  We present numerical calculations for cesium and mercury to estimate the
sensitivity of the scattering length to the variation of the fine structure
constant alpha. The method used follows ideas Chin and Flambaum [Phys. Rev.
Lett. 96, 230801 (2006)], where the sensitivity to the variation of the
electron to proton mass ratio, beta, was considered. We demonstrate that for
heavy systems, the sensitivity to variation of alpha is of the same order of
magnitude as to variation of beta. Near narrow Feshbach resonances the
enhancement of the sensitivity may exceed nine orders of magnitude.
