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

C. Romaniega; M. Gadella; R. M. Id Betan; L. M. Nieto

doi:10.1140/epjp/s13360-020-00388-7

EPJ

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

C. Romaniega¹, M. Gadella¹^*, R. M. Id Betan²^,3^,4 and L. M. Nieto¹

¹ Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
² Instituto de Física Rosario (CONICET-UNR), Bv. 27 de Febrero 210 bis, S2000EZP, Rosario, Argentina
³ Facultad de Ciencias Exactas, Ingeniería y Agrimensura (UNR), Av. Pellegrini 250, S2000BTP, Rosario, Argentina
⁴ Instituto de Estudios Nucleares y Radiaciones Ionizantes (UNR), Riobamba y Berutti, S2000EKA, Rosario, Argentina

Received: 9 March 2020
Accepted: 7 April 2020
Published online: 27 April 2020

Abstract

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.

12 Internat. Congress of the Balkan Physical Union
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EPJ

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

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