We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. The model assumes fusion in a potential that is screened by an effective electron cloud around colliding nuclei (extended Salpeter ion-sphere model). We calculate the mean field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical S factors, and enhancement factors of reaction rates. As a byproduct, we study analytic behavior of the screening potential at small separations between the reactants. In this model, astrophysical S factors depend not only on nuclear physics but on plasma screening as well. The enhancement factors are in good agreement with calculations by other methods. This allows us to formulate the combined, pure analytic model of strong plasma screening in thermonuclear reactions. The results can be useful for simulating nuclear burning in white dwarfs and neutron stars.
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