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Hyperfine transitions of 13CN from pre-protostellar sources

Recent quantum mechanical calculations of rate coefficients for collisional transfer of population between the hyperfine states of 13CN enable their population densities to be determined. We have computed the relative populations of the hyperfine states of the N = 0, 1, 2 rotational states for kinetic temperatures 5 $\le$ T $\le$ 20 K and molecular hydrogen densities 1 $\le$ n(H2) $\le$10 10 cm --3. Spontaneous and induced radiative transitions were taken into account. Our calculations show that, if the lines are optically thin, the populations of the hyperfine states, F, within a given rotational manifold are proportional to their statistical weights, (2F + 1) -- i.e. in local thermodynamic equilibrium -- over the entire range of densities. We have re-analysed IRAM 30 m telescope observations of 13CN hyperfine transitions (N = 1 $\rightarrow$ 0) in four starless cores. A comparison of these observations with our calculations confirms that the hyperfine states are statistically populated in these sources.