Nucleons structure

D1V.9. 1. Prigogine and F. Henin, On the structure of elementary particles in classical electrodynamics, in Nucleon Structure, R. Hofstadter and Schiff eds., Stanford University Press, Palo Alto, CA, 1964, pp. 334-336. 

Some information on the size of the correction for nucleon structure can be gained from a comparison of the difference between the experimental values for hydrogen and deuterium, 1 23 0 15 Mc/s with the difference between the theoretical values, l 24=l 0 035—est. This shows that e8t, the correction for nucleon structure (section 9.8) cannot be very large. 

Unfortunately, the theory is limited to much less precision [l2j by nucleon structure and radiative corrections with an estimated uncertainty of about 3 ppm. Similar calculations for muonium (no hadronic complication) are much more accurate, so that from a comparison between theory and experiment the following tt-value is obtained [133 ... 

R. Hofstadter (Stanford) pioneering studies of electron scattering in atomic nuclei and discoveries concerning the structure of the nucleons. 

In the model of nuclear structure you were given in Chapter 6, the nucleus was pictured as being built up of protons and neutrons. These two kinds of particles are given the general name nucleon. The mass number of a nucleus is equal to the number of nucleons present. The superscripts in our equation are mass numbers ... 

The discoveries of Becquerel, Curie, and Rutherford and Rutherford s later development of the nuclear model of the atom (Section B) showed that radioactivity is produced by nuclear decay, the partial breakup of a nucleus. The change in the composition of a nucleus is called a nuclear reaction. Recall from Section B that nuclei are composed of protons and neutrons that are collectively called nucleons a specific nucleus with a given atomic number and mass number is called a nuclide. Thus, H, 2H, and lhO are three different nuclides the first two being isotopes of the same element. Nuclei that change their structure spontaneously and emit radiation are called radioactive. Often the result is a different nuclide. 

I have found that the assumption that in atomic nuclei the nucleons are in large part aggregated into clusters arranged in closest packing leads to simple explanations of many properties of nuclei. Some aspects of the closest-packing theory of nuclear structure are presented in the following paragraphs.1... 

The structural interpretation of the principal quantum number of nucleonic orbital wave functions and the structural basis provided by the close-packed-spheron theory for the neutron and proton magic numbers are discussed in notes submitted to Phys. Rev. Letters and Nature (L. Pauling, 1965). 

During recent decades a great amount of knowledge about the properties of atomic nuclei has been gathered. An extensive theory of nucleonic interactions and nuclear structure [liquid-drop theory (7), shell theory (2, 3), unified theory (4), cluster theory (5—7)] has been developed... 

The nature of spheron-spheron interactions is such that maximum stability is achieved when each spheron ligates about itself the maximum number of neighbors, to produce a nucleus with a closest-packed structure. A simple argument (12) leads to the conclusion that the spherons in a nucleus are arranged in concentric layers. The packing radius of a spheron varies from 1.28 f for the dineutron to 1.62 f for the helion. The radius (to nucleon density half that of the inner region) of the largest nucleus is 6.8 f... 

The conclusion that each inner-core spheron in a stable core should ligate its neighbors about itself in a way corresponding to local stability is a reasonable consequence of the self-generating character of the potential energy function for nucleons in nuclei (mutual interdependence of structure and potential energy function) and the short range of internucleonic forces. 

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

After reducing this TBF to an effective, density dependent, two-body force by the averaging procedure described earlier, the resulting effective two-nucleon potential assumes a simple structure,... 

The consequences for the structure of the neutron stars are illustrated in Fig. 9, where we display the resulting neutron star mass-radius curves, comparing now results obtained with different nucleonic TBF, in analogy to Fig. 5. One notes that while in Fig. 5 the different TBF still yield quite different maximum masses, the presence of hyperons equalizes the results, leading now to a maximum mass of less than 1.3 solar masses for all the nuclear TBF. 

Besides the crust and the hadron shell, the hybrid star contains also a quark core. Both the nucleon shell and the quark core can be in superconducting phases, in dependence on the value of the temperature. Fluctuations affect transport coefficients, specific heat, emissivity, masses of low-lying excitations and respectively electromagnetic properties of the star, like electroconductivity and magnetic field structure, e.g., renormalizing critical values of the magnetic field (/ ,, Hc, Hc2). 

Since the discovery of the parton substructure of nucleons and its interpretation within the constituent quark model, much effort has been spent to explain the properties of these particles and the structure of high density phases of matter is under current experimental investigation in heavy-ion collisions [17]. While the diagnostics of a phase transition in experiments with heavy-ion beams faces the problems of strong non-equilibrium and finite size, the dense matter in a compact star forms a macroscopic system in thermal and chemical equilibrium for which effects signalling a phase transition shall be most pronounced [8],... 

For two and three dimensions, it provides a crude but useful picture for electronic states on surfaces or in crystals, respectively. Free motion within a spherical volume gives rise to eigenfunctions that are used in nuclear physics to describe the motions of neutrons and protons in nuclei. In the so-called shell model of nuclei, the neutrons and protons fill separate s, p, d, etc orbitals with each type of nucleon forced to obey the Pauli principle. These orbitals are not the same in their radial shapes as the s, p, d, etc orbitals of atoms because, in atoms, there is an additional radial potential V(r) = -Ze2/r present. However, their angular shapes are the same as in atomic structure because, in both cases, the potential is independent of 0 and (f>. This same spherical box model has been used to describe the orbitals of valence electrons in clusters of mono-valent metal atoms such as Csn, Cu , Na and their positive and negative ions. Because of the metallic nature of these species, their valence electrons are sufficiently delocalized to render this simple model rather effective (see T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange, J. Phys. Chem. 95, 6421 (1991)). 

The electronic structure parameters describing the P,T-odd interactions of electrons (sections 7, 8, and 10) and nucleons (section 9) including the interactions with their EDMs should be reliably calculated for interpretation of the experimental data. Moreover, ab initio calculations of some molecular properties are usually required even for the stage of preparation of the experimental setup. Thus, electronic structure calculations suppose a high level of accounting for both correlations and relativistic effects (see below). Modern methods of relativistic ab initio calculations (including very... 

Investigating the Structure of the Nucleon with Real Photons By F. Wissmann 2003. 68 figs., VIII, 142 pages... 

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