More Comment on Large complex Nuclei
((This Commentary is relevant to, and linked to, my main article, entitled: “Nuclear Fusion Mass Lost, Crevices between Nucleons, and an Improved Method of Calculating Binding Energies.”))
As said in my main article, there are over 200 stable isotopes, and we chose to concentrate on modeling mainly the most basic ones. But that small group includes, by far, the most commonly occurring isotopes and atoms in our universe. And therefore they have special importance.
But we shall also make some comments, below, about the less common nuclei, which are generally more massive and more complex. We will limit our comments about them, because those increasing complexities and subtleties seem not efficiently nor very effectively treated by our raw ‘Basics’ approach. Other more practical approaches actually handle more subtle, but important details and characteristics about large nuclei, and we will comment about some of those approaches. (That sort of ‘evolution’ in approach and methodology was advocated by ‘Francis Bacon’ as a way to more quickly obtain and handle vast, reliable knowledge. Bacon was a contemporary of Shakespeare, Galileo, and Gilbert.)
But getting away from Bacon’s empirical emphasis, I cannot resist making one more rather speculative (optional) comment: It may be that space is filled with highly energized and spinning ethereal spheres of various sizes and energies, but exhibiting certain ‘averages’ in behavior. And those spheres may, by wave action or subtle interactions, communicate their conditions to nuclei. And then the nuclei may imitate some of the characteristics of those ethereal spheres and their actions. That speculation may sort of overstretch one’s imagination, but in a sense -- so do aspects of the complex ‘Shell Models of a Nuclei’, that we will mention later in this article.
First some Basic Comment about even Non-basic Complex Nuclei:
Around 1900, Physics took a great step forward, with the help of the great scientist, Max Planck. Many scientists regard that as the beginnings of ‘modern physics’ because that is when Planck devising the so-called “Planck’s constant” to successfully treat certain ‘spectral problems’. Previously, so-called ‘classical physics’ had not found the solutions. (That was because classical physics did not generally use a ‘quantum’ approach to tackle many questions.)
Just as some physical concepts, such as ‘work’ or ‘energy’ is expressed in its appropriate units, ‘force x length’ — so Planck’s constant can be expressed in appropriate units, for example, ‘mass x length x velocity’. That is more recognizable as Angular Momentum. In fact, Planck’s constant is a ‘discrete’ (quantum) amount of the angular momentum. All nuclei (or their parts), and stable particles such as the electron, are found to have angular momentum (as they spin or orbit in very small regions).
Those discrete amounts of angular momentum seem to be simple, ‘cozy’ multiples of one-another. For example, the proton, electron, and neutron each have ½ unit of angular momentum, while other small entities, such as 2 fused nucleons or a ‘photon’, have “2 times (½ unit) of angular momentum,” or (1 unit) of angular momentum. And some nuclei, with many nucleons, have 2 or 3 units of angular momentum. (The relationship between a “Planck’s constant” amount of angular momentum and the amount of angular momentum of each conventional particles named above -- involves a very simple ratio related to a circle’s radius to its circumference.)
Even an unstable fairly large massive particle with no net angular momentum, tends to break up into particles that do have a discrete amount of angular momentum, like the stable particles or nuclei described in the previous paragraph. Important, some people (including myself) believe that that is because ‘space’ itself (and I would say the ether in space) is spinning in eddy currents with an average angular momentum equal to the discrete amount which stable particles or nuclei have. Or a simple multiple times it.
That implies that there can be (and I think likely are) ether flows in space, (and likely loops of ether flow in space). That seems to me exactly what an array of 3 or 4 touching nucleons, (with openings or ‘donut-like holes’ between them) – requires in order to produce a ‘Venturi effect’. (That effect is related to Bernoulli’s equation for fluid flow.) That produces the internal reduced pressure, between nucleons, so they ‘attract’! We addressed that important point in the main article which also has a link to ‘Fig. 1’. ((We optionally addressed the ether’s velocity, (i.e., many magnitudes faster than light) and the ether’s density -- in another article with links to it found on my Homepage.))
((It may also be that ethereal flow, or its push, starts some thick nuclear fluid circularly flowing -- in, out, and around -- those tunnels between the touching nucleons. In that case, the thick nuclear flow is the immediate cause of their ‘nuclear’ attraction. If that is so, then ether’s flow, interaction, or ‘push’ against the thick nuclear fluid and against the nucleons -- is the indirect, ‘behind-the-scenes’, cause of great nucleon-to-nucleon ‘attraction’.))
With the above in mind, we will make a few speculative comments about nuclei with more than 4 nucleons:
Somewhat strangely, no stable nucleus exists with 5 nucleons! That might be partly due to a situation arising if that 5th nucleon touches 3 nucleons of the 4 touching nucleons making up Helium-4. That is directly against a region where normal flow enters or exits Helium-4, one of its two flow paths. That 5th nucleon would seem to obstruct the nice flow and its symmetry, perhaps previously maintained by a pretty good ‘line-of-sight’ between inlet and outlet ‘holes’. (That is 1 pair of the 2 pairs of holes existing when just 4 nucleons touch in a tetrahedral array.) The momentary added 5th nucleon might provide a new inlet hole & outlet hole for a new flow path, but that might not make up for the path it obstructs.
That momentarily added 5th nucleon may even provide a spare hole, in additional to the new inlet and outlet hole it provides. But it still leaves either ‘only one inlet hole’ or ‘only one outlet hole’, and that might limit the ‘flow traffic’ like a one-lane bridge. That is, in effect, regardless of the widening of either ‘only the inlet region’ or ‘only widening of the outlet region’ – just widening only one of the two does not help significantly. And suppose that spare opening had some far away ‘partner’ opening? Still, not being a nearby partner hole, the pair might lack a fairly good line-of-sight view through the pair. Or lack a simple curved path linking one opening to the rather far away partner’s opening – even if that other spare opening is present.
All the above in pretty speculative, but may imply that that 5th attempted nucleon would not increase the total ‘binding energy’ of the bundle much, if at all. So, although it might not explain, especially by itself, why nature rejects the 5-nucleon option so vigorously, it does imply that it would be much less welcome than the 4-nucleon array, and many other possibilities. If that 5th nucleon touched just 1 or 2 nucleons of the 4-nucleon bundle, that might seem to add a slight amount of ‘binding energy’ for the total bundle, but that might be negated by flow interferences or flow source competition, due to added asymmetries.
The next somewhat strange fact is that there are also no stable nuclei with 8 nucleons! But from the standpoint of flows through openings and the general approach proposed in this article, the addition of the 8th nucleon would seem to contribute satisfactorily to a bundle’s increased ‘binding energy’. But an 8-nucleon bundle may lack a long ‘half-life’ anyway because of the following geometry related reason: Even if 2 of the 8 nucleons momentarily slide only a little bit to a different position, that new momentary positioning might create a formation where (2) loosely linked (4-nucleon arrays) appear present. And the binding energies of those two (4-nucleon arrays) may be greater and more conducive to stability than even the pretty compact 8-nucleon bundle, that seemed at first appealing. So in about a second, the 8-nucleon bundle decays, and two separate 4-nucleon arrays appear, i.e., two ‘Helium-4’. (Also, remember that the more protons we add to a bundle of nucleons, the more repelling that arises.)
Inherent in the above descriptions – is that when one or a few nucleons are envisioned to be added to a bundle, it is as if nature takes a quick statistical survey of the advantages of all positions. And the bundle’s final ‘binding energy per nucleon’ is somewhat based on average of the efficacies of all those surveyed positions. That may seem a pretty dubious stretch of the imagination, but there are hints, beyond what space allows me to cover here, that that may occur to some extent, or such behavior as gives such effect, anyway.
It is interesting to imagine a nice symmetrical display that would be formed by bringing one nucleon at the corner of each of (3) separated sets of 4 touching nucleons – together. That is so they form an additional triangular array where the 3 sets touch. Then, although the total number of nucleons still remains at 12, another ‘donut-like hole’ has been created for a flow entering & exiting, at the center of the fancy display. And so an increase in fusion mass lost seems likely to occur. And, yes, a nucleus with as many as 12 nucleons (finally) exhibits a greater binding energy per nucleon than a nice single 4-nucleon array.
((And similarly when (4) separated sets of 4 touching nucleons are envisioned as brought together to form an extra tetrahedral array where they touch. Even though the number of nucleons, (16), does not change.)) All this and the above paragraph are intended to show is that we shouldn’t be surprised by the following: With growing numbers of nucleons in a large bundle or display – the binding energy per nucleon does tend to rise above that of a single simple 4-nucleon bundle.
Many books present graphs or ‘curves’ of how the average ‘binding energy per nucleon’ changes as more and more nucleons are added to a bundle. For example, a bundle of 2, 3, 4, 6, 7, and etc., up to well over 200 nucleons. The ‘binding energy per nucleon’ is quite high for the nice ‘4-nucleon’ case. But for a short length thereafter, the ‘graph curve’ droops somewhat erratically -- for the next up to 6 more nucleons added. But thereafter, as we head toward roughly 60 nucleons added to the bundle, the ‘binding energy per nucleon’ generally increases to roughly 20% greater than even for the nice 4-nucleon bundle. Thereafter, generally as the nucleon count further increases, the binding energy per nucleon gradually decreases until it is nearer to the ‘4-nucleon’ case, again. And when the count gets substantially greater than 200 nucleons, then such large nucleus becomes unstable. And it then decays (back) until the number of nucleons in the main bundle is not much greater than 200.
The gradual increase of the number of the protons in the nuclear bundle of nucleons leads to great proton against proton repelling. (I.e., remember that in electrostatics, ‘like charges’ repel -- as Coulomb’s law states.) That is a major consideration that other treatments of nucleons and of binding energy handles well, especially for nuclei with many nucleons. So its time we describe some of those other treatments.
Other Treatments Regarding Binding Energy and Nucleus Stability:
There exists the “Weizsacker’s formula”, also known as the “Bethe-Weizsacker formula”, which is a semi-empirical mathematical formula for estimating the ‘Binding Energy’ for the more than 200 stable isotopes. And for many unstable isotopes, too. It not only takes into account proton-to-proton repelling, which becomes especially important in larger nuclei, but also ‘spins’, various symmetries and asymmetries, and several other factors. As mentioned in my separate ‘List of References’, a pretty good description of this formula and its usage is described in a Wikipedia article.
In a textbook by Pauling, General Chemistry, there are some sections on ‘Nuclear Chemistry’, as also mentioned in my ‘List of References’. Pauling covers the gradual development of various treatments and models, as they improve. It includes a brief description of the ‘Shell Models’. (I, myself, am not altogether comfortable with many ‘Shell Models’, because some seem to require ultra small particles of ultra high density to orbit in fancy groups around centers. Perhaps, like the very old concept of various layers of glass spheres or shells, it tends to over-stretch my imagination.)
In Pauling’s book, he presents some arguments favoring the ‘Alpha-particle’ or ‘Helion-Triton’model for nuclear structure. That emphasis ‘on the importance of a set of 4 and a set of 3 nucleons’ seems to have at least one aspect in common with my ‘tetrahedron and triangular’ arrays (approach) in my main article.
There is also a book, Elementary Theory of Nuclear Shell Structure, by M. G. Mayer and J. H. D. Jensen. It is also mentioned in my List of References because those authors are generally regarded as the main pioneers of the sort of refined ‘shell’ modeling that mainstream physics seems to use today. That is -- to address nuclei with many nucleons and of increased complexity.
That includes the reality of, say, one atom, with a fixed number of protons existing in its nucleus, but with many different numbers of neutrons possible also existing in that atom’s nucleus, and the nucleus is still stable. In other words, a certain atom may have many stable isotopes. And that contrasting with another atom, with a different given number of protons, but being stable with only one or a few different numbers of neutrons also in its nucleus. For example the element, Phosphorus, is stable only with 15 protons and 16 neutrons in its nucleus, i.e., it exists as only one stable isotope, in the case of that element. The ‘Shell Models’ help address that.
Carl R. Littmann
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my Email and address, see my Homepage