  Nuclear fusion cross-sections considerably higher than corresponding
theoretical predictions are observed in low-energy experiments with metal
matrix targets and accelerated deuteron beams. The cross-section increment is
significantly higher for liquid than for solid targets. We propose that the
same two-body correlation entropy used in evaluating the metal melting entropy
explains the large liquid-solid difference of the effective screening potential
that parameterizes the cross-section increment. This approach is applied to the
specific case of the $^6$Li(d,$\alpha$)$^4$He reaction, whose measured
screening potential liquid-solid difference is $(235 \pm 63)$ eV. Cross
sections in the two metals with the highest two-body correlation entropy (In
and Hg) have not yet been measured: increments of the cross sections in liquid
relative to the ones in solid metals are estimated with the same procedure.
