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.

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

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

Table of n, a(n) for n=1..22.

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