The abundance of molecular hydrogen and atomic helium in the universe makes them an important system to study in various fields. A mixture of molecular hydrogen and helium is the main component of the atmospheres of gas giants in the Solar System and is predicted to be a dominant constituent of the atmospheres of some types of exoplanets [1]. The hydrogen molecule is also the simplest molecule, the structure of which can be calculated from first principles, which makes it well suited for accurate tests of ab initio calculations. In particular, HD molecule, despite its lower abundance than H₂ isotopologue is noticeable in spectroscopic studies due to the presence of its dipole moment even in the electronic ground state. Moreover, studies of the H₂–rich atmospheres are well suited for measuring the D/H ratio, which is crucial for understanding the evolution of the Universe and planets’ atmospheres [2, 3]. Studies show [4] that in some cases the uncertainty of astronomical observations of hydrogen molecule spectra is dominated by the uncertainties of collisional parameters, including pressure broadening and pressure shift coefficients. An accurate list of the line–shape parameters is necessary for a correct interpretation of molecular spectra from the atmospheres of gas giants [4] and exoplanets [5].

We present the methodology and results of ab initio calculations of collisional effects for 12 purely rotational and 60 rovibrational electric dipole transitions in R and P branches: from R(0) to R(5) and from P(1) to P(6) in the 0–0 to 5–0 vibrational bands. We used state-of-the-art potential energy surface [6] - an improved version of the one reported by Bakr, Smith, and Patkowski [7]. We also carefully examined the validity of the usually assumed approximation for rovibrational transitions - centrifugal distortion neglection - in the case of the HD-He system. Available experimental studies [8][9] are in good agreement with our calculations for most transitions, however, some of the results are beyond the estimated uncertainty. The experimental values for rovibrational lines only consist of R₁(0) and R₁(1) transitions at 77 K. This, together with the fact that the measurements were using less accurate line-shape models, and current experimental techniques are more accurate, show that there is a strong need for new accurate experimental studies of collisional line-shape parameters.

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