login
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.
9
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
1,1
COMMENTS
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
REFERENCES
M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955).
LINKS
HyperPhysics, G.S.U., Shell Model of Nucleus
Library of Halexandria, Nuclear shell model, Table 1.
FORMULA
a(n) = 2*A212121(n).
EXAMPLE
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;
...
CROSSREFS
Row sums give A210842. Partial sums give A212124.
Other versions are A162630, A212012, A213362, A213372.
Sequence in context: A278526 A162630 A213362 * A213372 A286601 A340071
KEYWORD
nonn,tabf,hard,more
AUTHOR
Omar E. Pol, Jun 03 2012
STATUS
approved