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 A213372 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. 8
 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 8, 6, 12, 4, 2, 8, 10, 14, 4, 6, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First differs from A212122 at a(14). 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 REFERENCES W. E. Meyerhof, Elements of Nuclear Physics (McGraw-Hill, New York, 1967), Chap. 2. LINKS HyperPhysics, G.S.U., Shell Model of Nucleus W. E. Meyerhof, Energy Levels of Nucleons in a Smoothly-Varying Potential Well, MIT OpenCourseWare FORMULA a(n) = 2*A213371(n). EXAMPLE Illustration of initial terms on one of views of a three-dimensional shell model of nucleus. . .  |---------------------- i ----------------------| .  |                                               | .  |   |------------------ h ------------------|   | .  |   |                                       |   | .  |   |   |-------------- g --------------|   |   | .  |   |   |                               |   |   | .  |   |   |   |---------- f ----------|   |   |   | .  |   |   |   |                       |   |   |   | .  |   |   |   |   |------ d ------|   |   |   |   | .  |   |   |   |   |               |   |   |   |   | .  |   |   |   |   |   |-- p --|   |   |   |   |   | .  |   |   |   |   |   |       |   |   |   |   |   | .  |   |   |   |   |   |   s   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   2   |   |   |   |   |   | .  |   |   |   |   |   4   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   2   |   |   |   |   | .  |   |   |   |   6   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   2   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   4   |   |   |   | .  |   |   |   8   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   4   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   6   |   |   | .  |   |   |   |   |   |   |   2   |   |   |   |   | .  |   |  10   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   8   |   | .  |   |   |   |   6   |   |   |   |   |   |   |   | .  |  12   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   4   |   |   |   | .  |   |   |   |   |   |   2   |   |   |   |   |   | .  |   |   |   8   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   |  10   | . 14   |   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   4   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   6   |   |   | .  |   |   |   |   |   |   |   2   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |   |   |   |   |   |   | .  |   |   |   |   |   |   |1/2|   |   |   |   |   | .  |   |   |   |   |   |           |   |   |   |   | .  |   |   |   |   |   |----3/2----|   |   |   |   | .  |   |   |   |   |                   |   |   |   | .  |   |   |   |   |--------5/2--------|   |   |   | .  |   |   |   |                           |   |   | .  |   |   |   |------------7/2------------|   |   | .  |   |   |                                   |   | .  |   |   |----------------9/2----------------|   | .  |   |                                       |   | .  |   |-------------------11/2--------------------| .  | .  |-----------------------13/2------------------------ . For another view of the model see the example section of A212122, second part. 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: 2; 4, 2; 6, 2, 4; 8; 4, 6, 2, 10; 8, 6, 12, 4, 2; 8, 10, 14, 4, 6, 2; CROSSREFS Partial sums give A213374. Other versions are A162630, A212012, A212122, A213362. Cf. A213371, A213373. Sequence in context: A162630 A213362 A212122 * A286601 A340071 A102128 Adjacent sequences:  A213369 A213370 A213371 * A213373 A213374 A213375 KEYWORD nonn,tabf,hard,more AUTHOR Omar E. Pol, Jul 16 2012 STATUS approved

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Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)