login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A018226 Magic numbers of nucleons: nuclei with one of these numbers of either protons or neutrons are more stable against nuclear decay. 35
2, 8, 20, 28, 50, 82, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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]

Lutvo Kuric, Digital nuclear shell model, International Letters of Chemistry, Physics and Astronomy, 13(2) (2014) 160-173; ISSN 2299-3843; http://www.ilcpa.pl/wp-content/uploads/2013/10/ILCPA-132-2014-160-173.pdf

D. Steppenbeck et al. "Evidence for a new nuclear 'magic number' from the level structure of 54Ca" Nature, 2013 DOI: 10.1038/nature1252.

D. Warner, Not-so-magic numbers, Nature, 430 (Jul 29 2004), 517-519.

LINKS

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?]

R. Nave, Shell Model of Nucleus

R. Nave, Enhanced Abundance of Magic Number Nuclei

Rachele Nerattini, Johann S. Brauchart, 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. Weise, The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics

Wikipedia, Magic number (physics)

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

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.

Sequence in context: A192153 A190640 A230434 * A162626 A137306 A110856

Adjacent sequences:  A018223 A018224 A018225 * A018227 A018228 A018229

KEYWORD

nonn,fini,full

AUTHOR

John Raithel (raithel(AT)rahul.net)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 18:15 EST 2014. Contains 252324 sequences.