Nucleon Periodicity

Like elemental periodicity, which is a function of electron configuration, an empirical periodic function for nucleons, known as the magic-number pattern, has been derived. The reason why this function has been less successful 

Most of the empirical magic numbers are identified directly by the hem lines at Z/N = r. The hem lines, extrapolated to ratios of 1 and 0 also identify known magic numbers. The interesting conclusion to be drawn from this observation is that the nuclear periodic function remains constant under all cosmic conditions. 

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Notice that both the electric charge and the total number of nuclear particles (nucleons) are conserved in the nuclear decomposition. Careful study of the rate of this nuclear decay shows that in a given period of time a constant fraction of the nuclei present will undergo decomposition. This observation allows us to characterize or describe the rate of nuclear decay in a very simple manner. We simply specify the length of time it takes for a fixed fraction of the nuclei initially present to decay. Normally we pick the time for... 

Figure 12. Kepler period versus the rotational mass for purely hadronic stars as well as hybrid stars. The following core compositions are considered i) nucleons and leptons (dotted line) ii) nucleons, hyperons, and leptons (dashed line) in) hadrons, quarks, and leptons (solid line). The shaded area represents the current range of observed data.

An element is specified by the number of protons in its nucleus. This equals the atomic number of the respective element, and thus determines its place within the periodic table of the elements. The atomic number is given as a subscript preceding the elemental symbol, e.g., gC in case of carbon. Atoms with nuclei of the same atomic number differing in the number of neutrons are termed isotopes. One isotope differs from another isotope of the same element in that it possesses a different number of neutrons, i.e., by the mass number or nucleon number. The mass number m is the sum of the total number of protons and neutrons in an atom, molecule, or ion. [1] The mass number of an isotope is given as superscript preceding the elemental symbol, e.g.,... 

The energy release of nuclear fission is tied to the fact that the heaviest nuclei have about 0.1 percent more mass per nucleon than nuclei near the middle of the periodic table of elements. What would be the effect on energy release if the 0.1 percent figure were instead 1 percent ... 

The periodic table provides the chemist with a very brief and simple representation of the elements. Recall that most of the mass of an individual atom is contained in the nucleus. In addition, a nucleus contains one or more protons and, with the exception of ordinary hydrogen (1H), one or more neutrons. As discussed in chapter 2, the mass number (A) is an integer and is equal to the number of protons (Z) plus the number of neutrons (N) in the nucleus. It is the number of protons that determines what element a particular atom is. The general term nucleon is used to describe both neutrons and protons, or particles found in the atomic nucleus. 

Figure 4.10 Atomic-number periodicity derived from, golden-ratio packing of nucleons.

Details of the elemental and neutron periodicities follow directly as subsets of the 24-fold periodic function of the nucleons. The periodic ordinal numbers, derived in this way, define the stability limits of nuclides in terms of, either atomic number or neutron number, as shown in Figures 4.4 and 4.11 respectively. 

Problem 1.6 Ps is the lightest atom in the Universe. This atom has no nucleons with a mass of 0.0011 a.u., which is close to zero mass, which should be placed in Period 0. However it has one electron, which belongs to Group 1, or 1A in the existing Periodic Table of the Elements. A revised Periodic Table of the Elements is proposed, as in Figure 1.6, after one includes Ps. 

The nucleus of an element consists of two main building blocks the proton and the neutron. It is the proportions, in which the two nucleons are joined in nucleonic packs termed nuclei which give rise to the various chemical elements and their isotopes. We believe that the essential protons and neutrons needed for the synthesis of chemical elements were generated when the Universe was just a few seconds old. The existing temperature at that time, about 10 K, enabled neutrons to decouple. Further, neutrons and protons react with each other. Calculations showed that among the stable nuclei generated in the first 3 min were deuterium, helium-3, helium-4 and lithium-7. However, due to lack of stable nuclei at mass numbers 5 and 8, the heavier elements could not be created during this enter period. 

For the r-process the models for calculating /3-decay rates can again be divided into microscopic and statistical categories. Among the microscopic ones shell model is of limited use as this involves very neutron-rich nuclei all over the periodic table. Beyond the /p-shell nuclei shell model has been applied to nuclei with either a few valence particles or with more particles but with not too many valence orbits. The microscopic theory that has been widely used is the Random Phase Approximation (RPA) and its different improved version. We refer here to the review by Arnould, Goriely and Takahashi [39] for a detailed description and references. The effective nucleon-nucleon interaction is often taken to be of the spin-isospin type ([Pg.205]

Each nucleus is characterized by a definite atomic number Z and mass number A for clarity, we use the symbol M to denote the atomic mass in kinematic equations. The atomic number Z is the number of protons, and hence the number of electrons, in the neutral atom it reflects the atomic properties of the atom. The mass number gives the number of nucleons (protons and neutrons) isotopes are nuclei (often called nuclides) with the same Z and different A. The current practice is to represent each nucleus by the chemical name with the mass number as a superscript, e.g., 12C. The chemical atomic weight (or atomic mass) of elements as listed in the periodic table gives the average mass, i.e., the average of the stable isotopes weighted by their abundance. Carbon, for example, has an atomic weight of 12.011, which reflects the 1.1% abundance of 13C. 

On the left side it is seen that the uranium isotope has 92 protons in the nucleus (corresponding to the element number of 92 for uranium). It is also seen that the uranium isotope has 238 nucleons in total in the nucleus. When an alpha particle (2 neutrons + 2 protons) is emitted the remaining nucleus only contains 90 protons and a total of 234 nucleons. When the number of protons in the nucleus changes it corresponds to that uranium has decayed into another element which in this case is thorium (Th). Thorium has the element number of 90 in the periodic table (the periodic table will be described more in details in later sections). 

The mass of a neutron is l.(X)8 665 u while that of the hydrogen atom is l.(K)7 825 u. Since both neutrons and protons have almost unit atomic masses, the atomic mass of a nuclide should be close to the number of nucleons, i.e. the mass number. However, when the table of elements in the periodic system (Appendix I) is studied it becomes obvious that many elements have masses which are far removed from integral values. Chlorine, for example, has an atomic mass value of 35.453 u, while copper has one of 63.54 u. These values of the atomic masses can be explained by the effect of the relative abundances of the isotopes of the elements contributing to produce the observed net mass. 

As discrete numbers of nucleons are involved in the constitution of nuclides the periodicity of atomic matter is readily simulated in terms of the elementary number theory of rational fractions, Farey sequences and Ford circles. 

The proposed (Manuel et al., 2006) nuclear cycle that powers the cosmos has many elements in common with some of our arguments. Not unlike the periodic model of stable nuclides and the notion of cosmic self-similarity these authors suggest that stars are subject to the same types of interaction that occur in radioactive nuclides, which depend on the relative amounts of nucleons defined by the numbers A, Z and N. Because of chemical layering an accumulation of neutrons that resembles a neutron star develops at the core of an ordinary star. This core is left behind as the remains of a supernova. 

The periodic table of the elements is a subset of a more general periodic function that relates all natural nuclides in terms of integer numbers of protons and neutrons, the subject of elementary number theory. The entire structure is reproduced in terms of Farey sequences and Ford circles. The periodicity arises from closure of the function that relates nuclear stability to isotopic composition and nucleon number. It is closed in two dimensions with involution that relates matter to antimatter and explains nuclear stability and electronic configuration in terms of space-time curvature. The variability of electronic structure predicts a non-Doppler redshift in galactic and quasar light, not taken into account in standard cosmology. 

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