Mirror Nuclei of¹⁷O and¹⁷F in Relativistic and Nonrelativistic Shell Model

Abstract

We have investigated energy levels mirror nuclei of the 17 O and 17 F in relativistic and nonrelativistic shell model. The nuclei 17 O and 17 F can be modeled as a doubly-magic 17 O=n+(N=Z=8) and 17 F=p+(N=Z=8), with one additional nucleon (valence) in the ld5/2 level. Then we have selected the quadratic Hellmann potential for interaction between core and single nucleon. Using Parametric Nikiforov-Uvarov method, we have calculated the energy levels and wave function in Dirac and Schrodinger equations for relativistic and non-relativistic, respectively. Finally, we have computed the binding and excited energy levels for mirror nuclei of 17 O and 17 F and compare with other works. Our results were in agreement with experimental values and hence this model could be applied for similar nuclei.

Static Properties of Neutron-Rich and Proton-Rich Isotopes

“…(3) By applying parametric Nikiforov-Uvarov method [22,[25][26][27][28] the energy Eigen-value formula can be written as (4) The ground state and excited state energy of 9 Be, 9 B, 13 C, 13 N, 17 O, 17 F, 21 Ne, and 21 Na isotopes are compared with experimental results in Table 1.…”

“…Stable isotopes of neon are produced in stars. Neon has three stable isotopes, 20 Ne, 21 Ne and 22 Ne [21].…”

“…The 9 Be, 9 B, 13 C, 13 N, 17 O, 17 F, 21 Ne, and 21 Na isotopes can be modeled as a doubly magic (N=Z) with one additional nucleon out of core [22]. So, these isotopes can be investigated such as single particle in shell model.…”

Diatomic molecules and fermionic particles with improved Hellmann-generalized Morse potential through the solutions of the deformed Klein-Gordon, Dirac and Schrödinger equations in extended relativistic quantum mechanics and extended nonrelativistic quantum mechanics symmetries

“…In 2007, Koncak et al [11] studied the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method and obtained the bound state energy eigenvalues. This potential has many important applications; we mention one of the solidstate physics [12][13][14], alkali hydride molecules [15], innershell ionization problem [16], nuclear physics [17], among other applications. Furthermore, it was studied in both relativistic and non-relativistic quantum mechanics (see, e.g., [17][18][19][20]).…”

“…This potential has many important applications; we mention one of the solidstate physics [12][13][14], alkali hydride molecules [15], innershell ionization problem [16], nuclear physics [17], among other applications. Furthermore, it was studied in both relativistic and non-relativistic quantum mechanics (see, e.g., [17][18][19][20]).…”