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The localization length for isotopically disordered harmonic one-dimensionalchains is calculated for arbitrary impurity concentration and scattering crosssection. The localization length depends on the scattering cross section of asingle scatterer, which is calculated for a discrete chain having a wavelengthdependent pulse propagation speed. For binary isotopically disordered systemscomposed of many scatterers, the localization length decreases with increasingimpurity concentration, reaching a mimimum before diverging toward infinity asthe impurity concentration approaches a value of one. The concentrationdependence of the localization length over the entire impurity concentrationrange is approximated accurately by the sum of the behavior at each limitingconcentration. Simultaneous measurements of Lyapunov exponent statisticsindicate practical limits for the minimum system length and the number ofscatterers to achieve representative ensemble averages. Results are discussedin the context of future investigations of the time-dependent behavior ofdisordered anharmonic chains.Comment: 8 pages, 10 figures, submitted to PR

Wave localization in binary isotopically disordered one-dimensional harmonic chains with impurities having arbitrary cross section and concentration