  The magnetic moment of the ^{13}C nucleus is shown to provide a potentially
useful tool for analysing quiescent cold molecular clouds. We report discovery
of hyperfine structure in the H^{13}CO^{+}(1-0) transition. The doublet
splitting is observed to be 38.5 +/- 5.2 kHz, and is confirmed by calculations
which give 39.8 kHz and a line strength ratio of 3:1. We improve the
spectroscopic constants of H^{13}CO^{+} and determine the frequencies of its
low-J spectrum to better precision by analysing the dark cloud L1512.
Potentially high optical depths (3 to 5 in L1512) in quiescent clouds require
to consider the line's doublet nature when comparing to other molecular
species, possibly reversing previous conclusions from single-component
interpretations. We further confirm the hyperfine splitting in the ^{13}CO(1-0)
transition that had been predicted, and measured in the laboratory, to be about
46 kHz. By applying hyperfine analysis to the data set of the first IRAM
key-project we show that ^{13}CO optical depths can be estimated in narrow
linewidth regions without recourse to other transitions nor to assumptions on
beam filling factors, and linewidth and velocity determinations can be
improved. For the core of L1512 we find an inverse proportionality between
linewidth and column density resp. square root of optical depth, and a
systematic inside-out increase of excitation temperature and of the
^{13}CO:C^{18}O abundance ratio. Overall motion toward the innermost region is
suggested.
