Layering Of Shell Structures In Magic Numbers For Harmonic Oscillator Atomic Clusters

[pascal2]

Hi again folks- been a while since I last posted in this forum.  Some of you may remember that I've had a long held interest in Pascal Triangle mathematical motivation in atomic electronic and nuclear shell structure. This has included those of atomic clusters as well.

 

Some years back the Romanian nuclear physicist Dorin Poenaru had coauthored papers dealing with the pattern of shells and their magic number closures in atomic clusters- primarily in hemispheroidal ones, but also in sphere-based one, including those that were ellipsoidally deformed.

 

1)  D.N. Poenaru R.A., Gherghescu, I.H. Plonski, A.V. Solov’yov, and W. Greiner2Macroscopic-Microscopic Theory of Semi-Spheroidal Atomic Cluster, 

 

Eur. Phys. J. D 47, 379–393 (2008)

 

Available online at: https://link.springer.com/article/10.1140/epjd/e2008-00066-6

 

 

2)  D.N. Poenaru, R.A. Gherghescu, A.V. Solov’yov, W. Greiner,   Hemispheroidal quantum harmonic oscillator

 

Physics Letters A 372 (2008) 5448–5451

 

Deformed magics from the first article (p. 383) are:

 

A) – δ = −1 (a/c = 3): 2, 6, 20, 30, 42, 58, 78, 102, 130;

 

B ) – δ = −2/3 (a/c = 2): 2, 6, 12, 20, 32, 48, 68, 92, 122, 158;

 

C) – δ = −0.4 (a/c = 3/2): 2, 6, 12, 22, 36, 54, 78, 108, 144;

 

D) – δ = −0.8/3 (a/c = 17/13): 2, 6, 12, 22, 26, 36, 42, 56, 64, 82, 92, 114, 126, 154;

 

F) – δ = 0.8/3 (a/c = 13/17): 2, 6, 8, 14, 18, 28, 34, 48, 58, 76, 90, 114, 132;

 

G) – δ = 0.4 (a/c = 2/3): 2, 8, 18, 20, 34, 38, 50, 58, 64, 80, 92, 100;

 

H) – δ = 2/3 (a/c = 1/2): 2, 8, 20, 40, 70, 112, 168;

 

I) – δ =1(a/c = 1/3): 2, 8, 10, 14, 22, 26, 46, 54, 66, 84, 96, 114, 138, 156;

 

J) – δ = 1.2 (a/c = 1/4): 2, 4, 10, 16, 28, 40, 60, 80, 110, 140.

 

where δ is the delta deformation parameter and a/c is the oscillator ratio used in the Japan (the US tends to use the reciprocal), where a is the relative extent of the matter wave in the equatorial direction, and c in the polar direction).

 

The hemispheroidal atomic clusters used in these studies were composed of all-same elements and bound to a substrate on the flat side (bisecting the ellipsoid of rotation). More later.

 

Jess Tauber

Edited April 13, 2020 by pascal2