  In this paper, one uses a damped potential to present a description of the
running coupling constant of QCD in the confinement phase. Based on a
phenomenological perspective for the Debye screening length, one compares the
running coupling obtained here with both the Brodsky-de T\'eramond-Deur and the
Richardson approaches. The results seem to indicate the model introduced here
corroborate the Richardson approach. Moreover, the Debye screening mass in the
confinement phase depends on a small parameter, which tends to vanish in the
non-confinement phase of QCD.
