Mirror Nuclei of17O and17F in Relativistic and Nonrelativistic Shell Model

M Mousavi,M R Shojaei

doi:10.1155/2017/5841701

Abstract

We have investigated energy levels mirror nuclei of the17O and17F in relativistic and nonrelativistic shell model. The nuclei17O and17F can be modeled as a doubly magic17O = n + (N = Z = 8) and17F = p + (N = Z = 8), with one additional nucleon (valence) in the ld5/2level. Then we have selected the quadratic Hellmann potential for interaction between core and single nucleon. Using Parametric Nikiforov-Uvarov method, we have calculated the energy levels and wave function in Dirac and Schrodinger equations for relativistic and nonrelativistic, respectively. Finally, we have computed the binding and excited energy levels for mirror nuclei of17O and17F and compare with other works. Our results were in agreement with experimental values and hence this model could be applied for similar nuclei.

Highlights

Special interest resides in the study of masses and sizes for a given element along isotopic chains
Their determination is increasingly difficult as one approaches the neutron drip-line; as of today, the heaviest element with available data on all existing bound isotopes is oxygen (Z = 8) [1]
The properties of single particle energies and states with a strong quasi-particle content along an isotopic chain are expected to be strongly influenced by the nuclear spin-orbit force [3]

Summary

Introduction

Special interest resides in the study of masses and sizes for a given element along isotopic chains. The Dirac equation, which describes the motion of a spin-1/2 particle, has been used in solving many problems of nuclear and high-energy physics. In this work we use relativistic and nonrelativistic shell model for calculation of the energy levels for 17O and 17F isotope. Since these isotopes have one nucleon out of the core, Dirac and Schrodinger equations are utilized to investigation them in relativistic and nonrelativistic shell model, respectively. These isotopes could be considered as a single particle.

Energy Spectrum in Relativistic Shell Model

Energy Spectrum in Nonrelativistic Shell Model

Result and Discussion