[en] The inter-ionic density correlations and the associated screening potential are investigated for those dense, high-temperature plasmas with parameters appropriate to the inertially confined fusion experiments and the interior of main-sequence stars. The hypernetted chain scheme is used for the analysis of the correlations, where the screening effect of the electrons is taken into account via the dielectric function with inclusion of partial degeneracy and the local-field correction. We derive explicit analytic expressions for the enhancement rate of thermonuclear reactions applicable uniformly over the entire parameter domain of plasmas with the ionic charge Z = 1 and 2. (author)