  Screened potential, modified by non standard electron cloud distributions
responsible for the shielding effect on fusion of reacting nuclei in
astrophysical plasmas, is derived. The case of clouds with depleted tails in
space coordinates is discussed. The modified screened potential is obtained
both from statistical mechanics arguments based on fluctuations of the inverse
of the Debye-Huckel radius and from the solution of a Bernoulli equation used
in generalized statistical mechanics. Plots and tables useful in evaluating
penetration probability at any energy are provided.

Astrophysics;Statistical Mechanics;Nuclear Theory;Plasma Physics