A213362 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.

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

Offset: 1

Author

Omar E. Pol, Jun 23 2012

Keywords

• nonn
• tabf
• hard
• more

Comments

First differs from A212122 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), 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

Examples

			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   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
.|   |  12   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   8   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   4   |   |   |   |   |   |   |   |
.|  14   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |  10   |   |
.|   |   |   |   |   |   |   |   2   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   6   |   |   |   |
.|   |   |  10   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |  12   |
16   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   6   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   2   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   8   |   |   |
.|   |   |   |   |   |   |   |   |   4   |   |   |   |   |
.|   |   |   |   |   |   |   |   |   |   |   |   |   |   |
.|   |   |   |   |   |   |   |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;
6,   8,  2,  4, 12;
8,   4, 14, 10,  2,  6;
10, 12, 16,  6,  2,  8,  4;
...
		

References

• I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993).

Links

• Wikipedia, Nuclear shell model

Crossrefs

Partial sums give A213364. Other versions are A162630, A212012, A212122, A213372.

Cf. A018226, A130517, A213361, A213363.

Formula

a(n) = 2*A213361(n).