Nucleus collective model

Nuclei with certain even numbers of protons and of neutrons are the most stable. One model of the nucleus is the collective model, which pictures nucleons as occupying quantized energy levels and interacting with one another strongly. 

The other consequence is that Np Nn systematics offer a way to greatly simplify collective model calculations. Normally, such calculations are parameterized for each nucleus individually or for a set of isotopes. The Np Nn curves suggest that an entire region can be treated as a unit in which the collective parameters are taken as smooth functions of Np Nn only. Moreover, Fig. 3 suggests that the same set of parameters... 

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. 

Among collective models which have been developed for special purposes is the alpha particle model. If it is assumed that the four-structure already apparent in the supermultiplet theory of Wigner has some permanence in an actual nucleus, the methods of molecular physics may be applied to deduce a level sequence (Wheeler ). The S5nnmetry of the system imposes special restrictions on the level spins of the lower excited states. The energies of these states are obtained from a decomposition of the motion into rotation and vibration. The treatment is especially suitable for nuclei of mass number An, but it is not restricted to these 3 and the detailed application of the model to a number of nuclei is discussed in references [7] and [itf]. 

Inglis [10] has also discussed the possible application of a collective model of the alpha particle type to the Li nucleus, particularly with respect to the broad state at 6.56 MeV which finds no explanation in the LS or // schemes. 

This model incorporates features of both the shell and collective models of the nucleus, and involves the interaction between paired protons (p) and neutrons (n), each favoring Zero spin... 

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. 

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. 

Some recent developments of the model are reviewed (1) Collective bands of the y-soft nucleus Te are compared with experiment and with the 0(6) version of the IBM-2 model. (2)... 

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