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A Pythagorean Approach to Problems of Periodicity in Chemical and Nuclear Physics

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Advanced Topics in Theoretical Chemical Physics

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 12))

Abstract

A Pythagorean approach to numerical sequences in both chemical and nuclear physics has allowed us to show geometrical analogies based on figurate numbers (three-dimensional forms of Mendeleev’s periodic table and packing models for nuclei). Pascal’s triangle is used to deduce analytical equations, from which magic numbers through 12,360 for atoms and through 21,400 for nuclei are calculated.

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References

  1. D. Bonatsos, N. Karoussos, C. Daskaloyannis, S. B. Drenska, N. Minkov, P. P. Raychev, R. P. Roussev, and J. Maruani: “Symmetries in nuclei, molecules and atomic clusters”, XHIth International School on Nuclear Physics, Neutron Physics and Nuclear Energy ( Varna, Bulgaria, September 1999 ).

    Google Scholar 

  2. The Encyclopedia Britannica (CD ROM 2000 Deluxe Edition & www pages).

    Google Scholar 

  3. Pythagoras and the Pythagoreans http://www.math.tamu.edu/-don.allen/historv/pvthag/pythag.hto

  4. Pascal’s triangle http://mathfonm.org/dr.math/faq/faq.pascal.triangle.html

  5. Midhat J. Gazale, Gnomon: From Pharaohs to Fractals, Princeton University Press, 1999, 259 pages.

    Google Scholar 

  6. J. Schombert, Gnomones http://zebu.uoregon.edu/-is/glossary/gnomoties.html

  7. D. Weise, Principle of minimax and rising pnyllotaxis http://members.tripod.com/vismath/dima

  8. Magic numbershttp://www.ph.surrey.ac.uk/~phslsv/thesis/node28.html

  9. The shell model http://www.physics.carletonxa/courses/75.364/np-2html/nodc.html

    Google Scholar 

  10. Atomic nucleus and atomic shells http://www.apsidium.com/number/number.htm

  11. M. G. Mayer and J. H. D. Jensen, Elementary Theory of Nuclear Shell Structure, John Wiley, New York, 1955, 269 pages.

    Google Scholar 

  12. Linus Pauling, Research notebooks http:/7osulibrary.orst.edu/specialcollections/rnb/index.htinl Reseatth Notebook 25

    Google Scholar 

  13. V. Ladma, Magic numbers http://www.sweb.cz/vladimirjadma/english/notes/textsaicii.htm

  14. R. Jovanovic, Atomic structure and Pascal’s triangle http://milan.milanovic.org/math/english/atom/atom.html

  15. S. A. Moszkowski, Maria Goeppert Mayer Talk presented at APS meeting at India-napolis on May 4, 1996, UCLA, USA

    Google Scholar 

  16. Experiment: O. Echt, K. Sattler and E. Recknagel, Phys. Rev. Lett. 47 (1981) 1121; A. Ding and J. Hesslich, Chem. Phys. Lett. 94 (1983) 54; Theory: G. S. Anagnos-tatos, Phys. Lett. A 124 (1987) 85; ibid. 133 (1988) 419; ibid. 150 (1990) 303.

    Google Scholar 

  17. Experiment: W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou and M. L. Cohen, Phys. Rev. Lett. 52 (1984) 2141

    Google Scholar 

  18. C. Brechignac, Ph. Cahu-zac and J.-Ph. Roux, Chem. Phys. Lett. 127 (1986) 445

    Article  CAS  Google Scholar 

  19. Theory: D. Bonatsos, N. Karoussos, P. P. Raychev, R. P. Roussev and P. A. Terziev, Chem. Phys. Lett. 302 (1999) 392

    Article  Google Scholar 

  20. A. I. Kuleff, J. Maruani and P. P. Raychev, Adv. Quantum Chem. 40 (2001) 279

    Article  CAS  Google Scholar 

  21. D. Bonatsos, A. I. Kuleff, J. Maruani, P. P. Raychev and P. A. Terziev, Int. J. Quantum Chem. 89 (2002) 377.

    Article  CAS  Google Scholar 

  22. L Wang and L. Holmlid, Chem. Phys. Lett. 295 (1998) 500.

    Article  CAS  Google Scholar 

  23. S, Bj0rnholm, J. Borggreen, O. Hecht, K. Hansen, J. Pedersen and A. D. Rasmus-sen, The Influence of shells… on the abundance spectra of sodium metal clustershttp://pubpages.unh.edu/~oee/abstracts.htm

  24. Periodic Tables http://www.chemistrYCoach.com/periodic_tabIes.htm

  25. Extended Periodic Table http://www.sweethaven.com/chemele/pertabO1.html

  26. Dimitri Mendeleev’s Original Periodic Table (and other tables) http://chemlab.pc.maricopa.edu/periodic/foldedtable.html

  27. Jeries A. Rihani’s Extended Periodic Table of the Elements http://jeries.rihani.com/

  28. Dr Timmothy Stowe’s Physicists Periodic Table http://l40.198.18.108/periodic/stowetable.html

    Google Scholar 

  29. Emil Zmaczynski’s Triangular Long Form Periodic Table http://140.198.18.108/periodic/triangletable.html

    Google Scholar 

  30. D. Weise, ISIS Symmetry congress & exhibition http://wwwJsis-s.unsw.edu.au/mteract/gaIlery/imagefiles/wiese/weise.html

    Google Scholar 

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Weise, D. (2003). A Pythagorean Approach to Problems of Periodicity in Chemical and Nuclear Physics. In: Maruani, J., Lefebvre, R., Brändas, E.J. (eds) Advanced Topics in Theoretical Chemical Physics. Progress in Theoretical Chemistry and Physics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0635-3_19

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  • DOI: https://doi.org/10.1007/978-94-017-0635-3_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6401-1

  • Online ISBN: 978-94-017-0635-3

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