Energy Eigenvalues for a Spherical Well with an Exponentially Diffuse Boundary

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Abstract
The discrete energy eigenvalues of a spherical well with an exponentially diffuse boundary are obtained to a good approximation for a range of well parameters of interest in nuclear physics. The method used involves replacing the centrifugal energy in the exponentially diffuse region by an approximate expression which leads to analytic solutions of the wave equation. The matching of the internal and external wave functions is then accomplished by the use of specially prepared graphs and tables. The eigenvalues and eigenfunctions are thought to be of interest in connection with studies of the independent particle model of the nucleus.

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