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In this work, the 24Mg nucleus is considered in the cluster model by solvingthe Schrodinger and Klein- Gordon equations from the Nikiforov- Uvarov (NU)method. A local potential is used for these two equations that is compatiblewith the Hafstad-Teller potential. By substituting this potential in theSchrodinger and Klein- Gordon equations, the energy levels and wave functionsare obtained from NU method. We obtain a first order equation in terms of E forthe Schrodinger equation and a fourth-order equation in terms of ER for theKlein-Gordon equation. Therefore, the obtained equation from the Klein-Gordonequation has both the real solutions and imaginary solutions that we consideronly the real solutions for this equation. For more accuracy, the spin-orbitand tensor potentials are added to the central potential as the perturbed termsand the first-order correction value of the energy levels is calculated. Theseenergy levels are used for 24Mg nucleus and the good results are obtained inagreement with the experimental data. Of course, one can see that thecalculated results from the Schrodinger and Klein-Gordon equations, i.e.non-relativistic and relativistic respectively, are nearly the same. By usingthe Coulomb repulsive potential, it is shown that the structure of the groundstate and the first excited state of this nucleus is as octahedral and theconfiguration of the alpha particles for the second excited state is aspentahedral, i.e. as 12C +12C . Finally, we obtain the critical point for thecalculation of maximum energy of this nucleus in the cluster model.

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