Fine and hyperfine (de-)excitation of C₄H (X²Σ⁺) by collisions with He at low temperatures

¹ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadz Street 5, 87-100 Toruń, Poland
² Faculty of Chemistry, Nicolaus Copernicus University in Toruń, ul. Gagarina 7, 87-100 Toruń, Poland
³ Université de Tunis, Ecole Nationale Supérieure d’Ingénieurs de Tunis, Laboratoire de Spectroscopie et Dynamique Moléculaire (LSDM), 5 Av. Taha Hussein, 1008 Tunis, Tunisia
⁴ Université Gustave Eiffel, COSYS/IMSE, 5 Bd Descartes, 77454 Champs sur Marne, France

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 August 2025
Accepted: 9 December 2025

Abstract

We present a quantum scattering study of the fine and hyperfine rotational (de-)excitation of the linear carbon-chain radical C₄H (X²Σ⁺) in collisions with helium atoms at low temperatures relevant to the interstellar medium (ISM). For those purposes, a new highly accurate two-dimensional potential energy surface (2D-PES) for the C₄H–He weakly bound complex was generated using the spin-restricted explicitly correlated coupled-cluster RCCSD(T)-F12 approach in conjunction with the aug-cc-pVTZ basis sets and full counterpoise corrections. The resulting 2D-PES exhibits pronounced anisotropy, featuring a global minimum at a T-shaped configuration and a secondary local minimum at linear geometry. Such anisotropy significantly affects the collisional dynamics. Based on this 2D-PES, we performed quantum close-coupling scattering calculations followed by angular momentum recoupling techniques to obtain state-to-state inelastic cross sections and temperature-dependent rate coefficients for transitions between the fine and hyperfine structure levels of C₄H radical. Our computations reveal a marked preference for Δj = ΔN = ±2 fine-structure transitions, governed by the dominant second-order anisotropic term in the Legendre expansion of the interaction potential. Additionally, hyperfine-resolved rate coefficients display enhanced probabilities for transitions with ΔF = Δj, particularly at high rotational levels. This study provides the first set of fine- and hyperfine-resolved rate coefficients for the C₄H–He system, offering essential input for non-local thermodynamic equilibrium modeling of C₄H absorption and emission in cold astrophysical environments. Indeed, the present set of data should enable more accurate interpretations of observational spectra from cold molecular clouds and circumstellar envelopes, and contribute to our understanding of the excitation dynamics and chemical evolution of carbon-chain radicals in the ISM.