  We develop an alternative scaling approach to determine the criteria for
Anderson localization in one-dimensional tight-binding models with random site
energies having a bandwidth that decays as a power law in space, $H_{ij}
\propto |i - j|^{-\alpha}$. At the first order in perturbation theory the scale
dependence of the exchange-narrowed energy of the disorder is compared to the
energy level spacing of the ideal system to establish whether or not the
disorder has a perturbative effect on the Bloch states. We find that at $\alpha
=1$, the perturbative condition is satisfied and for sufficiently weak disorder
strength all states are extended. For $\alpha > 1$, all states are localized
for arbitrary disorder strength, in agreement with the earlier renormalization
group treatment by Levitov.
