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tokens: 13 C ratio is larger. Fig. 7 12 CN/ 13 CN ratio as a function of n H , for different temperatures, at t 1 ( top right panel ), t 2 ( bottom left panel ), and t 3 ( bottom right panel ). The large pink circles in the bottom panels represent the result of the model that simulates the physical conditions in the centre of the pre-stellar core B1b observed by Daniel et al. (2013) . The 12 CN/ 13 CN ratio observed by Daniel et al. (2013) is represented by the green star. We note that the error bar is within the symbol. In all panels, the black horizontal dashed line represents the initial 12 C/ 13 C ratio of 68. We also performed a parameter-space exploration for a fixed n H of 2 × 10 4 cm −3 , varying the temperatures from 10 up to 50 K and the cosmic-ray ionisation rate between ζ low and ζ high . In particular, as already done in Sect. 3.2 , we focused the analysis on HNC, HCN, and CN ( Figs. 11 – 13 ). The main trend is that the 12 C/ 13 C ratios are highest for ζ high . This is related to the fact that secondary photon reactions maintain a high efficiency of low-temperature isotopic exchange reactions that involve C 3 , and the atomic 12 C/ 13 C ratio (and that of related molecules) remains higher than 68 (see also Fig. C.2 , right panel). 4 Conclusions We developed a new chemical network to study, in detail, how important isotopic exchange reactions are to the chemistry of carbon-containing species in the low temperature (10–50 K) gas in star-forming regions with n H = 2 × 10 3 –2 × 10 7 cm −3 . In particular, we suggest the occurrence of 13 C exchange involving C 3 with atomic carbon and study the possible consequences of this reaction. The main results and conclusions of this work are summarised below: 1. We found that reaction ( 10 ) is mainly important for T gas 27 K (owing to its exothermicity), and leads to 12 C/ 13 C 68 for molecules that form from atomic carbon (e.g. C 2 , C 3 , and nitrile-bearing species). This behaviour occurs in the time period between the conversion of atomic carbon into CO, andthe time when CO is almost completely frozen out onto dust grains. 2. We performed a detailed study of the 12 C/ 13 C ratios for the nitrile-bearing species HCN, HNC, and CN, as a function of density and for different temperatures. Our model can partially reproduce the carbon isotopic ratios derived by Daniel et al. (2013) and Magalhães et al. (2018) from observations towards low-mass pre-stellar cores. 3. We also used our grid of models to evaluate how far we are from the correct 12 C/ 13 C ratio, assumed to be 68 in the local ISM, to derive the 14 N/ 15 N ratios in the sample of high-mass star-forming regions analysed by Colzi et al. (2018a ). Our chemical model predicts that we are overestimating or underestimating the assumed 12 C/ 13 C ratios by factors ~0.8–1.9, even up to ~3.5, depending on the evolutionary time that we choose for the analysis. Considering these factors, the average nitrogen fractionation value of ~330 derived by