Nucleon orbitals

The Relation between the Shell Model and Layers of Spherons.—In the customary nomenclature for nucleon orbitals the principal quantum number n is taken to be nr + 1, where nr> the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nT + l + 1.) The nucleon distribution function for n = 1 corresponds to a single shell (for Is a ball) about the origin. For n = 2 the wave function has a small negative value inside the nodal surface, that is, in the region where the wave function for n = 1 and the same value of l is large, and a large value in the region just beyond this surface. 

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). 

Nuclear nomenclature Helion for alpha-particle. Nature 201 (1964) 61. [65-13] Structural significance of the principal quantum number of nucleonic orbital wave functions. Phys. Rev. Lett. 15 (1965) 499. 

High-spin states were observed also in nearly spherical nuclei, e.g., in 4 Gdg3. In this case, the level scheme does not show the regular pattern of collective rotation, and the reduced E2 transition probabilities are close to the Weisskopf unit. The high-spin states are produced by the alignment of individual nucleonic orbits. This is the case of non-collective rotation. The irregularities are related to the occupation of different single-particle states. 

Cluster emission is an exotic decay that has some commonalities with a-decay. In a-decay, two protons and two neutrons that are moving in separate orbits within the nucleus come together and leak out of the nucleus as a single particle. Cluster emission occurs when other groups of nucleons form a single particle and leak out. Several of the observed decays are shown in Table 10. The emitted clusters include C, Ne, Mg, and Si. The... 

Summary.—The assumption that atomic nuclei consist of closely packed spherons (aggregates of neutrons and protons in localized Is orbitals—mainly helions and tritions) in concentric layers leads to a simple derivation of a subsubshell occupancy diagram for nucleons and a simple explanation of magic numbers. Application of the close-packed-spheron model of the nucleus to other problems, including that of asymmetric fission, will be published later.13... 

Fig. 2. The sequence of nucleonic energy levels with spin-orbit coupling, redrawn, with small changes, from 3, p. 58.

I assume that in nuclei the nucleons may. as a first approximation, he described as occupying localized 1. orbitals to form small clusters. These small clusters, called spherons. arc usually hclions, tritons, and dincutrons in nuclei containing an odd number of neutrons, an Hc i cluster or a deuteron may serve as a spheron. The localized l.v orbitals may be described as hybrids of the central-field orbitals of the shell model. 

Electrons of 2s orbitals have lower energy than those of 2p orbitals because electrons in 2s orbitals tend, on the average, to be much closer to the nucleons than electrons in 2p orbitals. 

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 spin of a proton is, like an electron, a neutron also has spin In addition to spin angular momentum, the nucleons in a nucleus have orbital angular momentum the orbital angular-momentum quantum number of a nucleon can be 0,1,2, The spin angular momentum of each nucleon... 

Although the predominant part of the nuclear potential is the part described above that is derived from the central force produced by the average effects of all other nucleons in the system on the individual nucleon under observation, evidence exists that nonsymmetnc tensor and spin-orbit coupling terms must be included in the description of the nuclear potential. 

These are derived frum a. lensui force resulting from a coupling between individual pairs of nucleons and from the coupling between spin and orbital angular moments of the individual nucleus, as described by the shell model of the nucleus. 

Quantum Number (Orbital). A quantum number characterizing the orbital angular momentum of an electron in an atom or of a nucleon in the shell-model description of the atomic nucleus. The symbol for the orbital quantum number is l. 

Nuclear electromagnetic decay occurs in two ways, y decay and internal conversion (IC). In y-ray decay a nucleus in an excited state decays by the emission of a photon. In internal conversion the same excited nucleus transfers its energy radia-tionlessly to an orbital electron that is ejected from the atom. In both types of decay, only the excitation energy of the nucleus is reduced with no change in the number of any of the nucleons. 

With a general understanding of the form of nuclear potentials, we can begin to solve the problem of the calculation of the properties of the quantum mechanical states that will fill the energy well. One might imagine that the nucleons will have certain finite energy levels and exist in stationary states or orbitals in the nuclear well similar to the electrons in the atomic potential well. This interpretation is... 

Figure 6.3 Energy level pattern and spectroscopic labeling of states from the schematic shell model. The angular momentum coupling is indicated at the left side and the numbers of nucleons needed to fill each orbital and each shell are shown on the right side. From M. G. Mayer and J. H. D. Jenson, Elementery Theory of Nuclear Shell Structure, Wiley, New York, 1955.

Due to the large amount of cancellation of the spins and angular momenta due to the strong coupling of nucleons in matching orbitals and pairing of spins, we should... 

As we have seen, the nucleons reside in well-defined orbitals in the nucleus that can be understood in a relatively simple quantum mechanical model, the shell model. In this model, the properties of the nucleus are dominated by the wave functions of the one or two unpaired nucleons. Notice that the bulk of the nucleons, which may even number in the hundreds, only contribute to the overall central potential. These core nucleons cannot be ignored in reality and they give rise to large-scale, macroscopic behavior of the nucleus that is very different from the behavior of single particles. There are two important collective motions of the nucleus that we have already mentioned that we should address collective or overall rotation of deformed nuclei and vibrations of the nuclear shape about a spherical ground-state shape. 

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