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

ID BETAN, R. M.; ROMANIEGA, C.; NIETO, L. M.; GADELLA, M.

The European Physical Journal Plus

The European Phys. J. Plus

Año: 2020 vol. 135 p. 1 - 27

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 theWoods?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 132Sn and 208Pb with an extra neutron.