  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, both
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 a neutral 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.
