Investigation of the energy levels and the structure of the different states of the 24Mg nucleus

TL;DR

This paper models the energy levels and structure of the 24Mg nucleus using cluster models and solving Schrödinger and Klein-Gordon equations with the NU method, achieving results consistent with experimental data and revealing geometric configurations.

Contribution

It introduces a combined non-relativistic and relativistic approach to analyze 24Mg nucleus structure using NU method with a local potential, including spin-orbit and tensor corrections.

Findings

Energy levels agree with experimental data.

Ground and first excited states have octahedral structure.

Second excited state configuration as pentahedral (12C+12C).

Abstract

In this work, the 24Mg nucleus is considered in the cluster model by solving the Schrodinger and Klein- Gordon equations from the Nikiforov- Uvarov (NU) method. A local potential is used for these two equations that is compatible with the Hafstad-Teller potential. By substituting this potential in the Schrodinger and Klein- Gordon equations, the energy levels and wave functions are obtained from NU method. We obtain a first order equation in terms of E for the Schrodinger equation and a fourth-order equation in terms of ER for the Klein-Gordon equation. Therefore, the obtained equation from the Klein-Gordon equation has both the real solutions and imaginary solutions that we consider only the real solutions for this equation. For more accuracy, the spin-orbit and tensor potentials are added to the central potential as the perturbed terms and the first-order correction value of the energy levels is calculated. These energy levels are used for 24Mg nucleus and the good results are obtained in agreement with the experimental data. Of course, one can see that the calculated results from the Schrodinger and Klein-Gordon equations, i.e. non-relativistic and relativistic respectively, are nearly the same. By using the Coulomb repulsive potential, it is shown that the structure of the ground state and the first excited state of this nucleus is as octahedral and the configuration of the alpha particles for the second excited state is as pentahedral, i.e. as 12C +12C . Finally, we obtain the critical point for the calculation of maximum energy of this nucleus in the cluster model.