An approximation to the Woods-Saxon potential based on a contact interaction

Abstract

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-${\delta }^{\prime }$ contact interaction at the well edge. This contact potential is defined by appropriate matching conditions for the radial functions, thereby fixing a self adjoint extension of the non-singular Hamiltonian. Since this model admits exact solutions for the wave function, we are able to characterize and calculate the number of bound states. We also extend some well-known properties of certain spherically symmetric potentials and describe the resonances, defined as unstable quantum states. Based on the Woods-Saxon potential, this configuration is implemented as a first approximation for a mean-field nuclear model. The results derived are tested with experimental and numerical data in the double magic nuclei ${}^{132}$Sn and ${}^{208}$Pb with an extra neutron.

arXiv comment19 pages, 9 figures, 4 tables

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Cited by in corpus (3)

• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Simple bounds with best possible accuracy for ratios of modified Bessel functions
• Casimir self-energy of a δ-δ' sphere