Abstract
In this paper, we give a definition of the Fermi function, or the so called Woods-Saxon potential, a well-known potential in nuclear physics; then, we give a few of its applications as examples. Some important integrals, which involve this function, are computed discussing the integrability and convergence of these integrals. Following, we derive formulae that encounter the above mentioned function to get nuclear and generalized moments; the radial Fourier transformation is also exposed. Some related applications are then given that use such important integrals; in particular, we give the computation in con-junction with the problem of getting the optical-model potential for heavy ion interactions at intermediate energies. Finally, we conclude with important remarks to do with the evolution of the subject.