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

• Published in: European physical journal plus Vol. 135; no. 4; p. 372
• Main Authors: Romaniega, C., Gadella, M., Id Betan, R. M., Nieto, L. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020; Springer Nature B.V
• Subjects: Applied and Technical Physics; Approximation; Atomic; Complex Systems; Condensed Matter Physics; Contact potentials; Energy; Exact solutions; Hamiltonian functions; Lead isotopes; Mathematical and Computational Physics; Molecular; Nuclear models; Optical and Plasma Physics; Physics; Physics and Astronomy; Quantum physics; Regular Article; Relativistic particles; Theoretical; Wave functions
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-020-00388-7

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.