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Ortho-para-H$_2$ conversion processes in astrophysical media

We report in this review recent fully-quantum time-independent calculations of cross sections and rate constants for the gas phase ortho-to-para conversion of H$_2$ by H and H$^+$. Such processes are of crucial interest and importance in various astrophysical environments. The investigated temperature ranges was 10$-$1500 K for H+H$_2$ and 10$-$100 K for H$^+$+H$_2$. Calculations were based on highly accurate H$_3$ and H$_3^+$ global potential energy surfaces. Comparisons with previous calculations and with available measurements are presented and discussed. It is shown that the existence of a long-lived intermediate complex H$_3^+$ in the (barrierless) H$^+$+H$_2$ reaction give rise to a pronounced resonance structure and a statistical behaviour, in contrast to H+H$_2$ which proceeds through a barrier of $\sim 5000$ K. In the cold interstellar medium ($T\leq 100$ K), the ortho-to-para conversion is thus driven by proton exchange while above $\sim$300 K, the contribution of hydrogen atoms become significant or even dominant. Astrophysical applications are briefly discussed by comparing, in particular, the relative role of the conversion processes in the gas phase ({\it via} H, H$^+$, H$_2$ and H$_3^+$) and on the surface of dust particles. Perspectives concerning future calculations at higher temperatures are outlined.