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The most acurate calculation of the nuclear physics


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The most acurate calculation of the nuclear physics



The magnetic moment of atomic nuclei is the only nuclear property through which one can safely assess how much a theoretical model of an atomic nucleus approaches the real structure of nuclei existing in Nature.

This stems from the fact that any minimal difference (which exists between the structure of the theoretical model and the real structure existing in Nature) has a huge difference between the value calculated by the theoretical model and the value measured by experiments.

In the case of light nuclei, all theoretical models of current nuclear physics have failed to obtain good results in calculating the magnetic moment. This failure stems from the following fact:

In light nuclei, the statistical behavior


of the distribution of nucleons (protons and neutrons)


within the nucleus does not predominate




As the number of protons and neutrons grows, the statistical behavior begins to grow, and the tendency of the result of the calculation of the magnetic moment to approach the value measured in experiments begins to grow.


In some cases, as a consequence of the lack of predominance of statistical behavior in light nuclei, even the theoretical nuclear spin differs from the value obtained by experiments. The case of greatest divergence occurs with 5B10, whose nuclear spin (according to the nuclear models of current nuclear physics) should be 1, but experiments have detected that the nuclear spin of 5B10 has a value of 3.

This difference between what is predicted by current models of nuclear physics (with regard to light nuclei) stems from the fact that the distribution of protons and neutrons in the theoretical model is completely different from the existing distribution in Nature.

In my book Quantum Ring Theory, published in 2006, a new nuclear model is proposed in which a 2He4 occupies the center of the nucleus. Figure 1 shows the structure of 5B10. As you can see, in 5B10 the 2He4 is not central, it occupies the bottom part of the nucleus, and this explains why this nucleus is so exotic, and behaves in a completely different way from what is expected from current nuclear models.

Figure 1


Another intriguing nuclear phenomenon is that, due to the predominance of statistical distribution, according to current nuclear physics models, the electric quadrupole moment of 7N14 should be greater than that of 5B10.

Figure 2 illustrates what the electric quadrupole moment Q(b) is all about.



Figure 2



Figure 3 compares what the 5B10 and 7N14 formats should look like, according to the models of current nuclear physics:

• On the left what their formats would be, according to current nuclear physics.

• On the right, how experiments have detected



Figure 3



The values measured in the experiments were these:

Q(b)5B10  = +0.0847

Q(b)7N14 = +0.02

That is, instead of being smaller, as predicted by current nuclear theory, Q(b)5B10  is eight times larger than Q(b)7N14.



In my book The New Nuclear Physics, soon to be published in England, the magnetic moments of Q(b)5B10 and Q(b)7N14 are successfully calculated. And, from the same structure with which the magnetic moments were calculated, the quadrupole moments Q(b)5B10 and Q(b)7N14 are also calculated, as shown in figure 4.



Figure 4

Only from a new nuclear model (in which symmetry does not play a

fundamental rule for the distribution of protons and neutrons)

can one find the real distribution of nucleons in 5B10, which promotes for boron-10

an electric quadrupole moment four times that of nitrogen-14.



Therefore, from the same structures of Q(b)5B10 and Q(b)7N14, seen in figure 4, both the magnetic moments and the quadrupole moments of these two nuclei are calculated in the book The New Nuclear Physics. Such a feat is difficult to obtain from current nuclear physics. Because for many light nuclei, when you use one model to calculate the magnetic moment, and then use the same model to get the electric quadrupole moment, the calculation fails.

Among light nuclei, the one with the simplest structure is lithium-6, because it has only the central 2He4, around which a deuteron revolves. And because it's so simple, that's why calculating its magnetic moment is one of the most accurate calculations in nuclear physics, as we'll see below.





Calculation of the magnetic moment of lithium-6




In my book Subtle is the Math, 16 articles are presented, including two articles published in the peer-reviewed journal Physics Essays. The following Annex is displayed at the end of article number 3, entitled "Calculation of proton’s radius from the well-known equation α = Ke²/ħc".







================ ANNEX ================

It was said in this present paper that the calculation of the magnetic moment of 3Li6, through the equation a= Ke²/hc, is among the most accurate calculations in physics. In order to show the reader one among the procedures of calculations of magnetic moments used in the book New Foundations of Nuclear Physics, ahead is reproduced the calculation for 3Li6, which wasthe first one made by me, with the equation a= Ke²/hc, when I was on vacationat the end of Dec 2018, on the beach in Cabo Frio, a city near Rio de Janeiro.

Calculation of the magnetic moment of 3Li6

From 3Li6 structure shown in Print 1, the deuteron moves with orbit radius R1H2 around Z-axis. The rotation of the proton, responsible for its spin ½, is counterclockwise, inducing positive magnetic moment, m= +2.793 mN. As the proton motion around Z-axis is clockwise, its rotation induces a negative magnetic moment.



Print 1. Calculation of the magnetic moment for 3Li6.




Total magnetic moment of lithium-6 has two components:

1- First component- Intrinsic magnetic moment of deuteron, m= +0.857 mN.


2- Second component- Magnetic moment caused by proton charge moving around Z-axis, which is negative.



The energy of mass defect is shared by six nucleons, three protons and three neutrons. But the rotation of the neutron around Z-axis does not contribute to the magnetic moment of 3Li6, because the neutron has no charge. Only the proton contributes. Therefore, for the calculation of 3Li6 magnetic moment, the energy of mass defect must be divided by six, which is the portion absorbed by the proton. Ahead is calculated the magnetic moment due to the proton orbit around the Z-axis.

Lithium-6 has isotopic mass 6.0151229 u, see cell E2 of Print 1. Mass defect, in unity u, seen in cell E3, is converted to kg in cell E4, calculated in Eq. 1.



The orbit radius of the deuteron moving around Z-axis is calculated in cell E8, from a=Ke²/hc, the Coulomb’s law, and the centripetal force on the deuteron, as follows:


The radius R= 7.08473x10-17 m is not the real radius of the orbit, because inside atomic nuclei the permeability constant mo is not equal to that of the vacuum, as considered in current nuclear physics, but actually it is two orders of magnitude larger than in the vacuum, as calculated in the book New Foundations of Nuclear Physics.

As the rotation of the deuteron around Z-axis, seen in Print 1, is negative, and therefore contrary to the direction of the rotation of the proton’s intrinsic spin inside the structure of the deuteron, then the magnetic moment induced by the rotation of the proton charge is negative, and its value is calculated with Bohr’s equation, from the deuteron rotation around Z-axis, where the speed was calculated in Eq. 3, and the orbit radius in Eq. 5.



There is no way to know what the difference from the experimental is, because in 1967 was measured the value +0.822567(3), and +0.8220473(6) in 1974. So, one may consider that there is no difference with the experimental, since the theoretical value is situated between the two measurements

================ END OF ANNEX ================




NOTE: Deuteron 1H2 also has a very simple structure, and its magnetic moment is calculated in the book The New Nuclear Physics, through a similar procedure of calculation used for lithium-6 exposed here. The value achieved for 1H2 is m1H2= 0,857348 mN, and the experimental is m1H2= 0,857438 mN. Helium-3 and triton 1H3 also have the value of their magnetic moments achieved very close to the experimental, in that book.









Calculations according to current nuclear physics




Despite lithium-6 has a very simple structure, the calculation from current nuclear physics is very controversial, and the value achieved is not so accurate.

See this discussion shown in figures 5, 6 and 7. 

Figure 5 shows that “sunrise” asks help for the calculation of the magnetic moment of lithium-6.



Figure 5




In Figure 6 Oscar Rondon shows his calculation, but the value achieved is 0,88, not so close to 0,822.



Figure 6



In Figure 7 “user 4552” and “Vicky” exchange ideas, whereas “phys-ics” shares the opinion that the calculation made by Oscar Rondon is wrong.

Figure 7




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