  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.
