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%I #28 Sep 03 2012 07:14:25
%S 2,4,2,6,2,4,8,4,6,2,10,8,6,12,4,2,8,10,14,4,6,2
%N Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
%C First differs from A212122 at a(14).
%C The list of the spin-orbit coupling of this version of the nuclear shell model starts: 1s_(1/2), 1p_(3/2), 1p_(1/2), 1d_(5/2), 2s_(1/2), 1d_(3/2), 1f_(7/2), 2p_(3/2), 1f_(5/2), 2p_(1/2), 1g_(9/2), 1g_(7/2), 2d_(5/2), 1h_(11/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 7, 5, 11,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 8, 6, 12,... Other sequences that arise from this sequence are A213371, A213373, A213374. - _Omar E. Pol_, Sep 02 2012
%D W. E. Meyerhof, Elements of Nuclear Physics (McGraw-Hill, New York, 1967), Chap. 2.
%H HyperPhysics, G.S.U., <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html">Shell Model of Nucleus</a>
%H W. E. Meyerhof, <a href="http://www.flickr.com/photos/mitopencourseware/3772864128/in/set-72157621892931990">Energy Levels of Nucleons in a Smoothly-Varying Potential Well</a>, MIT OpenCourseWare
%F a(n) = 2*A213371(n).
%e Illustration of initial terms on one of views of a three-dimensional shell model of nucleus.
%e .
%e . |---------------------- i ----------------------|
%e . | |
%e . | |------------------ h ------------------| |
%e . | | | |
%e . | | |-------------- g --------------| | |
%e . | | | | | |
%e . | | | |---------- f ----------| | | |
%e . | | | | | | | |
%e . | | | | |------ d ------| | | | |
%e . | | | | | | | | | |
%e . | | | | | |-- p --| | | | | |
%e . | | | | | | | | | | | |
%e . | | | | | | s | | | | | |
%e . | | | | | | | | | | | | |
%e . | | | | | | | | | | | | |
%e . | | | | | | 2 | | | | | |
%e . | | | | | 4 | | | | | | |
%e . | | | | | | | 2 | | | | |
%e . | | | | 6 | | | | | | | |
%e . | | | | | | 2 | | | | | |
%e . | | | | | | | | 4 | | | |
%e . | | | 8 | | | | | | | | |
%e . | | | | | 4 | | | | | | |
%e . | | | | | | | | | 6 | | |
%e . | | | | | | | 2 | | | | |
%e . | | 10 | | | | | | | | | |
%e . | | | | | | | | | | 8 | |
%e . | | | | 6 | | | | | | | |
%e . | 12 | | | | | | | | | | |
%e . | | | | | | | | 4 | | | |
%e . | | | | | | 2 | | | | | |
%e . | | | 8 | | | | | | | | |
%e . | | | | | | | | | | | 10 |
%e . 14 | | | | | | | | | | | |
%e . | | | | | 4 | | | | | | |
%e . | | | | | | | | | 6 | | |
%e . | | | | | | | 2 | | | | |
%e . | | | | | | | | | | | | |
%e . | | | | | | | | | | | | |
%e . | | | | | | |1/2| | | | | |
%e . | | | | | | | | | | |
%e . | | | | | |----3/2----| | | | |
%e . | | | | | | | | |
%e . | | | | |--------5/2--------| | | |
%e . | | | | | | |
%e . | | | |------------7/2------------| | |
%e . | | | | |
%e . | | |----------------9/2----------------| |
%e . | | | |
%e . | |-------------------11/2--------------------|
%e . |
%e . |-----------------------13/2------------------------
%e .
%e For another view of the model see the example section of A212122, second part.
%e Written as an irregular triangle in which row n represents the n-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
%e 2;
%e 4, 2;
%e 6, 2, 4;
%e 8;
%e 4, 6, 2, 10;
%e 8, 6, 12, 4, 2;
%e 8, 10, 14, 4, 6, 2;
%Y Partial sums give A213374. Other versions are A162630, A212012, A212122, A213362.
%Y Cf. A213371, A213373.
%K nonn,tabf,hard,more
%O 1,1
%A _Omar E. Pol_, Jul 16 2012
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