Shells in Nuclei
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Independence of the motion of nucleons in the nucleus and the self-consistent potential. Lying at the basis of the shell model of the nucleus is the assumption that the nucleons in the nucleus move almost independently of each other, despite the existence of the strong interaction between free nucleons. The interaction of nucleons with each other reduces in the shell model to the interaction of the individual nucleons with a self-consistent field. Generally speaking, each nucleon moves in the field created by the other nucleons. In the shell model, it is assumed that this field is the same for all the nucleons. The potential of this self-consistent field is assumed to be static and spherically symmetric. Because of the short-range character of the nuclear forces, the potential of the self-consistent field varies in almost the same way as the nuclear density: it is constant inside the nucleus and goes to zero outside the nucleus. As a result, the one-particle wave functions depend on the distance from the centre of the nucleus and go to zero outside the nucleus.
KeywordsIrreducible Representation Orbital Angular Momentum Permutation Group Total Angular Momentum Young Tableau
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