Analytical determination of the non-relativistic quantum mechanical properties of near doubly magic nuclei

Abstract

A non-relativistic analytical study of some atomic nuclei near doubly-magic nuclei, namely 41Ca and 41Sc.
These nuclei under study are considered to have a closed core with a single nucleon orbiting the core, thus
agreeing perfectly with the nuclear shell model. The superposition of Hulthen potential plus Spin – orbit
interaction plus adjusted Coulomb is used as the nucleon – nucleon potential for this study. This superposition
forms a suitable potential model useful in describing the net force mediating the interactions between
nucleons in a nuclear system. The combined potentials effectively represent three basic interactions within
the nucleus. By employing the Nikiforov – Uvarov method of solving the Schrodinger equation, we have
calculated the energy eigenvalues and the eigen function of these nuclei. Also, the expectation values for radius,
kinetic energy and momentum of each nucleus under study are also evaluated analytically. The results
obtained are in agreement with experiment. As such, the constructed potential model used in the present
work is recommended for similar nuclei.

Key words: Schrödinger equation, Hulthen potential, spin-orbit interaction, Coulomb potential, energy
eigenvalues eigenfunction, expectation values.