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A018226
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Magic numbers of nucleons: nuclei with one of these numbers of either protons or neutrons are more stable against nuclear decay.
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33
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OFFSET
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1,1
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COMMENTS
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A web search on `"2,8,20,28,50" Magic number` will turn up hundreds of other links.
First seven positive terms of A162626. [From Omar E. Pol, Jul 07 2009]
In the shell model for the nucleus, magic numbers are the numbers of either protons or neutrons at which a shell is filled.
[Daniel Forgues, April 2, 2011] (Start excerpts form Wikipedia)
The seven most widely recognized magic numbers as of 2007 (...)
Unlike the magic numbers 2-126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. Before this was realized, higher magic numbers, such as 184, were predicted based on simple calculations that assumed spherical shapes. It is now believed that the sequence of spherical magic numbers cannot be extended in this way. (...)
Nuclei which have neutron number N and proton (atomic) numbers Z each equal to one of the magic numbers are called "double magic", and are especially stable against nuclear decay.
(End excerpts form Wikipedia)
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REFERENCES
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A brief description is given under "Magic numbers" in the Encyclopedia Britannica.
S. Bjornholm, Clusters..., Contemp. Phys. 31 1990 pp. 309-324 (p. 312).
Dictionary of Science (Simon and Schuster), see the entry for "Magic number".
J. Fridmann et al., 'Magic' nucleus 42-Si, Nature, 435 (2005), 922-924 and 897-898.
J. Glanz, Uut and Uup Add Their Atomic Mass to Periodic Table, New York Times, Feb 01, 2003, pages 1 and 26.
R. V. F. Janssens, Unexpected doubly magic nucleus, Nature, 459 (jun 25 2009), 1069-1070. _Added by N. J. A. Sloane, Jul 05 2009]
D. Warner, Not-so-magic numbers, Nature, 430 (Jul 29 2004), 517-519.
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LINKS
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Table of n, a(n) for n=1..7.
Radoslav Jovanovic, Magic Numbers and the Pascal Triangle
V. Ladma, Magic Numbers
NAPC Isotope Hydrology Section, Chapter 2, Atomic Systematics and Nuclear Structure [Broken link?]
D. Weise, The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics [Broken link?]
R. Nave, Shell Model of Nucleus
R. Nave, Enhanced Abundance of Magic Number Nuclei
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FORMULA
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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. [From Omar E. Pol, Jul 07 2009] [This needs to be clarified, Joerg Arndt, May 3 2011]
[Daniel Forgues, May 2, 2011, May 3, 2011] (Start)
If 1 <= n <= 3 then a(n) = 2 T_n, else
if 4 <= n <= 7 then a(n) = 2 (T_n - t_{n-1}),
where T_n is the n_th tetrahedral number, t_n the n_th triangular number.
G.f.: (2*x*(1 - 6*x^3 + 14*x^4 - 11*x^5 + 3*x^6))/(1 - x)^4, 1 <= n <= 7.
Using those formulas for n >= 0 gives A162626. (End)
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CROSSREFS
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Cf. A018227 Number of electrons (which equals number of protons) such that they are arranged into complete shells within the atom.
Cf.A033547, A110856.
Cf. A130598, A162626. [From Omar E. Pol, Jul 07 2009]
Cf. A046939, A046940.
Sequence in context: A108180 A192153 A190640 * A162626 A137306 A110856
Adjacent sequences: A018223 A018224 A018225 * A018227 A018228 A018229
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KEYWORD
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nonn,fini,full
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AUTHOR
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John Raithel (raithel(AT)rahul.net)
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STATUS
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approved
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