Models nuclear shell

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

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).

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. 

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. 

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. 

Effective Hamiltonians and effective operators are used to provide a theoretical justification and, when necessary, corrections to the semi-empirical Hamiltonians and operators of many fields. In such applications, Hq may, but does not necessarily, correspond to a well defined model. For example. Freed and co-workers utilize ab initio DPT and QDPT calculations to study some semi-empirical theories of chemical bonding [27-29] and the Slater-Condon parameters of atomic physics [30]. Lindgren and his school employ a special case of DPT to analyze atomic hyperfine interaction model operators [31]. Ellis and Osnes [32] review the extensive body of work on the derivation of the nuclear shell model. Applications to other problems of nuclear physics, to solid state, and to statistical physics are given in reviews by Brandow [33, 34], while... 

A nuclear shell model is suggested by Mayer, Haxd, Jensen and Suess. 

R.D. Lawson, Theory of the Nuclear Shell Model (Clarendon Press, Oxford, 1980) p. 208. 

M.W. Kirson, in Nuclear Shell Models, eds. M. Vallieres and B.H. Wildenthal (World Scientific, Singapore, 1985)... 

The nuclear shell model is treated in detail by Lane and Elliott in vol. XXXIX of this Encyclopedia. See also R. J. Blin-Stoyle Rev. Mod. Phys. 28, 75 (1956) for a recent discussion of nuclear models. 

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