Ground State Structure of Helium and Phosphorus Isotopes using the Radial Wave Functions of Harmonic-Oscillator and Hulthen Potentials

Ameen M. Hameed; Arkan R. Ridha

doi:10.24996/ijs.2023.64.5.13

Authors

Ameen M. Hameed Department of Physics, College of Science, University of Baghdad, Baghdad-Iraq
Arkan R. Ridha Department of Physics, College of Science, University of Baghdad, Baghdad-Iraq https://orcid.org/0000-0002-8968-1089

DOI:

https://doi.org/10.24996/ijs.2023.64.5.13

Keywords:

exotic nuclei, size radii, density distributions, electron scattering charge form factors, shell model, Helium isotopes, phosphorate isotopes, Hulthen potential

Abstract

The ground state density distributions and electron scattering Coulomb form factors of Helium (^4,6,8He) and Phosphorate (^27,31P) isotopes are investigated in the framework of nuclear shell model. For stable (⁴He) and (³¹P) nuclei, the core and valence parts are studied through Harmonic-oscillator (HO) and Hulthen potentials. Correspondingly, for exotic (^6,8He) and (²⁷P) nuclei, the HO potential is applied to the core parts only, while the Hulthen potential is applied to valence parts. The parameters for HO and Hulthen are chosen to reproduce the available experimental size radii for all nuclei under study. Finally, the CO component of electron scattering charge form factors are also investigated. Unfortunately, there is no analytic solution to the Hulthen potential except for the states which are harnessed to the current calculation.