### Lie-isotopic representation of stable nuclei I: Apparent insufficiencies of quantum mechanics in nuclear physics

#### Abstract

Abstract

In this paper, we recall the majestic axiomatic consistency of quantum me- chanics for point-like particles and electromagnetic waves in vacuum. By following the 1935 historical argument by A. Einstein, B. Podolsky and N. Rosen that quantum mechanics is not a complete theory, we identify a number of apparent insufficiencies of quantum mechanics in nuclear physics with particular reference to the lack of numerically exact representation in one century of nuclear data, the prohibition by Heisenberg’s uncertainty principle to represent the neutron synthesis from the electron and the pro- ton in the core of stars despite their extremely big Coulomb attraction and the ensuing inability to represent the nuclear stability. We then point out that the axiomatic origin of the indicated insufficiencies appears to be due to the representation of nuclear constituents as dimensionless particles, compared to the experimentally measured extended character of the charge distribution of protons and neutrons in conditions of partial mutual penetration within a nuclear structure, with consequential strong interactions of nonlinear, non- local and nonpotential. In the second paper, we attempt a resolution of the indicated insufficiencies with ensuing exact and invariant representation of the Deuteron data. In the third paper, we present a consequential representa- tion of nuclear stability with ensuing new means of recycling nuclear waste by nuclear power plants and other advances.

#### Keywords

#### Full Text:

PDF#### References

R. M. Santilli

Einstein, A. Podolsky, B. and Rosen, N.: Can quantum-mechanical descrip- tion of physical reality be considered complete?, Phys. Rev. 47, 777-780 (1935),

http://www.eprdebates.org/docs/epr-argument.pdf

Berkowitz, R.: Macroscopic systems can be controllably entangled and lim- itlessly measured, Physics Today July issue, 16-18 (2021).

Santilli, R. M.: A quantitative representation of particle entanglements via Bohm’s hidden variables according to hadronic mechanics, Progress in Physics 18, 131-137 (2022), www.santilli-foundation.org/docs/pip-entanglement-2022.pdf

Fadel, M. et al.: Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates. Science 360, 409–415 (2018), www.santilli-foundation.org/Basel-paper.pdf

Colciaghi, P. et al.: Einstein-Podolsky-Rosen Experiment with Two Bose- Einstein Condensates, Phys. Rev. X 13, 021031-1/021031-10 (2023), https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.021031

Aspect, A. et al.: Experimental Realization of Einstein-Podolsky-Rosen- Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities, Phys. Rev. Lett. 49, 91-94 (1982), https://ui.adsabs.harvard.edu/abs/1982PhRvL..49...91A

Miller, J. P. et al.: Muon (g2): experiment and theory. Rep. Prog. Phys. 70, 795–881 (2007), news.fnal.gov/2021/04/first-results-from-fermilabs-muon-g-2-experiment- strengthen-evidence-of-new-physics

Santilli, R. M.: Apparent Unsettled Value of the Recently Measured Muon Magnetic Moment, Progress in Physics 18, 15–18 (2022), http://www.santilli-foundation.org/docs/muon-meanlife-2022.pdf

Santilli, R. M.: Representation of the anomalous magnetic moment of the muons via the Einstein-Podolsky-Rosen completion of quantum into hadronic mechanics, Progress in Physics 17, 210–215 (2021), https://www.santilli-foundation.org/muon-anomaly-pp.pdf

Santilli, R. M.: Representation of the anomalous magnetic moment of the muons via the novel Einstein-Podolsky-Rosen entanglement in: H. M. C.

Apparent insufficiencies of quantum mechanics in nuclear physics

Garcia, J. J. C. Guzman, L. H. Kauffman and H. Makaruk, Editors,Scientific Legacy of Professor Zbigniew Oziewicz, World Scientific (2024), https://www.santilli-foundation.org/docs/santilli-546-(1).pdf

Schukraft, K.: Heavy-ion physics with the ALICE experiment at the CERN Large Hadron Collider. Trans. R. Soc. A370, 917–932 (2012), royalsocietypublishing.org/doi/10.1098/rsta.2011.0469

Cardone, F., Mignani, R. and Santilli, R. M.: On a possible energy- dependence of the K0 lifetime. Part I J. Phys. G: Part. Phys. 18, L141-L144 (1992),

www.santilli-foundation.org/docs/Santilli-32.pdf

Cardone, F., Mignani, R. and Santilli, R. M.: On a possible energy- dependence of the K0 lifetime. Part II J. Phys. G: Part. Phys., 18, L61-L65 (1992),

www.santilli-foundation.org/docs/Santilli-32.pdf

Santilli, R. M.: Nonlocal formulation of the Bose-Einstein correlation within the context of hadronic mechanics, Hadronic J. 5, 1–50 and 15, 81–133 (1992),

www.santilli-foundation.org/docs/Santilli-116.pdf

Cardone, F. and Mignani, R.: Nonlocal approach to the Bose-Einstein corre- lation, JETP 83, 435 (1996), www.santilli-foundation.org/docs/Santilli-130.pdf

Ahmar,H.etal.:AdditionalexperimentalconfirmationsofSantilli’sIsoRed- Shift and the consequential lack of expansion of the universe, Journal of Computational Methods in Sciences and Engineering 13, 321-375 (2013), www.santilli-foundation.org/docs/IRS-confirmations-212.pdf

Mignani, R.: Quasars redshift in isominkowski space, Physics Essay 5, 531 (1992),

http://www.santilli-foundation.org/docs/Santilli-31.pdf

Santilli, R. M.: Experimental Verifications of IsoRedShift with Possible Ab- sence of Universe Expansion, Big Bang, Dark Matter and Dark Energy, The Open Astronomy Journal, 3, 124-132 (2010), www.santilli-foundation.org/docs/Isoredshift-Letter.pdf

Santilli, R. M. Generalization of Heisenberg’s uncertainty principle for strong interactions, Hadronic J. 4, 642-663 (1981), www.santilli-foundation.org/docs/generalized-uncertainties-1981.pdf

R. M. Santilli

Santilli, R. M. Isorepresentation of the Lie-isotopic S U (2) Algebra with Ap- plication to Nuclear Physics and Local Realism,Acta Applicandae Mathe- maticae 50, 177-190 (1998), www.santilli-foundation.org/docs/Santilli-27.pdf

Santilli, R. M.: Studies on the classical determinism predicted by A. Ein- stein, B. Podolsky and N. Rosen, Ratio Mathematica 37, 5-23 (2019), www.eprdebates.org/docs/epr-paper-ii.pdf

Santilli, R. M.: Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles, Lettere Nuovo Cimento 37, 545-555 (1983), www.santilli-foundation.org/docs/Santilli-50.pdf

IAEA, Nuclear data services, website: https://www.iaea.org/about/organizational-structure/department-of- nuclear-sciences-and-applications/division-of-physical-and-chemical- sciences/nuclear-data-section

Vonsovsk, S.: Magnetism of Elementary Particles, Mir Publishers (1975).

Rau, S., et al.: Penning trap measurements of the deuteron and the HD+ molecular ion, Nature 585, 43-47 (2020), doi.org/10.1038/s41586-020-2628-7

ScienceDirect, Helium nucleus, website, //www.sciencedirect.com/topics/mathematics/helium-nucleus

Pohl, R.: Antognini, A. and Kottmann, F.: The size of the proton, Nature 466, 213-216 (2010),

www.nature.com/articles/nature09250

Heisenberg, W.: Nachr. Akad. Wiss. Gottingen IIa, 111 (1953), https://link.springer.com/chapter/10.1007/978-3-642-70079-8 23

StanfordEncyclopediaofPhilosophy,Bohmian(deBroglie-Bohm)Mechan- ics (2021),

https://plato.stanford.edu/entries/qm-bohm/

Santilli, R. M.: Foundation of Theoretical Mechanics, Springer-Verlag, Hei- delberg, Germany, Vol. I (1978) The Inverse Problem in Newtonian Mechan- ics,

http://www.santilli-foundation.org/docs/Santilli-209.pdf

Apparent insufficiencies of quantum mechanics in nuclear physics

Santilli, R. M.: Foundation of Theoretical Mechanics, Springer-Verlag, Hei- delberg, Germany, Vol. II (1983) Birkhoffian Generalization of Hamiltonian Mechanics,

http://www.santilli-foundation.org/docs/santilli-69.pdf

Santilli, R. M.:Elements of nuclear physics according to hadronic mechan- ics, II: Exact Lie-isotopic representation of the Deuteron data, submitted to Ratio Mathematica.

Santilli, R. M.: Elements of nuclear physics according to hadronic mechan- ics, III: Exact Lie-isotopic representation of the nuclear stability, submitetd to Ratio Mathematica.

Yukawa, H.: On the interaction of elementary particles, Proc. Phys. Math. Soc. Jpn. 17, 48-57 (1935).

Woods, R. D. and Saxon, D. S.: Diffuse Surface Optical Model for Nucleon- Nuclei Scattering, Phys. Rev. 95, 577-578 (1954).

Reid, R. V.: Local phenomenological nucleon–nucleon potentials, Annals of Physics 50, 411–448 (1968).

Rabi,I.I.:Science:TheCenterofCulture,WorldPublishingCo.,NewYork. NY (1970).

Ahmadov, A. I. et al.: Approximate bound state solutions of the Klein- Gordon equation with the linear combination of Hulthe ́n and Yukawa po- tentials, Physics Letters A 383 (24), 3010-3017 (2019), https://www.sciencedirect.com/science/article/abs/pii/S0375960119305791

Christman, J. R.: The Strong Interaction, Project PHYSNET Physics Bldg. Michigan State University East Lansing (2001), http://www.physnet.org/modules/pdf modules/m280.pdf

Fermi, E.: Nuclear Physics, University of Chicago Press (1949).

Blatt, J. M. and Weisskopf, V. F.: Theoretical Nuclear Physics, Wiley and

Sons (1952).

Rutherford, H.: Bakerian Lecture: Nuclear Constitution of Atoms, Proc. Roy. Soc. A, 97, 374 (1920), royalsocietypublishing.org/doi/10.1098/rspa.1920.0040

R. M. Santilli

Santilli, R. M.: Need of subjecting to an experimental verification the valid- ity within a hadron of Einstein special relativity and Pauli exclusion princi- ple, Hadronic J. 1, 574-901 (1978), http://www.santilli-foundation.org/docs/santilli-73.pdf

Santilli, R. M.: Reduction of Matter in the Universe to Protons and Electrons via the Lie-isotopic Branch of Hadronic Mechanics, Progress in Physics, 19, 73-99 (2023),

https://www.ptep-online.com/2023/PP-65-09.PDF

Norman, R. et al.: Experimental Confirmation of the Synthesis of Neutrons and Neutroids from a Hydrogen Gas, American Journal of Modern Physics 6, 85-104 (2017), www.santilli-foundation.org/docs/confirmation-neutron-synthesis-2017.pdf

Santilli, R. M.: Apparent Resolution of the Coulomb Barrier for Nuclear Fusions Via the Irreversible Lie-admissible Branch of Hadronic Mechanics, Progress in Physics, 18, 138-163 (2022), http://www.santilli-foundation.org/hyperfusion-2022.pdf

Santilli, R. M.: Elements of Hadronic Mechanics, Ukraine Academy of Sci- ences, Kiev (1995), Vol. I, Mathematical Foundations, http://www.santilli-foundation.org/docs/Santilli-300.pdf

Santilli, R. M.: Elements of Hadronic Mechanics, Ukraine Academy of Sci- ences, Kiev (1995), Vol. II, Theoretical Foundations, www.santilli-foundation.org/docs/Santilli-301.pdf

Santilli, R. M.: Elements of Hadronic Mechanics, Ukraine Academy of Sciences, Kiev (2016), Vol. III, Experimental verifications, www.santilli- foundation.org/docs/elements-hadronic-mechanics-iii.compressed.pdf

Anderson, R.: Collected OA Papers on Hadronic Mathematics, Mechanics and Chemistry,

https://www.santilli-foundation.org/docs/HMMC.pdf

Anderson, R.: Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli. American Journal of Modern Physics, 2016, v. 6, 1–16,

www.santilli-foundation.org/docs/HMMC-2017.pdf

Santilli, R. M. and Sobczyk, G.: Representation of nuclear magnetic mo- ments via a Clifford algebra formulation of Bohm’s hidden variables, Scien- tific Reports 12, 1-10 (2022), www.santilli-foundation.org/Santilli-Sobczyk.pdf

Apparent insufficiencies of quantum mechanics in nuclear physics

Santilli, R. M.: Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels, Nuovo Cimento B121, 443 - 485 (2006), www.santilli-foundation.org/docs//Lie-admiss-NCB-I.pdf

Santilli, R. M. and Vougiouklis, T.: A New Conception of Living Organ- isms and its Representation via Lie-Admissible Hv-Hyperstructures, Alge- bras, Groups and Geometries 37, 741-764 (2020), www.santilli-foundation.org/docs/Santilli-Vougiouklis-2020-epr.pdf

DOI: http://dx.doi.org/10.23755/rm.v52i0.1607

### Refbacks

- There are currently no refbacks.

Copyright (c) 2024 Ruggero Santilli

This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.