Neutron imbalance

Figure 4.1 Neutron imbalance as a function of mass number for the isotopes of selected elements...

Before the discovery of neutrons, the familiar empirical form of the periodic table was established as a function of atomic number, which represents less than half the matter that makes up an atom, except for hydrogen and 3He. Later work has shown that nuclear stability is related to nuclear composition, characterized by a neutron imbalance that increases with mass number. For a nucleus of N neutrons and Z protons, neutron imbalance is represented either by the ratio r = Z/N or the relative excess Nx = (N — Z)/Z. These parameters are plotted against mass number for selected elements in Figure 4.1. 

The relative energies of sub-levels and hence the order in which these are occupied by electrons cannot be predicted in detail, but this pattern is revealed when the periodicity of the nuclides is examined as a function of atomic number. This distribution of stable nuclides as a function of neutron imbalance is shown in Figure 4.4. To ensure that the grouping into sets... 

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. 

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... 

Fig. 6 Neutron imbalance of atomic nuclei is defined either by the ratio Z/iV or the relative excess (N — Z)/Z. As functions of mass number, these quantities map the isotopes of a given element to respective circular segments and straight lines, the intersection of which defines the golden ratio...

On the other hand, 14gO has 8 protons but only 6 neutrons. This imbalance of protons and neutrons can be corrected if a proton is transformed into a neutron as is summarized by the equation... 

Likewise, even nuclei (with even numbers of protons) have lower probability (cross-section) for neutron capture than odd nuclei, and this results in a greater abundance of the former. The even-odd imbalance is manifested once again. 

The s process builds up an abundance distribution with peaks at mass numbers (A = Z + N) 87,138 and 208 and pronounced even-odd imbalance. The main component of the s process is associated with thermal pulsations of stars in the asymptotic giant branch (1-3 Mq) which produce neutron densities between 10 and 10 cm (Fig. 5.6). 

We can imderstand why the N Z ratio must increase with atomic number in order to have nuclear stability when we consider that the protons in the nucleus must experience a repulsive Coulomb force. The fact that stable nuclei exist means that there must be an attractive force tending to hold the neutrons and protons together. This attractive nuclear force must be sufficient in stable nuclei to overcome the disruptive Coulomb force. Conversely, in unstable nuclei there is a net imbalance between the attractive nuclear force and the disruptive Coulomb force. As the number of protons increases, the total r ulsive Coulomb force must increase. Therefore, to provide sufficient attractive force for stability the number of neutrons increases more rapidly than that of the protons. 

As you progress through the periodic table each successive atom has one more proton and neutron compared with the previous atom. The protons are useful for attracting electrons, and the neutrons are useful for stabilizing the nucleus. When there is an imbalance between the two nuclear particles (proton and neutron), the nucleus becomes unstable, and these types of atoms are called isotopes. If they are radioactive, they are called radioisotopes, and they can be useful, for example, in medical applications. 

Worth remarking the results of type (2.7) and (2.9), here based on chemical reactivity specialization of Heisenberg type equations (2.1) and/or (2.2), were previously obtained at the level of neutron-protonic imbalance, inside the atomic nuclei, based on well-founded empirical observations (Boeyens Levendis, 2008). The present golden ratio appearance is ultimately sustained also by the deviation from the N=Z condition for so-called quark atoms (as another way in considering the atoms in a quantum valence state), earlier identified as true matter s entities responsible for matter s reactivity at the atomic level (Lackner Zweig, 1983). 

Thrust imbalances due to reactor asymmetries and unbalanced flux of neutrons and charged particles from the reactor. 

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