A comparative interpretation of the thermodynamic functions of a relativistic bound state problem proposed with an attractive or a repulsive surface effect

A generalized symmetric Woods-Saxon potential (GSWSP) energy well has a significant importance not only in nuclear physics, but also in atomic and molecular physics. A GSWSP energy well takes the surface effects (describing, e.g., repulsive interaction at the nucleus edge in nuclear physics) into account in addition to the volume effect. These effects can be, in general, either repulsive or attractive. In this paper, the recently obtained bound state solution of the Klein-Gordon equation with vector and scalar GSWSP energy in the spin symmetry limit is used to calculate pion's energy spectra in attractive and repulsive cases via various potential parameters. Then, the spectra are employed to find the thermodynamic functions such as Helmholtz free energy, entropy, internal energy, and specific heat. These functions in the attractive and repulsive cases are compared comprehensively. Finally, the role of the shape parameters on the thermodynamic functions in repulsive and attractive cases, respectively, is analyzed.