Mirror Nuclei of 17O and 17F in Relativistic and Non- Relativistic Shell Model

TL;DR

This study compares the energy levels of mirror nuclei 17O and 17F using relativistic and non-relativistic shell models, employing the Hellmann potential and Nikiforov-Uvarov method, with results aligning well with experimental data.

Contribution

It introduces a combined relativistic and non-relativistic shell model approach using the Hellmann potential and Nikiforov-Uvarov method for mirror nuclei analysis.

Findings

Calculated energy levels agree with experimental data.

Model effectively describes mirror nuclei 17O and 17F.

Applicable to similar nuclear systems.

Abstract

We have investigated energy levels mirror nuclei of the 17O and 17F in relativistic and non-relativistic shell model. The nuclei 17O and 17F can be modeled as a doubly-magic 17O=n+(N=Z=8) and 17F=p+(N=Z=8), with one additional nucleon (valence) in the ld5/2 level. 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 non-relativistic, respectively. Finally, we have computed the binding and excited energy levels for mirror nuclei of 17O and 17F and compare with other works. Our results were in agreement with experimental values and hence this model could be applied for similar nuclei.