We develop a method of analyzing radio frequency spectral line observations to derive data on the temperature, density, velocity, and molecular abundance of the emitting gas. The method incorporates a radiative transfer code with a new technique for handling overlapping hyperfine emission lines within the accelerated lambda iteration algorithm and a heuristic search algorithm based on simulated annnealing. We apply this method to new observations of N_2H^+ in three Lynds clouds thought to be starless cores in the first stages of star formation and determine their density structure. A comparison of the gas densities derived from the molecular line emission and the millimeter dust emission suggests that the required dust mass opacity is about kappa_{1.3mm}=0.04 cm^2/g, consistent with models of dust grains that have opacities enhanced by ice mantles and fluffy aggregrates.
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