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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
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.
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.
Sequence in context: A162630 A213362 A212122 * A286601 A340071 A102128
KEYWORD
nonn,tabf,hard,more
AUTHOR
Omar E. Pol, Jul 16 2012
STATUS
approved