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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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36
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OFFSET
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1,1
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COMMENTS
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In the shell model for the nucleus, magic numbers are the numbers of either protons or neutrons at which a shell is filled.
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."
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REFERENCES
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Dictionary of Science (Simon and Schuster), see the entry for "Magic number".
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LINKS
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Lutvo Kuric, Digital nuclear shell model, International Letters of Chemistry, Physics and Astronomy, 13(2) (2014) 160-173; ISSN 2299-3843.
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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. - Omar E. Pol, Jul 07 2009 [This needs to be clarified. - Joerg Arndt, May 03 2011]
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.
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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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