By J.W. Negele, Erich W. Vogt
This quantity includes significant articles, one delivering a historic retrospective of 1 of the good triumphs of nuclear physics within the 20th century and the opposite offering a didactic creation to 1 of the quantitative instruments for realizing powerful interactions within the twenty-first century. this article is appropriate just for complex graduate classes in nuclear physics.
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Additional info for Advances in Nuclear Physics, Volume 27 (Advances in the Physics of Particles and Nuclei)
Matrix elements of the two-body interaction were calculated between shell model wave functions. Disagreement with experiment was often blamed on effects due to admixtures of higher configurations. The re-emergence of the shell model raised again old arguments against the independent nucleon picture of the nucleus. The question asked was whether such a picture could hold in view of the short-range strong interaction between nucleons. At that time it was not known how singular this interaction really is.
The submatrices with given J of all rotations form an irreducible representation of the rotation group O(3). The eigenstates which define a given submatrix of the Hamiltonian form a basis of the given irreducible representation. In general, eigenstates of a Hamiltonian with a given symmetry belong to certain bases of irreducible representations of the symmetry group. The labels of these irreducible representations can serve as quantum numbers which characterize eigenstates, like J in the example described above.
Fifty years ago, this solution was not available, nor is it now. Thus, these predictions of the shell model, as unexpected and strikingly successful as they turned out to be, are only qualitative. Quantitative results were expected for calculations of the mutual interaction (“residual interaction”) between valence nucleons. All states which several valence nucleons can form, have the same energy in the central potential well. This degeneracy may be removed by considering the mutual interaction of the valence nucleons.
Advances in Nuclear Physics, Volume 27 (Advances in the Physics of Particles and Nuclei) by J.W. Negele, Erich W. Vogt