An approximation to the Woods–Saxon potential based on a contact interaction - Romaniega, C.; Gadella, M.; Id Betan, R. M.; Nieto, L. M. (European physical journal plus, 2020)
We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial δ - δ ′ 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.