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Context.Ever since they were first detected in the interstellar medium, the radio wavelength (3.3 GHz) hyperfine-structure splitting transitions in the rotational ground state of CH were observed to show anomalous excitation. Astonishingly, this behaviour was uniformly observed towards a variety of different sources probing a wide range of physical conditions. While the observed level inversion could be explained globally by a pumping scheme involving collisions, a description of the extent of ‘over-excitation’ observed in individual sources required the inclusion of radiative processes, involving transitions at higher rotational levels. Therefore, a complete description of the excitation mechanism in the CH ground state, observed towards individual sources entails observational constraints from the rotationally excited levels of CH and in particular that of its first rotationally excited state (²Π_3/2,N= 1,J= 3/2). Aims.Given the limited detections of these lines, the objective of this work is to characterise the physical and excitation properties of the rotationally excited lines of CH between the Λ-doublet levels of its²Π_3/2,N= 1,J= 3/2 state near 700 MHz, and investigate their influence on the pumping mechanisms of the ground-state lines of CH. Methods.This work presents the first interferometric search for the rotationally excited lines of CH between the Λ-doublet levels of its²Π_3/2,N= 1,J= 3/2 state near 700 MHz carried out using the upgraded Giant Metrewave Radio Telescope (uGMRT) array towards six star-forming regions, W51 E, Sgr B2 (M), M8, M17, W43, and DR21 Main. Results.We detected the two main hyperfine structure lines within the first rotationally excited state of CH, in absorption towards W51 E. To jointly model the physical and excitation conditions traced by lines from both the ground and first rotationally excited states of CH, we performed non-local thermodynamic equilibrium (LTE) radiative transfer calculations using the code MOLPOP-CEP. These models account for the effects of line overlap and are aided by column density constraints from the far-infrared (FIR) wavelength rotational transitions of CH that connect to the ground state and use collisional rate coefficients for collisions of CH with H, H₂and electrons (the latter was computed in this work using cross-sections estimated within the Born approximation). Conclusions.The non-LTE analysis revealed that physical properties typical of diffuse and translucent clouds best reproduced the higher rates of level inversion seen in the ground-state lines at 3.3 GHz, observed at velocities near 66 km s⁻¹along the sightline towards W51 E. In contrast, the excited lines near 700 MHz were only excited in much denser environments withn_H~ 10⁵cm⁻³towards which the anomalous excitation in two of the three ground state lines is quenched, but not in the 3.264 GHz line. This is in alignment with our observations and suggests that while FIR pumping and line overlap effects are essential for exciting and producing line inversion in the ground state, excitation to the first rotational level is dominated by collisional excitation from the ground state. For the rotationally excited state of CH, the models indicated low excitation temperatures and column densities of 2 × 10¹⁴cm⁻². Furthermore, modelling these lines helps us understand the complexities of the spectral features observed in the 532/536 GHz rotational transitions of CH. These transitions, connecting sub-levels of the first rotationally excited state to the ground state, play a crucial role in trapping FIR radiation and enhancing the degree of inversion seen in the ground state lines. Based on the physical conditions constrained, we predict the potential of detecting hyperfine-splitting transitions arising from higher rotationally excited transitions of CH in the context of their current non-detections. 

Abstract Observations of CH⁺are used to trace the physical properties of diffuse clouds, but this requires an accurate understanding of the underlying CH⁺chemistry. Until this work, the most uncertain reaction in that chemistry was dissociative recombination (DR) of CH⁺. Using an electron–ion merged-beams experiment at the Cryogenic Storage Ring, we have determined the DR rate coefficient of the CH⁺electronic, vibrational, and rotational ground state applicable for different diffuse cloud conditions. Our results reduce the previously unrecognized order-of-magnitude uncertainty in the CH⁺DR rate coefficient to ∼20% and are applicable at all temperatures relevant to diffuse clouds, ranging from quiescent gas to gas locally heated by processes such as shocks and turbulence. Based on a simple chemical network, we find that DR can be an important destruction mechanism at temperatures relevant to quiescent gas. As the temperature increases locally, DR can continue to be important up to temperatures of ∼600 K, if there is also a corresponding increase in the electron fraction of the gas. Our new CH⁺DR rate-coefficient data will increase the reliability of future studies of diffuse cloud physical properties via CH⁺abundance observations.