Quantum Mechanical Rate Coefficient of Formation of HD Molecule at Ultracold Temperatures: Its Importance in Interstellar Cooling

Abstract

Molecular hydrogen and its isotope HD acted as one of the most important interstellar coolants in the primordial gas medium. In this paper, we present accurate time-independent quantum mechanical (TIQM) rate coefficients of formation of ultracold HD molecules by \({\rm D} +{\rm H}_2(v,j)\to {\rm HD}(v', j')+{\rm H}\) reaction at very low collision energy. State resolved integral cross sections between different rotational \((j)\) and vibrational \((v)\) levels and corresponding Boltzmann-averaged thermal rate coefficients are computed between temperature \(\rm T = 10^{-8}K\)-\(\rm 10K\). We found the exponential decrease of the rate coefficients with reducing temperature following Arrhenius' empirical equation is not valid at ultracold temperature limit. At lower temperatures, the rate coefficients become independent of temperature (constant) and Wigner's threshold laws are obeyed. Since cooling of the primordial gases lead to the formation of the first structures of the universe, inclusion of the accurate low-temperature rate coefficients will lead to improved modeling for the evolution of the early universe.