Cross sections are presented for dissociative recombination and electron-impact vibrational excitation of the ArH+ molecular ion at electron energies appropriate for the interstellar environment. The R-matrix method is employed to determine the molecular structure data, i.e. the position and width of the resonance states. The cross sections and the corresponding Maxwellian rate coefficients are computed using a method based on the Multichannel Quantum Defect Theory. The main result of the paper is the very low dissociative recombination rate found at temperatures below 1000K. This is in agreement with the previous upper limit measurement in merged beams and offers a realistic explanation to the presence of ArH+ in exotic interstellar conditions.
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