A study of confined quantum systems using the Woods-Saxon potential

Abstract

We propose the Woods-Saxon (WS) potential to simulate spatial confinement. The great advantage of our methodology is that it enables the study of a wide range of systems and confinement regimes by varying two parameters in the model potential. To test the methodology we have studied the confined harmonic oscillator in two different regimes: when the confinement potential exhibits a sudden jump; and when the confinement is described by a smooth function. We have also applied the present procedure to a realistic problem, a confined quantum dot-atom. The numerical calculation is performed with the equally spaced discrete variable representation (DVR). Our results are in close agreement with those available in the literature, and we believe our method to be a good alternative for studying confined quantum systems.

Study of Electromagnetic Multipole Transition Half-Lives of One-Hole 15O–15N and One-Particle 17O–17F Mirror Nuclei

“…The transition probability is decreased drastically by increasing the multi-polarity. Therefore the most probable transition is the lowest allowed multi-polarity by the angular momentum and parity selection rules [4]. For a λ -pole transition between nuclear states of angular momenta J i and J f , the angular momentum selection rule is |J f − J i | ≤ λ ≤ |J f + J i |, and the parity selection rule is [2] …”

Effective Mass and Pseudoscalar Interaction in the Dirac Equation with Woods–Saxon Potential

“…In heavy-ion physics it permits to model the internuclear potential in the coupled-channels calculations [44]. It has been also applied in the study of spectra of rotating nuclei [45] and confined quantum systems [46]. We also mention that the WSP has the advantages of being exactly solvable with the one-dimensional Dirac equation which renders the study of bound states and scattering processes more tractable.…”

The Relativistic Transmission and Reflection Coefficients for Woods-Saxon Potential

“…The Woods-Saxon potential (WSP for short), which is normally considered as a mean field one, lies within this category. It has been used in the study of nuclei outside A = 110−210 [1], high spin states in 146 Gd [2], parametrization of the n-208 Pb mean field [3], two-centre formalism [4], shell model calculations [5], spectra of rotating nuclei [6], confined quantum systems [7], collective models [8] and the wobbling excitations [10]. The solution of the Klein-Gordon equation under the WSP has been obtained in [11].…”