## Searching Harmonics in Nuclei Gyromagnetic Ratios. Startling Emergence of Scaling, Pseudo Octaves, and the Fine-Structure Constant from a Seemingly Random Network.

**Authors:** Bruno R. Galeffi

A plot of the nuclei gyromagnetic ratios vs. corresponding mass numbers was intuitively fitted with classic damped sinusoids of the form [asin(bx+c)+d]exp(-kx) using the interactive QtiPlot software. The outcome was a 2D interlaced network from which unexpected scaling emerged. The sine waves frequencies in descending order were found to follow the intriguing correlation b/2π=0.0100+0.137exp(-N/1.306) with N=0,1,2... The amplitude value at 0.137 is interpreted as 10^-3/α with α being the fine-structure constant. The scaling factor exp(1/1.306) which is ≈2.15 is discussed in relation to stretched octaves and probable connection to the golden ratio. The sinusoids equivalent energy range is found at E=7.29-107 MeV. The asymptotic energy value at 7.29 is interpreted as 10^3α, from which a nucleon mean radius at ≈0.85 fm is deduced.

**Comments:** 5 Pages. Thank you

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### Submission history

[v1] 2018-08-27 12:43:04

[v2] 2018-08-29 09:51:51

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