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%I #29 Jan 23 2023 09:10:24
%S 2,4,2,6,2,4,8,4,6,2,10,6,8,2,4,12,8,4,14,10,2,6,10,12,16,6,2,8,4
%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(12).
%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), 2d_(5/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 5,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 6,... Note that in the Talmi's table there is a typo: instead 2f_(1/2) should be 2f_(7/2), see references, page 6. Other sequences that arise from this sequence are A213361, A213363, A213364. - _Omar E. Pol_, Sep 02 2012
%D I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Nuclear_shell_model">Nuclear shell model</a>
%F a(n) = 2*A213361(n).
%e Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
%e .
%e .|-------------------------- j --------------------------|
%e .| |
%e .| |---------------------- i ----------------------| |
%e .| | | |
%e .| | |------------------ h ------------------| | |
%e .| | | | | |
%e .| | | |-------------- g --------------| | | |
%e .| | | | | | | |
%e .| | | | |---------- f ----------| | | | |
%e .| | | | | | | | | |
%e .| | | | | |------ d ------| | | | | |
%e .| | | | | | | | | | | |
%e .| | | | | | |-- p --| | | | | | |
%e .| | | | | | | | | | | | | |
%e .| | | | | | | s | | | | | | |
%e .| | | | | | | | | | | | | | |
%e .| | | | | | | 2 | | | | | | |
%e .| | | | | | 4 | | | | | | | |
%e .| | | | | | | | 2 | | | | | |
%e .| | | | | 6 | | | | | | | | |
%e .| | | | | | | 2 | | | | | | |
%e .| | | | | | | | | 4 | | | | |
%e .| | | | 8 | | | | | | | | | |
%e .| | | | | | 4 | | | | | | | |
%e .| | | | | | | | | | 6 | | | |
%e .| | | | | | | | 2 | | | | | |
%e .| | | 10 | | | | | | | | | | |
%e .| | | | | 6 | | | | | | | | |
%e .| | | | | | | | | | | 8 | | |
%e .| | | | | | | 2 | | | | | | |
%e .| | | | | | | | | 4 | | | | |
%e .| | 12 | | | | | | | | | | | |
%e .| | | | 8 | | | | | | | | | |
%e .| | | | | | 4 | | | | | | | |
%e .| 14 | | | | | | | | | | | | |
%e .| | | | | | | | | | | | 10 | |
%e .| | | | | | | | 2 | | | | | |
%e .| | | | | | | | | | 6 | | | |
%e .| | | 10 | | | | | | | | | | |
%e .| | | | | | | | | | | | | 12 |
%e 16 | | | | | | | | | | | | | |
%e .| | | | | 6 | | | | | | | | |
%e .| | | | | | | 2 | | | | | | |
%e .| | | | | | | | | | | 8 | | |
%e .| | | | | | | | | 4 | | | | |
%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 .|---------------------------15/2-------------------------
%e .
%e ..........................................................
%e .
%e .|-------------------------- j --------------------------|
%e .* |
%e .* |---------------------- i ----------------------| |
%e .| * | *
%e .| * |------------------ h ------------------| | *
%e .* | * | * |
%e .* | * |-------------- f --------------| | * |
%e .| * | * | * | *
%e .| * | * |---------- e ----------| | * | *
%e .* | * | * | * | * |
%e .* | * | * |------ d ------| | * | * |
%e .| * | * | * | * | * | *
%e .| * | * | * |-- p --| | * | * | *
%e .* | * | * | * | * | * | * |
%e .* | * | * | * s | * | * | * |
%e .| * | * | * | * * | * | * | *
%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 .|---------------------------15/2-------------------------
%e .
%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 6, 8, 2, 4, 12;
%e 8, 4, 14, 10, 2, 6;
%e 10, 12, 16, 6, 2, 8, 4;
%e ...
%Y Partial sums give A213364. Other versions are A162630, A212012, A212122, A213372.
%Y Cf. A018226, A130517, A213361, A213363.
%K nonn,tabf,hard,more
%O 1,1
%A _Omar E. Pol_, Jun 23 2012