  The exact analytical solution of the Schr\"odinger equation for a generalized
symmetrical Woods-Saxon potential are examined for a nucleon in Fluorine 17
nucleus for bound and quasi-bound states in one dimension. The wave functions
imply that the nucleon is completely confined within the nucleus, i.e., no
decay probability for bound states, while tunneling probabilities arise for the
quasi-bound state. We have calculated the temperature dependent Helmholtz free
energies, the internal energies, the entropies and the specific heat capacities
of the system. It is shown that, when the quasi-bound state is included, the
internal energy and entropy increase, while the Helmholtz energy decreases at
high temperatures. Very high excitation temperatures imply that the nucleus
does not tend to release a nucleon. The calculated quasi bound state energy is
in reasonable agreement with the experimental data on the cumulative fission
energy issued by IAEA.
