Vibrational spectroscopy ofH2+: Hyperfine structure of two-photon transitions

Abstract

We present the computation of two-photon transition spectra between ro-vibrational states of the H + 2 molecular ion, including the effects of hyperfine structure and excitation polarization. The reduced two-photon matrix elements are obtained by means of a variational method. We discuss the implications of our results for high-resolution spectroscopy of H + 2 .

Determination of the ionization and dissociation energies of the hydrogen molecule

“…This value corresponds to the center of gravity of the hyperfine structure components of the N + = 1 level of H 2 + . 25 The 54p1 1 ͑0͒ level has three hyperfine components, separated by ϳ0.000 11 and ϳ0.000 05 cm −1 as determined from the transition frequencies in Ref. 6, and were not resolved in the present experiment.…”

Theoretical Determination of the Dissociation Energy of Molecular Hydrogen

“…Very recently Liu et al 16 described a hybrid, experimental-theoretical determination of D 0 based on several transition frequency measurements [16][17][18][19] and theoretical calculations of the energy levels of the H + 2 ion. [20][21][22][23] The dissociation energy D 0 = 36118.06962 cm −1 determined in this way 16 has been reported with uncertainty of ±0.00037 cm −1 -almost two orders of magnitude smaller than that of the previous most accurate determination D 0 = 36118.062 ± 0.010 cm −1 of Zhang et al 15 The best available theoretical predictions of 36118.049 cm −1 from Kolos and Rychlewski 11 and 36118.069 cm −1 from Wolniewicz 12 are significantly less precise and have been reported without any error bar estimates. Both of these predictions involve an incomplete treatment of α 3 QED corrections 24 so it is not clear if the perfect agreement between the experiment and Wolniewicz's calculation is not fortuitous.…”

Note: A high transmission Faraday optical isolator in the 9.2 μm range

“…The transmission of the former system is 0.9 (polarizer) ×0.98 (quarter-wave plate) = 0.88. Since the intensity of the considered two-photon lines is 8.5 larger in linear polarization [16], and the transition rate being proportional to the square of the laser intensity, the net gain is a factor 8.5 × (0.635/0.88) 2 = 4.4. Table III summarizes published characteristics of Faraday isolators in the 9-10 µm range and at 5.4 µm together with the present results.…”

“…The QCL beam (≈54 mW) is mode-matched to a high finesse (≈1000) Fabry-Perot cavity, that is required both to ensure a Doppler-free geometry with perfectly counterpropagating beams, and to enhance the transition rate (two-photon ro-vibrational transitions in H + 2 being very weak). Optical feedback from the high-finesse cavity is a problem in such an experiment; in the initial setup, isolation was obtained by combining a quarter-wave plate and polarizer with an acousto-optic modulator providing a 6 dB additional isolation through its strongly polarization-dependent efficiency [16]. The total isolation ratio, slightly over 30 dB, was just sufficient to achieve stable operation of the QCL.…”

“…The total isolation ratio, slightly over 30 dB, was just sufficient to achieve stable operation of the QCL. However, probing the transitions with a circularly polarized beam has two important drawbacks: (i) two-photon transition rates in H + 2 are almost an order of magnitude smaller with respect to the linear polarization case [16], and (ii) transition frequencies are much more sensitive (by 4-5 orders of magnitude) to the Zeeman shift due to the |∆M | = 2 selection rule [17], requiring a high level of magnetic field control.…”