[seqfan] New atomic nuclear sequence found

Jess Tauber tetrahedralpt at gmail.com
Wed Mar 25 10:22:41 CET 2020

Hi folks- some years back I had been briefly active in the group, even
posting about the presence in nuclear shell structures the OEIS sequence
A051890 <https://oeis.org/A051890>, which links the counts of nucleons
having parallel suborbital designations though in different shells.

This past week I've been revisiting these issues after a long hiatus, and
have found another sequence attested for such connections: 2, 6, 12, 22,
36, 54, 76, 102, 132, 166, 204, 246...

While A051890 is formed by summed pairs of every other doubled triangular
number, this new sequence, which isn't in the OEIS database, is formed from
summed pairs of every THIRD doubled triangular number.

The basic sequence found in spherical nuclei, under a simple harmonic
oscillator model (where shell sizes are always consecutive terms of Pascal
Triangle diagonals) consists of doubled triangular numbers, and the
connections between like suborbital designations  are all half/doubled
square numbers, which are produced by taking summed pairs of every
consecutive doubled triangular number.

Depending on how one configures tables of shell structures, one can see ALL
THREE mathematical patterns outlined above. It makes things a LOT more
interesting than a mere one-size-fits-all scenario.

Jess Tauber

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