The transmission probability of charged particle reactions in a stellar plasma is examined by considering the effective potential between the interacting charges as having an exponential factor in the Coulomb term arising out of the spherical distribution of electrons with its uniform background of positive charges (Debye-Hückel electrolyte). The expression for the ratio of this transmission probability to that due to pure Coulomb field, called the enhancement factor, is then obtained. Thermonuclear reactions of astrophysical interest such as¹²C(α, γ)¹⁶O and¹⁶O(α, γ)²⁰ Ne are then considered. Our enhancement factor in the¹²C(α, γ)¹⁶O reaction rate is found to agree reasonably well with those calculated from the expression given by Alastuey and Jancovici.