THE $3\nu_{2}$ OVERTONE BAND OF $H_{3}^{+}$

$^{1}$. B.M. Dinelli, S. Miller, and J. Tennyson, J. Mol. Spectrose. 153, 718-725(1992) $^{2}$. B.M. Dinelli, private communication.Author Institution: Department of Engineering Physics, McMaster University; Department of Chemistry and Department of Astronomy and Astrophysics., The University of ChicagoBecause of the small mass of hydrogen and the relatively shallow vibrational potential, the transition probabilities of overtone bands of $H_{3}^{+}$ do not decrease as drastically as those of other molecules. According to the first principle calculation by Dinelli, Miller, and $Tennyson^{1}$, the spontaneous emission probability of the second overtone band $3\nu_{2} (\ell = 1) \rightarrow 0$ is smaller than that of the fundamental band by a factor of less than 10. This corresponds to the reduction of absorption coefficient of about 180 and the spectrum is observable at the $H_{3}^{+}$ ion concentration of $3 \times 10^{10} cm^{-3}$. We have observed 15 vibration rotation transitions from 7265.9 to $6806 cm^{-1}$. InGaAsP diode lasers were used in a short-external cavity configuration to achieve laser operation in a single longitudinal mode. The observed frequencies agree with earlier prediction by Miller and Tennyson within $3 cm^{-1}$ but agree better with their new $prediction^{2}$