A210842 -id:A210842 - cp's OEIS frontend

A212124 Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.

2, 6, 8, 14, 16, 20, 28, 32, 38, 40, 50, 58, 64, 68, 70, 82, 92, 100, 106, 110, 112, 126, 136, 142, 154, 162, 164, 168, 184

Offset: 1

Omar E. Pol, Jun 03 2012

First differs from A213364 at a(12).

			Example 1: written as a triangle in which apparently row i is related to the (i-1)st level of nucleus. Triangle begins:
2;
6,     8;
14,   16,  20;
28,   32,  38,  40;
50,   58,  64,  68,  70;
82,   92, 100, 106, 110, 112;
126, 136, 142, 154, 162, 164, 168;
...
Example 2: written as an irregular triangle in which row j is related to the j-th shell of nucleus. In this case note that row 4 has only one term. Triangle begins:
2;
6,     8;
14,   16,  20;
28,
32,   38,  40,  50;
58,   64,  68,  70,  82;
92,  100, 106, 110, 112, 126;
136, 142, 154, 162, 164, 168, 184;
...
First seven terms of right border give the "magic numbers" A018226.

M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955).

Library of Halexandria, Nuclear shell model, Table 1.

Partial sums of A212122. Other versions are A210984, A212014, A213364, A213374.

Cf. A007290, A018226, A033547, A210842, A212121, A212123.

a(n) = 2*A212123(n).

A212122 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.

Original entry on oeis.org

2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 8, 6, 4, 2, 12, 10, 8, 6, 4, 2, 14, 10, 6, 12, 8, 2, 4, 16

Offset: 1

Omar E. Pol, Jun 03 2012

First differs from A213362 at a(12).

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), 2d_(3/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 7, 5, 3,... 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, 4,... Other sequences that arise from this sequence are A212121, A212123, A212124. - Omar E. Pol, Sep 02 2012

			Illustration of initial terms: two views of a three-dimensional shell model of nucleus.
|-------------------------- j --------------------------|
|                                                       |
|   |---------------------- i ----------------------|   |
|   |                                               |   |
|   |   |------------------ h ------------------|   |   |
|   |   |                                       |   |   |
|   |   |   |-------------- g --------------|   |   |   |
|   |   |   |                               |   |   |   |
|   |   |   |   |---------- f ----------|   |   |   |   |
|   |   |   |   |                       |   |   |   |   |
|   |   |   |   |   |------ d ------|   |   |   |   |   |
|   |   |   |   |   |               |   |   |   |   |   |
|   |   |   |   |   |   |-- p --|   |   |   |   |   |   |
|   |   |   |   |   |   |       |   |   |   |   |   |   |
|   |   |   |   |   |   |   s   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
|   |   |   |   8   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   6   |   |   |   |
|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
|   |   |  10   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
|   |  12   |   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   |   |  10   |   |
|   |   |   |   8   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   6   |   |   |   |
|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
|  14   |   |   |   |   |   |   |   |   |   |   |   |   |
|   |   |  10   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   |   |   |  12   |
|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
16  |   |   |   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |1/2|   |   |   |   |   |   |
|   |   |   |   |   |   |           |   |   |   |   |   |
|   |   |   |   |   |   |----3/2----|   |   |   |   |   |
|   |   |   |   |   |                   |   |   |   |   |
|   |   |   |   |   |--------5/2--------|   |   |   |   |
|   |   |   |   |                           |   |   |   |
|   |   |   |   |------------7/2------------|   |   |   |
|   |   |   |                                   |   |   |
|   |   |   |----------------9/2----------------|   |   |
|   |   |                                           |   |
|   |   |-------------------11/2--------------------|   |
|   |                                                   |
|   |-----------------------13/2------------------------|
|
|---------------------------15/2-------------------------
.
..........................................................
.
|-------------------------- j --------------------------|
*                                                       |
*   |---------------------- i ----------------------|   |
|   *                                               |   *
|   *   |------------------ h ------------------|   |   *
*   |   *                                       |   *   |
*   |   *   |-------------- f --------------|   |   *   |
|   *   |   *                               |   *   |   *
|   *   |   *   |---------- e ----------|   |   *   |   *
*   |   *   |   *                       |   *   |   *   |
*   |   *   |   *   |------ d ------|   |   *   |   *   |
|   *   |   *   |   *               |   *   |   *   |   *
|   *   |   *   |   *   |-- p --|   |   *   |   *   |   *
*   |   *   |   *   |   *       |   *   |   *   |   *   |
*   |   *   |   *   |   *   s   |   *   |   *   |   *   |
|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
|   *   |   *   |   *   |   *   *   |   *   |   *   |   *
*   |   *   |   *   |   *   |   |   *   |   *   |   *   |
*   |   *   |   *   |   *   |1/2|   *   |   *   |   *   |
|   *   |   *   |   *   |           |   *   |   *   |   *
|   *   |   *   |   *   |----3/2----|   *   |   *   |   *
*   |   *   |   *   |                   |   *   |   *   |
*   |   *   |   *   |--------5/2--------|   *   |   *   |
|   *   |   *   |                           |   *   |   *
|   *   |   *   |------------7/2------------|   *   |   *
*   |   *   |                                   |   *   |
*   |   *   |----------------9/2----------------|   *   |
|   *   |                                           |   *
|   *   |-------------------11/2--------------------|   *
*   |                                                   |
*   |-----------------------13/2------------------------|
|
|---------------------------15/2-------------------------
.
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,  4,  2, 12;
10,  8,  6,  4,  2, 14;
10,  6, 12,  8,  2,  4, 16;
...

M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955).

HyperPhysics, G.S.U., Shell Model of Nucleus
Library of Halexandria, Nuclear shell model, Table 1.

Row sums give A210842. Partial sums give A212124.
Other versions are A162630, A212012, A213362, A213372.
Cf. A018226, A002378, A130517, A130598, A210842, A212121, A212123.

a(n) = 2*A212121(n).

cp's OEIS Frontend

A212124 Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.

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