Download Experimental Nuclear Physics - Volume 2 by Emilio Segre PDF

By Emilio Segre

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All such functions may be expressed as linear combinations of an independent set of functions. Even if there are several such independent functions they do not correspond to independent states of the system. They are all needed for construction of eigenstates which are fully antisymmetric in space, spin and isospin variables of the nucleons. An eigenfunction fully symmetric in space coordinates should be simply multiplied by a fully antisymmetric state of spin and isospin variables. In other cases, linear combinations should be formed of spatial eigenfunctions which transform among themselves under permutations multiplied by spin-isospin states with the dual (“opposite”) symmetry.

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 new version of the model raised also a new problem - the origin of the strong spin-orbit interaction.

It includes a linear term in T which is sometimes called the “Wigner term”. Such a term is indeed necessary for reproducing nuclear binding energies. These results are very general and completely independent of any assumption on the spatial parts of the eigenfunctions. Other observables of the lowest states in this approximation, like nuclear magnetic moments calculated by Margenau and Wigner (1940), can also be evaluated. m. m. Taking the expectation value of the component of the µ operator in the state with and inserting the values of S and Y mentioned above, we obtain the following values for the magnetic moment of the spin The spin S should be coupled to the total orbital angular momentum L, which has a definite value in any eigenstate of SU(4) Hamiltonians, to form the total spin J.

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