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%I #76 Feb 21 2022 09:52:19
%S 2,8,20,28,50,82,126
%N Magic numbers of nucleons: nuclei with one of these numbers of either protons or neutrons are more stable against nuclear decay.
%C In the shell model for the nucleus, magic numbers are the numbers of either protons or neutrons at which a shell is filled.
%C First seven positive terms of A162626. - _Omar E. Pol_, Jul 07 2009
%C Steppenbeck: "The results of the experiment indicate that 54Ca's first excited state lies at a relatively high energy, which is characteristic of a large nuclear shell gap, thus indicating that N = 34 in 54Ca is a new magic number, as predicted theoretically by the University of Tokyo group in 2001. By conducting a more detailed comparison to nuclear theory the researchers were able to show that the N = 34 magic number is equally as significant as some other nuclear shell gaps."
%D Dictionary of Science (Simon and Schuster), see the entry for "Magic number".
%H S. Bjornholm, <a href="http://dx.doi.org/10.1080/00107519008213781">Clusters, condensed matter in embryonic form</a>, Contemp. Phys. 31 1990 pp. 309-324 (p. 312).
%H Encyclopedia Britannica, <a href="https://www.britannica.com/science/magic-number-atomic-structure">magic number</a>
%H J. Fridmann et al., <a href="http://dx.doi.org/10.1038/nature03619">'Magic' nucleus 42-Si</a>, Nature, 435 (2005), 922-924 and 897-898.
%H J. Glanz, <a href="http://www.nytimes.com/2004/02/01/science/01ELEM.html">Uut and Uup Add Their Atomic Mass to Periodic Table</a>, New York Times, Feb 01, 2003, pages 1 and 26.
%H R. V. F. Janssens, <a href="http://dx.doi.org/10.1038/4591069a">Unexpected doubly magic nucleus</a>, Nature, 459 (Jun 25 2009), 1069-1070. [_Added by N. J. A. Sloane, Jul 05 2009]
%H Radoslav Jovanovic, <a href="http://milan.milanovic.org/math/english/atom/proton.html">Magic Numbers and the Pascal Triangle</a>
%H Lutvo Kuric, <a href="http://www.ilcpa.pl/wp-content/uploads/2013/10/ILCPA-132-2014-160-173.pdf">Digital nuclear shell model</a>, International Letters of Chemistry, Physics and Astronomy, 13(2) (2014) 160-173; ISSN 2299-3843.
%H V. Ladma, <a href="http://www.sweb.cz/vladimir_ladma/english/notes/texts/magicn.htm">Magic Numbers</a>
%H NAPC Isotope Hydrology Section, <a href="http://www.iaea.or.at/programmes/ripc/ih/volumes/vol_one/cht_i_02.pdf">Chapter 2, Atomic Systematics and Nuclear Structure</a> [Broken link?]
%H R. Nave, <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html">Shell Model of Nucleus</a>
%H R. Nave, <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell2.html">Enhanced Abundance of Magic Number Nuclei</a>
%H Rachele Nerattini, Johann S. Brauchart, and Michael K.-H. Kiessling, <a href="http://arxiv.org/abs/1307.2834">Magic numbers in Smale's 7th problem</a>, arXiv:1307.2834v1 [math-ph], July 10, 2013.
%H Phys.org, <a href="http://phys.org/news/2013-10-evidence-nuclear-magic.html">Evidence for a new nuclear 'magic number'</a>, Oct 9, 2013.
%H D. Steppenbeck et al., <a href="http://dx.doi.org/10.1038/nature12522">Evidence for a new nuclear 'magic number' from the level structure of 54Ca</a>, Nature, 2013 DOI: 10.1038/nature12522.
%H D. Warner, <a href="http://dx.doi.org/10.1038/430517a">Not-so-magic numbers</>, Nature, 430 (Jul 29 2004), 517-519.
%H D. Weise, <a href="http://www.mi.sanu.ac.rs/vismath/weise1/">The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_number_(physics)">Magic number (physics)</a>
%F If 1 <= n <= 3 then a(n)=n*(n+1)*(n+2)/3, else if 4 <= n <= 7 then a(n)=n(n^2+5)/3. - _Omar E. Pol_, Jul 07 2009 [This needs to be clarified. - _Joerg Arndt_, May 03 2011]
%F From _Daniel Forgues_, May 03 2011: (Start)
%F If 1 <= n <= 3 then a(n) = 2 T_n, else
%F if 4 <= n <= 7 then a(n) = 2 (T_n - t_{n-1}),
%F where T_n is the n-th tetrahedral number, t_n the n-th triangular number.
%F G.f.: (2*x*(1 - 6*x^3 + 14*x^4 - 11*x^5 + 3*x^6))/(1 - x)^4, 1 <= n <= 7.
%F Using those formulas for n >= 0 gives A162626. (End)
%F a(n) = n*(n^2+5)/3 + (4*n-6)*A171386(n). - _Omar E. Pol_, Aug 14 2013
%Y Cf. A018227 Number of electrons (which equals number of protons) such that they are arranged into complete shells within the atom.
%Y Cf. A033547, A110856, A130598, A162626, A046939, A046940.
%K nonn,fini,full
%O 1,1
%A John Raithel (raithel(AT)rahul.net)
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