Farey and Ford Analysis

It is of interest to explore the possibility of an independent identification of magic numbers and the neutron spectrum by the relationship between neutron number and Farey sequences as mapped by Ford circles. Such an analysis presupposes the occurrence of periodic sequences of 32, 18, 8 and 

All of the primary and secondary sequences can be traced back to tangent Ford circles. The two independent patterns have common points at the four most significant, generally accepted, magic numbers 2, 50, 82 and 126. The points at which the eleven hem lines intersect the golden ratio line are indicated by arrows. Ford circles from the Farey sequence (2k2 = 50) appear 

The details of nuclear structure depend on the interplay of three periodic functions, regulated by A, Z and N respectively. Only the A periodicity is of central-field type. The physical properties of nuclides, the subject of nuclear physics, are conditioned by the irregular coincidences of the three types of energy level and will not be pursued here any further. The effect of nuclear structure on chemistry is minimal. 

It has been customary for many years to look at quantum mechanics for theoretical guidance in chemistry. In retrospect it is evident that little more than a qualitative picture has emerged from this pursuit. For a quantitative 

There is no quantum-mechanical guidance to elucidate the relative stability of different nuclides or define the number of naturally occurring stable elements and their isotopes. Nuclear periodicity in terms of the Elsasser magic numbers remains an empirical scheme. 

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