We analyze the enhancement factors of nuclear reaction rates in binary mixtures. This factor is directly coupled with plasma screening function at zero separation, H_jk(0), for two ions (of types j=1,2 and k=1,2). The H_jk(0) is estimated by two methods: (1) from the difference of Helmholtz Coulomb free energies at large and zero separations; (2) by fitting the Widom expansion of H_jk(x) in powers of interionic distance x to Monte Carlo data. These methods are shown to be in good agreement. For illustration, we analyze the plasma screening enhancement of nuclear burning rates in dense stellar matter.

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