Thermal Properties and Magnetic Susceptibility of Hellmann Potential in Aharonov–Bohm (AB) Flux and Magnetic Fields at Zero and Finite Temperatures

TLDR: In this article, the effect of external magnetic and AB flux fields on the energy spectra of the system is examined in detail, and it is found that the AB field performs better than the magnetic field in its ability to remove degeneracy.

Abstract: In this research work, the Hellmann potential is studied in the presence of external magnetic and AB flux fields within the framework of Schrodinger equation using the Nikiforov–Uvarov functional analysis method. The energy equation and wave function of the system are obtained in closed form. The effect of the fields on the energy spectra of the system is examined in detail. It is found that the AB field performs better than the magnetic field in its ability to remove degeneracy. Furthermore, the magnetization and magnetic susceptibility of the system were discussed at zero and finite temperatures. We evaluate the partition function and use it to evaluate other thermodynamic properties of the system such as magnetic susceptibility, $$ \chi_{\text{m}} \left( {\vec{B},\varPhi_{\text{AB}} ,\beta } \right) $$ , Helmholtz free energy $$ F\left( {\vec{B},\varPhi_{\text{AB}} ,\beta } \right) $$ , entropy $$ S\left( {\vec{B},\varPhi_{\text{AB}} ,\beta } \right) $$ , internal energy $$ U\left( {\vec{B},\varPhi_{\text{AB}} ,\beta } \right) $$ and specific heat $$ C_{v} \left( {\vec{B},\varPhi_{\text{AB}} ,\beta } \right) $$ . A comparative analysis of the magnetic susceptibility of the system at zero and finite temperatures shows a similarity in the behavior of the system. A straightforward extension of our results to three dimensions shows that the present result is consistent with what is obtained in the literature.