  Using the results of extensive Monte Carlo simulations we discuss corrections
to the linear mixing rule in strongly coupled binary ionic mixtures. We analyze
the plasma screening function at zero separation, H_{jk}(0), for two ions (of
types j=1,2 and k=1,2) in a strongly coupled binary mixture. The function
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
on the radial pair distribution function g_{jk}(x). 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.
