Advances in Nuclear Physics: Volume 7

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As much by chance as by design, the present volume comes closer to having a single theme than any of our earlier volumes. That theme is the properties of nuclear strength functions or, alternatively, the problem of line spreading. The line spreading or strength function concepts are essential for the nucleus because of its many degrees of freedom. The description of the nucleus is approached by using model wave functions-for example, the shell model or the collective model-in which one has truncated the number of degrees of freedom. The question then is how closely do the model wave functions correspond to the actual nuclear wave functions which enjoy all the degrees of freedom of the nuclear Hamiltonian? More precisely, one views the model wave functions as vectors in a Hilbert space and one views the actual wave functions as vectors spanning another, larger Hilbert space. Then the question is: how is a single-model wave function (or vector) spread among the vectors corresponding to the actual wave functions? As an example we consider a model state which is a shell-model wave function with a single nucleon added to a closed shell. Such a model state is called a single-particle wave function. At the energy of the single-particle waVe function one of the actual nuclear wave functions may resemble the single-particle wave function closely.