The spectral problem of a mean-field nuclear model based on a contact interaction
Year: 2019
Type: preprint
Abstract: We study a simplified mean-field potential consisting of a finite radial square well plus a radial $\delta$-$\delta'$ contact potential in order to describe single neutron energy levels. This is a limiting case of the Woods-Saxon potential, where the Dirac-$\delta$ takes account of the nuclear spin-orbit interaction. This contact potential is defined by appropriate matching conditions for the wave functions at the well edge, 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. The results obtained are tested with experimental and numerical data in the double magic nuclei $^{132}$Sn and $^{208}$Pb with an extra neutron. The presence of resonances, defined as unstable quantum states, is also considered.
Source: arXiv (Cornell University)
Authors: C. Romaniega, M. Gadella, R. Id Betán, L. M. Nieto
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2989714673