Quantum mechanical nuclear-shell model

However, the hquid drop model is powerless to explain the more detailed features within the binding energy per nucleon curve, such as the various discontinuities that are superimposed on it, reflecting the enhanced stabihties of nuclei of He, C, 0, Ne, and Mg. To explain these more subtle features, we need to consider the quantum mechanical nuclear-sheU model, which bears a number of similarities to the electron-shell model as described in chapters 7 and 9. 

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. 

The mechanisms and data of the fission process have been reviewed recently by Leachman (70). Several different approaches have been used in an effort to explain the asymmetry of the fission process as well as other fission parameters. These approaches include developments of the liquid drop model (50, 51,102), calculations based on dependence of fission barrier penetration on asymmetry (34), the effect of nuclear shells (52, 79, 81), the determinations of the fission mode by level population of the fragments (18, 33, 84), and finally the consideration of quantum states of the fission nucleus at the saddle point (15, 108). All these approaches require a mass formula whereby the masses of the fission fragments far removed from stability may be determined. The lack of an adequate mass formula has hindered the development of a satisfactory theory of fission. The fission process is highly complex and it is not surprising that the present theories fall short of a full explanation. 

The a-decay theory was the first successful (quantum mechanical) explanation of radioactive decay, and as such played a major role in further developm t of nuclear theories and models. Although its simplicity causes it to fail for nonspherical nuclei as well as those near closed shells, such effects can be tak into account in more advanced Nilsson-type calculations. 

For the time being, however, the microscopic theoretical framework for modeling nuclear structure and reactions is mainly quantum mechanics. The most common models are the shell model and its truncated approximations (e.g., IBM), the mean-field theories (like the... 

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