cp's OEIS Frontend

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), 2p_(1/2), etc. The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 1, ... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 2, ... Other sequences that arise from this sequence are A A130517, A210983, A210984. - Omar E. Pol, Sep 02 2012

First differs from A213364 at a(12).

For another version see A213361. First differs from A213361 at a(12).

What defines this sequence? (This appears to be some sort of permutation of A130517 by shifting columns down or upwards in some randomized way.) - R. J. Mathar, Jul 22 2012

Also triangle read by rows in which row i lists the first i positive even numbers in decreasing order.

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), 1d_(3/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 3,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 4,... Other sequences that arise from this sequence are both A212013 and A212014. - Omar E. Pol, Sep 02 2012

First differs from A213363 at a(12).

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

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

Additional comments from Omar E. Pol, Sep 02 2012: (Start)

Q: What are energy levels?

A: See the link sections of A212122, A213362, A213372. For example, see this link related to A213372: http://www.flickr.com/photos/mitopencourseware/3772864128/in/set-72157621892931990

Q: What defines the order in A212121?

A: The order of A212121 is defined by A212122.

Note that there are at least five versions of the nuclear shell model in the OEIS:

Goeppert-Mayer (1950): A212012, A004736, A212013, A212014.

Goeppert-Mayer, Jensen (1955): A212122, A212121, A212123, A212124.

Talmi (1993): A213362, A213361, A213363, A213364.

Meyerhof: A213372, A213371, A213373, A213374.

For another version: A162630, A130517, A210983, A210984.

Each version is represented by four sequences: the first sequence is the main entry.

(End)

For additional information see A162630.

Partial sums of the first seven terms give the "magic numbers" A018226.

Also the partial sums of the first eight terms give the positive first eight terms of A162626 (and possibly more).