Nucleon valency

In the case of odd-A nuclei, In in the ground state is fixed by the single valency nucleon in the lowest vacant level shown in Fig. 2.3. In 150, for example, 8 protons fill closed shells up to 1 py2, 6 neutrons fill closed shells up to 1 /tv2 and the last neutron occupies py2 making the state. In 170, on the other hand, all states up to I/21/2 are filled by both protons and neutrons and the extra neutron occupies... 

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)). 

Nucleon a proton or a neutron, the number of nucleons in an atom equals the sum of protons and neutrons in the nucleus Octet Rule general rule that states that the most stable electron configuration occurs when an atom surrounds itself with eight valence electrons... 

Y has properties which are basically determined through the valence nucleons beyond the core 96Zr (or 94Sr). The existence of the isomer of three-quasiparticle character indicates that there is no particular softness against deformation even at high excitation energy. 

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]

In this chapter we review the recent history of and evidence for collective, moleculelike behavior of valence electrons in atoms and indicate some of the questions that will have to be explored in order to resolve the question of how well the electrons in atoms are described by independent-particle or collective models. We then turn the question around and ask whether atoms in a molecule could, under suitable circumstances, display independent-particle behavior, with their own one-particle angular momenta behaving like nearconstants of the motion. The larger question that emerges is then one of whether few-body systems—the valence electrons of an atom, the atoms that constitute a small polyatomic molecule, and perhaps others such as the nucleons in a nucleus, all of which have heretofore seemed nearly unrelated— share characteristics to the extent that we can devise a unifying picture of the dynamics of few-body systems that will expose their commonalities as well as their obvious differences. 

I. Angeli, Effect of valence nucleons on RMS charge radii and surface thickness, J. Phys. G 17 (1991) 439-454. 

Another limit of nuclear stability is the extreme of the neutron to proton ratio, N/Z. For certain very neutron-rich nuclei, such as Li, an unusual halo structure has been observed. In halo nuclei, a core of nucleons is surrounded by a misty cloud, a halo of valence nucleons that are weakly bound and extend out to great distances, analogous to electrons surrounding the nucleus in an atom. Halo nuclei are fragile objects, are relatively large, and interact easily with other nuclei (have enhanced reaction cross sections). The halo nucleus Li, which has a Ti core surrounded by a two-neutron halo is shown in Figure 1. Li is as large as ° Pb. Li and other... 

It is found in experiments that the nucleon vector current can to a good approximation be described as the sum of the corresponding valence quark vector currents. For the vector currents of the proton (p) and the neutron (n) we obtain therefore... 

To most of us, Tom Kuo is best known for this seminal work on the effective interaction of two valence nucleons in nuclei ( Kuo-Brown matrix elements ) published in 1966 [1]. One of the most fundamental goals of theoretical nuclear physics is to understand atomic nuclei in terms of the basic nucleon-nucleon (NN) interaction. Tom and Gerry s work of 1966 was the first successful step towards this goal. Microscopic nuclear structure has essentially two ingredients many-body theory and the nuclear potential. During the past 25 years, there has been progress in both of these fields. Tom Kuo has worked consistently on the improvement of the many-body approaches appropriate for nuclear structure problems [2,3]. On the other hand, there have also been substantial advances in our understanding of the NN interaction since 1966, when the Hamada-Johnston potential [4] was the only available quantitative NN potential. 

M. Hjorth-Jensen et al./Physics Reports 242 (1994) 37-69 4.1. Nuclei with two valence nucleons... 

Calcium isotopes with more than two valence nucleons... 

We conclude our discussion on the derived effective interactions by employing the two-body matrix elements in the calculation of the eigenvalues for nuclei with more than two valence nucleons. Here we limit our attention to two isotopes, i.e. and Sc. The effective interactions we use are those obtained by using the LS method with a third-order Q-box and by including excitations up to 6ho) in oscillator energy in the evaluation of the adhering diagrams. 

Level I. A nucleon (neutron, proton) consists of three (valence) quarks, clearly seen on the scattering image obtained for the proton. Nobody has yet observed a free quark. 

Each of the nucleons is composed of three quarks (called the valence quarks). 

Properties of nucleons (p, n). Quark structure symbol, electric charge (e), spin (A) and its direction. There are three valence quarks both in p and n, such that they are colorless... 

The weak interactions change quark and lepton flavors, e.g., a d-quark into -quark or a muon into an electron (this latter, e.g., in the p e Vet /i process). The quark structures of the proton and neutron as well as the properties of nucleons are presented in O Table 2.3. The baryons are built up from three (valence) quarks and massless gluons, but they contain also dynamical (or sea) quarks (quark-antiquark pairs) in a small quantity. The mesons are built up from quark-antiquark pairs and gluons. 

The basic assumption of the independent-particle model is that the valence nucleon(s) move in an average field produced by the inert core nucleons. 

For a spherical harmonic oscillator V(r) = ma> i l2, where to is the angular frequency of oscillation. If the valence nucleon is proton, V(r) must also contain a Coulomb term. 

The independent-particle model is best suited for the treatment of nuclei that have doubly closed-shell core 1 nucleon. In this case, the core has a rather well-defined spherical shape and the problem of the residual interaction between valence nucleons does not arise. 

Nevertheless, if there are several nucleons in the valance shell(s), the interaction between the valence nucleons may change the level spectrum. The experimental data show that the level sequence of the independent-particle model (O Fig. 2.9) can only be considered in general as a first approximation. The actual level scheme depends not only on the atomic or the neutron number, but also on the mass number. 

The interaction between valence nucleons not included in the average field is called the residual interaction. The residual interaction differs from the interaction between free nucleons in that it cannot result in binding into occupied orbits. 

If two valence nucleons move in the average field of the core, the residual interaction between them must also be taken into account. As the residual interaction usually gives a weak contribution to the binding, perturbation theory can be applied. In one type of calculation the residual interaction is approximated by a schematic (delta, surface delta, Schiffer, etc.) interaction. In another type of calculation, realistic interactions are used, which are derived approximately from free nucleon-nucleon interactions. In most calculations, empirically determined parameters are used. 

It is also possible to perform shell model calculations for nuclei, which have three or more valence nucleons. Nevertheless, the calculations become rapidly very complex with increasing number of valence nucleons. Large-scale shell model calculations were performed mainly for the light nuclides with A < 70. 

Seniority is defined as the number of unpaired nucleons in a state. In the low-seniority scheme, it is supposed that the ground states of even-even semi-magic nuclei consist of pairs of identical nucleons that are coupled to spin zero. In the excited states, one or more pairs are broken. In the ground state of odd-A nuclei, there is one valence nucleon and in the excited states, 1, 3, 5, etc., valence nucleons. The low-seniority scheme calculations (Lawson 1980 Allaart et al. 1988 Talmi 1993) give a reasonable description of numerous semi-magic nuclei that have not too many valence particles (or holes). 

Note that if there are more than one valence nucleons outside the douhle-closed core, the residual interaction between the valence nucleons may cause configuration mixing, which may strongly affect the transition rates. 

The basic idea of the unified model (Rainwater 1950 Bohr 1952 Bohr and Mottelson 1953) is that the nuclear core can perform collective motion (surface vibration and in the case of deformed nuclei, rotation), while the valence nucleons move on individual orbits. 

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