Shell nuclear

Table 11 illustrates the known closed proton and neutron shells and the predicted closed nuclear shells (shown in parentheses) that might be important in stabilising the superheavy elements. Included by way of analogy are the long-known closed electron shells observed in the buildup of the electronic stmcture of atoms. These correspond to the noble gases, and the extra stabiUty of these closed shells is reflected in the relatively small chemical reactivity of these elements. The predicted (in parentheses) closed electronic stmctures occur at Z = 118 and Z = 168. 

Maria Goeppert-Mayer (La Jolla) and J. H. D. Jensen (Heidelberg) discoveries concerning nuclear shell structure. 

Before concluding this section, it must be pointed out that there are other fields of application of the SRH formalism. Thus, Karwowski et al. have used it in the study of the statistical theory of spectra [30,38]. Also, the techniques used in developing the p-SRH algorithms have proven to be very useful in other areas such as the nuclear shell theory [39,40]. 

Flowers, B. H. The nuclear shell model. Progress in nuclear Physics 2,... 

Pryce, M. H. L. Nuclear shell structure. Reports on Progress in Phy-... 

Fig. 2.1. Approximate potentials for the nuclear shell model. The solid curve represents the 3-dimensional harmonic oscillator potential, the dashed curve the infinite square well and the dot-dashed curve a more nearly realistic Woods-Saxon potential, V(r) = — V0/[l + exp (r — R)/a ] (Woods Saxon 1954). Adapted from Cowley (1995).

Dalton, B. J. (1971), Nonrigid Molecule Effects on the Rovibronic Energy Levels and Spectra of Phosphorous Pentafluoride, J. Chem. Phys. 54,4745. de Shalit, A., and Talmi, 1. (1963), Nuclear Shell Theory, Academic Press, N.Y. 

Wiles, D. R., B. W. Smith, R. Horsley and H. G. Thode Fission Yields of the Stable and Longlived Isotopes of Caesium, Rubidium, and Strontium, and Nuclear Shell Structure. Canad. J. Physics 31, 419 (1953). 

The occurrence of nuclides in nature reflects relative stability. In general, nuclides whose mass numbers are multiples of 4 are exceptionally stable, because a group of two protons and two neutrons forms a closed shell (nuclear shells are to some extent analogous to the electron shells discussed in chapter 1). 

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

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.

Some have taken the viewpoint that, without the special stability associated with nuclear shell structure, elements as light as Z = 106-108 would have negligibly short half-lives. The mere existence of these nuclei with millisecond half-lives is said to be a demonstration that we have already made superheavy nuclei, according to this view. The shell stabilization of these nuclei, which are deformed, is due to the special stability of the N = 162 configuration in deformed nuclei. (The traditional superheavy nuclei with Z 114, N = 184 were calculated to have spherical shapes.)... 

The correlation of nuclear stability with special numbers of nucleons is reminiscent of the correlation of chemical stability with special numbers of electrons— the octet rule discussed in Section 6.12. In fact, a shell model of nuclear structure has been proposed, analogous to the shell model of electronic structure. The magic numbers of nucleons correspond to filled nuclear-shell configurations, although the details are relatively complex. 

Four decades ago, Bell [3] introduced a particle-hole conjugation operator CB into nuclear shell theory. Its operator algebra is essentially isomorphic to that of Cq (for example, CB is unitary), the filled Dirac sea now corresponding to systems with half-filled shells. This was later extended to other areas of physics. For example,... 

R. D. Lawson, "Theory of Nuclear Shell Model", Clarendon Press,... 

Basing on the nuclear shell-model and concentrating on the monopole,pairing and quadrupole corrections originating from the nucleon-nucleon force,both the appearance of low-lying 0+ intruder states near major closed shell (Z=50, 82)and sub-shell regions (Z=40,64) can be described.Moreover,a number of new facets related to the study of intruder states are presented. 

STa63] de Shalit A and Talmi 1 1963 Nuclear shell theory (Academic Press, New York and London). 

Element abundance data were useful not only in astrophysics and cosmology but also in the attempts to understand the structure of the atomic nucleus. [74] As mentioned, this line of reasoning was adopted by Harkins as early as 1917, of course based on a highly inadequate picture of the nucleus. It was only after 1932, with the discovery of the neutron as a nuclear component, that it was realized that not only is the atomic mass number related to isotopic abundance, but so are the proton and neutron numbers individually. Cosmochemical data played an important part in the development of the shell model, first proposed by Walter Elsasser and Kurt Guggenheimer in 1933-34 but only turned into a precise quantitative theory in the late 1940s. [75] Guggenheimer, a physical chemist, used isotopic abundance data as evidence of closed nuclear shells with nucleon numbers 50 and 82. 

The magic numbers were successfully explained by the nuclear shell model [5,6], and an extrapolation into unknown regions was reasonable. The numbers 126 for the protons and 184 for the neutrons were predicted to be the next shell closures. Instead of 126 for the protons also 114 or 120 were calculated as closed shells. The term superheavy elements, SHEs, was coined for these elements, see also Chapter 8. 

In 1955, J.A. Wheeler [1] concluded from a courageous extrapolation of nuclear masses and decay half-lives the existence of nuclei twice as heavy as the heaviest known nuclei he called them superheavy nuclei. Two years later, G. Scharff-Goldhaber [2] mentioned in a discussion of the nuclear shell model, that beyond the well established proton shell at Z=82, lead, the next proton shell should be completed at Z=126 in analogy to the known TV = 126 neutron shell. Together with a new A=184 shell, this shell closure should lead to local region of relative stability. These early speculations remained without impact on contemporary research, however. 

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