Nuclide mapping

The equivalence between Sk, the infinite Farey tree structure and the nuclide mapping is shown graphically in Figure 8.4. The stability of a nuclide depends on its neutron imbalance which is defined, either by the ratio Z/N or the relative neutron excess, (N — Z) jZ. When these factors are in balance, Z2 + NZ — N2 = 0, with the solution Z = N(—1 /5)/2 = tN. The minimum (Z/N) = r and hence all stable nuclides are mapped by fractions larger than the golden mean. 

In Figure 5.6 we arrange the natural numbers along a spiral with a pitch of 24. All prime numbers, except for 2 and 3, occur on eight radial lines as p = 6n 1. By mapping the natural elements to these radial lines the periodicity of 16 = 2 x 8 is accounted for at the same time as the nuclide periodicity of 24. This arrangement is known as Plichta s prime-number cross. It has the remarkable property that the sum of all numbers over any complete cycle is given by... 

Figure 5.4 signifies more than elemental or nuclide periodicity. It summarizes the appearance of ponderable matter in all modifications throughout the universe. Following the extended hemlines from top left at Z/N = 1.04 — bottom left at 0 —> top right at Z/N = 1.04 bottom right at 0, and back to top left, the involuted closed path, which is traced out, is mapped to the non-orientable surface of a Mobius band in Figure 5.7. The two sides of the double cover are interpreted to represent both matter and antimatter.

I developed an interest in the field on noticing that cosmological theories of nucleogenesis are totally out of fine with reality. The important clue came from the observed periodicity of the stable nuclides, which is governed by simple concepts of number theory. Any atomic nucleus consists of integral numbers of protons and neutrons such that the ratio Z/N is always a rational fraction, which can be ordered in Farey sequences and mapped by Ford circles. This ordering predicts a unique periodic function, which is readily demonstrated to predict the correct observed cosmic abundances of the elements. 

Radiation decay. In some salts, neutron activation of ftie salt leads to a radioactive decay process that creates high-energy electrons. As the electrons in the salt slow down, photons are emitted that peak in the blue part of the visible spectrum. Because this part of the spectrum is far from the thermal infrared signal caused by the high temperatures, it will be detectable. Depending upon half-lives of the activated nuclides and flow velocities, this phenomenon may allow mapping of salt flow patterns above the reactor core. 

A negative sign means that neutron scattering is accompanied by an anomalous reversal of phase. Such a nuclide will consequently appear in a ND Fourier map as a negative peak relative to the positive peaks which correspond to normal nuclei. A further difference is that the nucleus is virtually a point compared with the wavelengths ( 1 A) of the monochromatic thermal neutrons used in structure analysis. For this reason does not diminish with 8. To be sure, the nucleus is smeared by vibrational movements but ND peaks are noticeably sharper than electron-density peaks. To this extent, and for some other reasons, ND is inherently rather more exact than jlT-ray diffraction. 

This interpretation is supported [7] by analysis of the neutron imbalance of stable atomic species as a function of mass number, shown in Fig. 5. The region of nuclide stability is demarcated here by two zigzag lines with deflection points at common values of mass number A. Vertical hemlines through the deflection points divide the fleld into 11 segments of 24 nuclides each, in line with condition (c). This theme is developed in more detail in the paper on Atomic Structure in this volume. Defining neutron imbalance as either Z/N or (N — Z )jZ, the isotopes of each element, as shown in Fig. 6, map to either circular segments or straight lines that intersect where... 

The region of stability is mapped more precisely by two sets of straight-line segments with infiection points at common values of A. Through these inflection points, 11 hem lines divide the field of stability such that each block contains 24 nuclides. Although there is no general agreement on half lives that define stable nuclides, the set of nuclides identified by different schemes never deviates seriously from the 264 selected in Fig. 1. 

In all cases where the golden section or the golden spiral correlates with chemical phenomena, convergence to some singularity is observed. The most striking example, shown in Fig. 4, occurs as the composition of stable nuclides, measured as Z/N, converges to the golden ratio as Z 102. At the same time, the hem lines, which define nuclide periodicity of 24, map out the observed periodic table of the elements at Z / A = t. ... 

Fig. 4 Variability of the periodic table of the elements, a subset of the 24-member periodicity of stable nuclides, depends on space-time curvature and is mapped by 11 hem lines in the frame on the l. The field of stabUity is defined by the limiting lines that converge to r at Z = 102. The symmetrical version on the right is only resolved in 4D projective space...

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