V.B.'s. But if my EARLY appraisal of the situation is correct, that would seem to indicate that an inert form of carbon 12 should exist. From the point of view of a physicist, that caused me to ponder, have I missed some subtle clue? I've never heard of an inert form for C12, or for that matter, I have never even considered the possibility that there could be inert forms of elements that were not already designated as inert gases. The solution seems to be in not thinking so much like a physicist, rather, think like a chemist. It is the electron structure which links nuclei together with covalent bonds to form molecules. This C12 nucleus will clearly have three pairs of electrons attracted to it, and if the P6-30PB shell is presumed to take the outer shell position, then the C12 nucleus is pretty sticky as far as its electron structure goes. The helium 4 nucleus has one lone pair of electrons which can hover very near, or even enclose the helium 4 nucleus with an electron on either side, making it a very greasy atom. But what of neon, and the other inert gases? They will have multiple pairs of electrons attracted to them, why are they not "sticky" as the carbon 12 nucleus is? Well, I can only offer conjecture at this time, not having a good crop of solution sets for the neon shells. If I had to make this conjecture for the inert character of neon, I would hazard to guess that neon encloses the bulk of its electron structure within its outermost nuclear shell, and that shell is probably the neutron shell. Essentially, I'm suggesting neon may be built inside-out, an inversion of a typical atom, with the proton shell under the neutron shell, and electrons in the interior. If so, perhaps He4 is inverted too. I've found nothing in working with these strings which prohibits electrons from locating in the hollow interior of a nuclear shell. Since I can't find a prohibition, I'm suggesting that the arguments physicists give which insist that electrons cannot enter the nuclear interior may be flawed by either a logical fallacy, an inappropriate mathematical shortcut, or an incomplete understanding of nuclear structure and/or space-time structure. Or, maybe its simply due to the fact that there is already a full complement of electrons in the nuclear interior.

Some generalizations for shell stacking: Try stacking the proton shell on top. This permits the neutron shell underneath it to cancel much of the electrostatic force which is acting to push the proton shell apart, resulting in a reduction of the binding energy required to hold the nucleus together. That puts the nucleus in a lower energy state. If the model is a better fit with reality with the neutron shell on top, there are probably electrons in the nuclear interior acting to reduce the electrostatic repulsion of the proton shell upon itself. Again, the reason for doing this is to reduce the binding energy of the nucleus. The larger the shell model is, the more likely its strings are running at a higher frequency, giving it a smaller cross section. In other words, the more complex shells are probably underneath the simpler shells. This works out nicely, as the neutron shells are generally more complex and frequently carry more neutrons than the proton shells carry protons. With the neutron shells on the interior, the valence electron structure is preserved even though the neutron shell structures vary between different isotopes. In the case of inert gases, try stacking the neutron shell on top. This gives the nuclear interior a higher positive charge, which is likely to attract electrons into the interior where they cannot interact to form molecular bonds. The important numbers associated with the individual shell models are the loop ratios, as they will not change and are useful for scaling the models. You will need to scale the models to different frequencies to permit stacking the larger models under the smaller ones. This seems to be a normal state of affairs for the nucleus. Remember that the cross section of a nuclear shell depends on the frequency of the nuclear strings it is composed of, and no frequency data is available for individual shells. For now, we must estimate the frequency ratios between shells.

There is a somewhat oblate character to the polar star shells, and it grows more severe as the number of particles in the shell increase. I believe the P7 & N7 polar star shells are too distended to be useful for describing nitrogen, though they may be the wrapping paper of a heavier multi-shelled nucleus. I have been unable, thus far, to find a spherical solution for 7-particle shells, but my modeling technique is a tedious and frequently difficult trial-and-error process, more like a terse art form than a science. The polar star shells were refreshingly easy after the "great boron hunt," but I'm afraid they petered out quickly into distended wheels.

As far as tips go, the theory supposes two charge mirrors for all forms of the Down quark. For the Bogus Down quark I usually indicate the outer surface as negative, but I have no idea whether or not this will always be the case. If the radical string can be pinned to the underside of an Up quark, then that particular Bogus Down quark would have its charge mirrors flipped. I am also assuming that the genuine Down quark always presents its negative charge mirror on the outer surface. These are assumptions, and they may be incorrect. My advice is to use these simple assumptions to limit stacking solutions until there are sound reasons to discard them.

In general, by my preferred stacking model, an Up quark stacked on top of another Up quark is strongly repulsive. A Down quark over a Down quark will have both repulsive and attractive influences, the closer the shells are the greater the attractive force. An Up quark over any type down quark is moderately attractive. Any Down quark over an Up quark will have both an attractive and repulsive force, the closer the shells are the greater the repulsive force. A Bogus Down quark under any quark can hybridize the electron orbital associated with the radical string (if there are electrons pinned to it). These are generalizations, which may not all be true, they represent my best guess of what is likely to be found. Don't put too much faith in their accuracy.

Un-Answered Questions

One of the interesting things about stacking the shells is that confirming a few shell-stacking arrangements will tell us something about the laws governing quarks. I can put forward seven interpretations for stacking shells based on the structure of quarks and the laws which govern them. Only one of these interpretations is likely to hold water in actual practice. I cannot determine with any certainty which model is correct, partly due to the difficulty in stacking the wire-models of the shells for study, but mostly because there are not as yet enough examples to work with. As accurate solutions are found, it should become apparent which model is correct. (The "flexi-pin" models are starting to gain appeal to me as I ruminate on the possibility that inert gasses may be stacked inside-out, with electrons harbored in the nuclear interior.)

Standard Model: (No such thing as a Bogus Down Quark, 
Singly-Charged Surfaces.)
++ -- UP DN ++ --
Strict Modification of Standard Model: (Includes Bogus Down, but Maintains Singly-Charged Surfaces.)
++ -- -- UP DN BD ++ -- --
Modified Standard Model: (Includes Bogus Down with Two Charge Surfaces.)
++ -- -- UP DN BD ++ -- ++
Flexi-Pin Modified Standard Model: (With Flexible Radical Pinning.)
++ -- -- ++ UP DN BD BD ++ -- ++ --
My Preferred Model
++ -- -- UP DN BD ++ ++ ++
Flexi-Pin Modification to Preferred Model: (Allows P.V.B.'s to be pinned to the underside of an Up quark.)
++ -- -- ++ UP DN BD BD ++ ++ ++ --
Flexi-Down Model: (Allows Underside Pinning of P.V.B.'s as well as charge posturing of conventional Down quarks.)
++ -- ++ -- ++ UP DN DN BD BD ++ ++ -- ++ --

27MAR08 NOTE: Since I am entertaining the notion that electrons must also build shells comprised of lepton strings and leptonic quarks in the nuclear interior, it raises the possibility of the existence of leptonic neutron shells stabilized within the nuclear interior. As we seek stacking solutions, we need to be aware that nature exploits her options whenever it is convenient or efficient to do so. And nature could throw us a curve by popping in an unexpected leptonic neutron shell. They might even be common in heavy nuclei, it remains to be seen.

Chemistry Notes
Key to Nuclear Models
Nuclear Shells
How to Build Them