The harmonic oscillator approximation to the density matrix

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Abstract
The density matrix expansion for a system of nucleons moving in an isotropic harmonic oscillator potential is derived. This series is assumed to be a good approximation for the angle averaged density matrix of spherical nuclei, and is summed under a certain approximation. The form proposed by Campi and Bouyssy is obtained in our model as a special case. Other alternative forms are proposed and numerical comparisons are made using the Skyrme-III force.

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