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

• Published in: arXiv.org
• Main Authors: Romaniega, C, Gadella, M, R M Id Betan, Nieto, L M
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 07.04.2020
• Subjects: Approximation; Contact potentials; Energy levels; Lead; Nuclear models; Nuclear spin; Physics - Nuclear Theory; Physics - Quantum Physics; Spin-orbit interactions; Tin; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1911.10050

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial \(\delta\)-\(\delta'\) 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.