English

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

Nuclear Theory 2021-05-07 v2 Quantum Physics

Abstract

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial δ\delta-δ\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^{132}Sn and 208^{208}Pb with an extra neutron.

Keywords

Cite

@article{arxiv.1911.10050,
  title  = {An approximation to the Woods-Saxon potential based on a contact interaction},
  author = {C. Romaniega and M. Gadella and R. M. Id Betan and L. M. Nieto},
  journal= {arXiv preprint arXiv:1911.10050},
  year   = {2021}
}

Comments

19 pages, 9 figures, 4 tables

R2 v1 2026-06-23T12:24:33.078Z