Mar 17 2023

Nuclear Ideals

On April 10, 2008, it was put forth that “we would have gravitational energy replenishing Coulomb energy through both the electrons and the nucleus of an atom”, through absorption of gamma rays:

It wasn’t until 2022 that mathematics was applied to the process, and of course free nuclei and electrons would be absorbing gravitons as well to produce Coulomb fields.

In Krane’s work, the section on Spin-Orbit Potential starts on page 123. There, in the language of atomic physicists applied to nuclear physics: “total angular momentum j = l + s” ([1], pg. 124). In the same way, in the language of differential geometry, Lie groups, and manifolds, J can be called a nucleus, or “an isometry J of N” ([2], pg. 207). There is a “closed embedded submanifold N ⊂ M” ([3], pg. 165), and “N is closed in M” ([2], pg. 236). In this case N is the space atoms and molecules take up, to the outer reaches of the electron orbitals.

In “its ideal system J = (J, R(f), θ) is uniform” ([3], pg. 170). This infers that each different nuclei has a unique structure, and R(f) is the radius of the nuclear fibration. Since nuclei are normally parts of systems of atoms and molecules, θ refers to the angle of an electron arc, and each nucleus knows when to send spin flip signals for each electron arc for which it is responsible. The structure of nuclei is so complex that “covariant derivatives of J vanish” ([2], pg. 142).

As far as holding nuclear material and groups together, magnetic fields are mostly responsible, and serve as the function of chirality in Coulomb fields. As an example, “inductors correspond to, and characterize, pullback groupoids” ([3], pg. 83), as put out from a charged mass. Also, “(φ,f) is an inductor if φ!! is a diffeomorphism” ([3], pg. 176).

[1] Krane, Kenneth S., “Introductory Nuclear Physics”, c. 1988, John Wiley & Sons, Inc.

[2] Bishop, Richard L. and Crittenden, Richard J., “Geometry of Manifolds”, AMS CHELSEA PUBLISHING, Copyright 1964 held by the American Mathematical Society. Reprinted with corrections by the American Mathematical Society, 2001

[3] Mackenzie, Kirill C. H., “General Theory of Lie Groupoids and Lie Algebroids”, c. 2005 Kirill C. H. Mackenzie, London Mathematical Society

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