We present detections of absorption from the ground state and excited states of C I in the z = 1.9731 damped Lyα system of the QSO 0013 - 004. The excitation temperature between the J = 0 and J = 1 fine-structure levels of C I is 11.6 ± 1.0 K. We estimate other contributions to the excitation of the C I fine-structure levels, and use the population ratio of the excited state to the ground state to derive an estimate for the cosmic microwave background radiation (CMBR) temperature of T = 7.9 ± 1.0 K at 0.61 mm and z = 1.9731, which is consistent with the predicted value of T = 8.105 ± 0.030 K from the standard cosmology.
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