A018226 Magic numbers of nucleons: nuclei with one of these numbers of either protons or neutrons are more stable against nuclear decay.

2, 8, 20, 28, 50, 82, 126

Offset: 1

Author

John Raithel (raithel(AT)rahul.net)

Keywords

• nonn
• fini
• full

Comments

In the shell model for the nucleus, magic numbers are the numbers of either protons or neutrons at which a shell is filled.

First seven positive terms of A162626. - Omar E. Pol, Jul 07 2009

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."

References

• Dictionary of Science (Simon and Schuster), see the entry for "Magic number".

Links

• S. Bjornholm, Clusters, condensed matter in embryonic form, Contemp. Phys. 31 1990 pp. 309-324 (p. 312).
• Encyclopedia Britannica, 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]
• Radoslav Jovanovic, Magic Numbers and the Pascal Triangle
• Lutvo Kuric, Digital nuclear shell model, International Letters of Chemistry, Physics and Astronomy, 13(2) (2014) 160-173; ISSN 2299-3843.
• V. Ladma, Magic Numbers
• NAPC Isotope Hydrology Section, Chapter 2, Atomic Systematics and Nuclear Structure [Broken link?]
• R. Nave, Shell Model of Nucleus
• R. Nave, Enhanced Abundance of Magic Number Nuclei
• Rachele Nerattini, Johann S. Brauchart, and Michael K.-H. Kiessling, Magic numbers in Smale's 7th problem, arXiv:1307.2834v1 [math-ph], July 10, 2013.
• Phys.org, Evidence for a new nuclear 'magic number', Oct 9, 2013.
• D. Steppenbeck et al., Evidence for a new nuclear 'magic number' from the level structure of 54Ca, Nature, 2013 DOI: 10.1038/nature12522.
• D. Warner, Not-so-magic numbers, Nature, 430 (Jul 29 2004), 517-519.
• D. Weise, The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics
• Wikipedia, Magic number (physics)

Crossrefs

Cf. A018227 Number of electrons (which equals number of protons) such that they are arranged into complete shells within the atom.

Cf. A033547, A110856, A130598, A162626, A046939, A046940.

Formula

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]

From Daniel Forgues, May 03 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)

a(n) = n*(n^2+5)/3 + (4*n-6)*A171386(n). - Omar E. Pol, Aug 14 2013