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The modelling of emission spectra of molecules seen in interstellar cloudsrequires the knowledge of collisional rate coefficients. Among the commonlyobserved species, N$_2$H$^+$ is of particular interest since it was shown to bea good probe of the physical conditions of cold molecular clouds. Thus, we havecalculated hyperfine-structure resolved excitation rate coefficients ofN$_2$H$^+$(X$^1\Sigma^+$) by H$_2(j=0)$, the most abundant collisional partnerin the cold interstellar medium. The calculations are based on a new potentialenergy surface, obtained from highly correlated {\it ab initio} calculations.State-to-state rate coefficients between the first hyperfine levels werecalculated, for temperatures ranging from 5 K to 70 K. By comparison withpreviously published N$_2$H$^+$-He rate coefficients, we found significantdifferences which cannot be reproduced by a simple scaling relationship. As afirst application, we also performed radiative transfer calculations, forphysical conditions typical of cold molecular clouds. We found that thesimulated line intensities significantly increase when using the new H$_2$ ratecoefficients, by comparison with the predictions based on the He ratecoefficients. In particular, we revisited the modelling of the N$_2$H$^+$emission in the LDN 183 core, using the new collisional data, and found thatall three of the density, gas kinetic temperature and N$_2$H$^+$ abundance hadto be revised.

Hyperfine excitation of N$_2$H$^+$ by H$_2$: Toward a revision of N$_2$H$^+$ abundance in cold molecular clouds