A New Look at a Nonrelativistic Shell Model: Study of the Mirror Nuclei 17O and 17F in the Symmetries of NCQM


Abdelmadjid Maireche

In present work, the 3-dimensional modified Schrödinger equation is analytically solved for nuclei 17O and 17F, which can be modeled as a doubly magic isotope  and , with one additional nucleon (valence) in the  level under modified quadratic Hellmann potential in the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The new energy eigenvalues and the corresponding modified Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. It is found that the perturbative solutions of the discrete spectrum can be expressed by the Gamma function, the discreet subatomic quantum numbers  and the potential parameters ( ), in addition to the noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of the modified quadratic Hellmann potential changed to become equals to the value  instead of the initial values  in ordinary QM. Our results are in good agreement with the already existing literature in NCQM. 


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