IDENTIFICATION OF EXCITED GERADE STATES OF MOLECULAR HYDROGEN WITH EXTREME ULTRAVIOLET-VISIBLE DOUBLE RESONANCE EXCITATION TECHNIQUE

Extreme ultraviolet-visible double resonance excitation has been employed to populate selected rovibronic levels of the EF Z, H , q’Iv and J A states of H lying in the range between 115,000 and 117,600 cm above the ground state X lX;. qeunable coherent extreme ultraviolet radiation, generated by a four-wave mixing process in Xe, prepares H in the intermediate B 1)": (V 6, J) state. Subsequent absorption of the visible laser radiation brings H to the higher gerade states and the fluorescence light from these states is detected. Term values of 41 rovibronic levels in these gerade states, including 23 previously unidentified levels, were determined. The single rovibronic fluorescence lifetimes were also measured under the collision-free condition. The fluorescence lifetimes of the EF 5’. states exhibited significant rotational dependences. The nonadiabatic coupling among the adiabatic upper gerade vibronic states explained the observed rotational dependences successfully.


I INTRODUCTION
The spectroscopic study on excited gerade states of the hydrogen molecule which lie in the extreme ultraviolet (XUV) energy region above the ground states has a very long history. Richardson and Dieke 2,3 are pioneers who set the basis of spectroscopy of the gerade states. They have analyzed the emission spectra of hydrogen discharges, determined rovibronic term values and other constants, and identified the perturbing interactions. However, their assignments were only partial because of the spectral irregularity caused by the vibronic mixing among the upper gerade manifolds.
On the other hand, the hydrogen molecule and. its isotopic variants have long served as model molecular systems for theoretical treatments. Theoretical calculations on the 'double-minimum' excited states, EFI and GKI, have been carried out by Davidson. 4,5 Dressier and co-workers 6-have performed ab initio computation based on the nonadiabatic coupling functions involving the 1+ (EF, GK, and g H), Iqq, and j1A+g states, evaluating several important quantities such as energy eigenvalues and radiative lifetimes. Their calculations have, resulted in a revision of previous assignments and in new identification of the strongly mixed singlet gerade states below the H (n 1) + H (n 2) dissociation limit.
A systematic measurement of the radiative lifetimes as well as the term values of various rovibronic levels in the excited gerade states is a useful means to verify the theoretical treatments for this simple diatomic molecule. However, these states cannot be accessed by a single dipole-allowed optical transition from the ground state XE/. This difficulty has been circumvented by electron impact excitation and multig photon or double resonance excitation. The electron impact excitation has been mainly employed for fluorescence lifetime measurements. [3][4][5][6][7][8] For example, Day et al. 5 and Sanchez and Campos TM made use of a pulsed electron beam and measured the zero-pressure fluorescence lifetimes and the collisional quenching constants of the GKE, IlI-Ig, and JAg states. The multiphoton or double resonance excitation with monochromatic laser light provided a quantum-state-specific detection of hydrogen molecules. The first laser-based state-selective excitation of the 1+ state g was reported by Kligler and Rhodes. 9 Utilizing the energy coincidence between the two-photon energy of the ArF excimer laser radiation (193 nm) and the EFI (v'= 6) XIE / (v" 0) transition, they determined collision-free lifetimes of the g EFE (v' 6) state to be about 100 ns. Bjerre et al. 2 used an ArF excimer laser to prepare the EFIE (v' 6, J' 0, 1, 2) levels and a second laser to populate the states near the ionization limit. They confirmed the lifetimes reported by Kligler and Rhodes by changing the delay between the two laser pulses.
The progress in tunable coherent UV radiation sources brought a new insight on the identification of the upper 1E+ states. From the (2 + 1) multiphoton ionization g spectra taken with tunable radiation around 195 nm, Marinero et al. 2,22 carried out the first rotational analysis of the outer well of the double-minimum EF!E state. Chandler et al. 23 measured the zero-pressure lifetimes of EFIZ (v' 0, 3 and 6, J') of H, D:, and HD by a use of a pulsed tunable UV laser in combination with a tunable near-infrared laser.
Recently a double resonance excitation technique was developed to populate single rovibronic levels of the EFE, GI(I+ HIE+ ilrlg, and JIAg states by our group 24,25 g g and to excite singlet gerade s-and d-Rydberg states near the ionization limit by Rottke  Both beams are then focused by a fused silica lens (f 25 cm) into a mixing chamber in which Xe gas is provided from a valve as a pulsed jet synchronized with the laser pulses. Stainless steel parallel electrodes set at about 1 cm downstream of the valve monitors the electric current of Xe ions produced by (2 + 1) resonant-enhanced multi-photon ionization of UV photons to check the two-photon resonant condition of the UV frequency. The output energies of the dye lasers I and II are typically 5 and 2 mJ/pulse, respectively. The UV energy is estimated to be about 500 taJ/pulse. The resulting XUV radiation is introduced to a main chamber through a hole (d 5 mm).
The visible probe beam is the output of a dye laser (Lumonics, Hyper Dye 300: 0.08 cm bandwidth, pulse duration 10 ns) which is pumped by a XeC1 excimer laser (Lumonics Pulsemaster EX-700:308 nm output). The probe beam is collimated with a telescope and introduced into the main chamber from the opposite direction to the pump beam. In the main chamber the hydrogen gas is ejected from a pulsed valve. The tuning range between 510 nm and 580 nm is covered by Coumarin 500 and 540A dyes in methanol. The wavenumber of the probe radiation is calibrated by simultaneous recording of the 12 excitation spectrum as a wavenumber standard.
The whole system operates with the timing pulses of 10 Hz from a function generator. The delay between the pump and probe laser pulses is controlled by a digital delay generator (Stanford Research DG535). Both laser pulses are set to overlap because the lifetime of the intermediate state is short (--0.8 ns). The timing of the pump and probe light pulses is monitored with a fast p-i-n photodiode (Hamamatsu S1722-02). It is necessary to readjust frequently the delay so as to compensate the long term instability of the synchronization between the YAG laser and the excimer laser.
The fluorescence light from hydrogen molecules is converged onto a photomultiplier tube by two LiF lenses. The XUV coherent radiation was tuned to the single + Xl) by monitoring the rovibronic transition of the Lyman band system (B Eu ('-VUV fluorescence with a solar blind photomultiplier (Hamamatsu R1459: CsI cathode). The transitions from the BZ + state to the upper gerade states induced by the visible probe laser was then interrogated by observing the visible/near IR fluorescence corresponding to the transition between the upper gerade and lower ungerade (B + B'IZu+ Z, CFIg and states) with another photomultiplier (Hamamatsu R666: GaAs cathode) through suitable optical filters (Toshiba R-64, etc.). The pulse energy is kept below 300 tJ/pulse by the use of neutral density filters to avoid the saturation effect. The double resonance excitation spectrum is obtained by recording the visible/near IR fluorescence intensity as a function of the wavelength of the probe laser. For the lifetime measurement, the output is fed into a digital storage oscilloscope and then processed by a microcomputer. The measured lifetimes are dependent neither on the distance between the nozzle orifice and the probe laser beam nor on the stagnation pressure. This fact guarantees that the present experimental conditions prepare the collision-free environment. Further details of the experimental apparatus have been given in Reference 24. III RESULTS AND DISCUSSION III.1. Spectral assignments A typical double resonance excitation spectrum is shown in Figure 1 Table I and II, respectively. The plots of the term values against J' (J' + 1) are illustrated in Figure 2.
Following features are worth noting: (1) Our term values are 8.01 cm higher than those given by Dieke2,3, confirming the systematic error in his assignment as pointed out by Wolniewicz  (2) The term value (116,963.16 cm-1) determined for the J1A (v' 2, J' 3) level, which agrees excellently with Dieke's value after the correction of the systematic error, is 3.04 cm -1 higher than that for the J1A (v' = 2, J' 3) level.

Fluorescence lifetimes
The typical waveform of the fluorescence decay is illustrated in Figure 3, where open circles and solid line represent the experimental data and a single exponential fit to the data, respectively. Table III  predissociation induced by the nonadiabatic coupling with the ground state is taken into account in the latter (TQDW2). Therefore, TQDW2 is smaller than "rQDWl. We evaluated the calculated radiative lifetimes Tcalc for J' 0 5 after the procedure developed by Quadrelli et al.11. We employed, however, the simplified nonadiabatic wave functions consisting of only three adiabatic wavefunctions as listed in Table IV (v'-26, J'=0). This discrepancy can be attributed to the above-mentioned simplification. In the high vibrational levels there might be greater contributions of the short-lived states such as the GK (for J' > 0), I (for J' > 1), and J (for J' >_ 2) adiabatic states.
The excited singlet gerade states lie above the H(ls) + H(ls) dissociation limit of the ground state and therefore become predissociative through the interaction with the dissociation continuum. Recently, Quadrelli et al. 12 discussed the predissociation of the first three excited EF1Z, GKlY'., and HIE +g states lying below H(ls) + H(2s, 2p) dissociation limit.
The predissociation probabilities P of the vibronic states were summarized in Table  III of Reference 12. They vary over six orders of magnitude. For example, P is On the other hand, the EF1E (v' 25 and 26) states have considerably large nonradiative probabilities: the ratio P/(A + P) reaches 28% and 24%, respectively. in Table III corresponds  c) The EFE (v' 26) and the EFE (v' 25) states.
J'= 1 with the nonradiative rates calculated for J' 0. The radiative decay rates of J' 1 levels can significantly differ from those of J' 0 levels in case that the vibronic states, are coupled with the I1Flg state. On the other hand, the J dependence of the nonradiative rates can be assumed to be considerably smaller, because the predissociation of the J' 0 and 1 levels is governed entirely by the homogeneous 1+-1E+ interaction; the heterogeneous 111-1 -X + interaction does not contribute g g g g significantly to the predissociation of the J' 1 levels. In the following, the collision-free fluorescence lifetime is compared with the theoretical lifetime by Dressier and co-workers ,2 for each of the rovibronic levels in the J1A+g (V' 2) and EFIE (v' 25 28) states.
The j1A+ (v' 2) state g The fluorescence lifetimes for the jIA+g (v' 2) state are measured to be 25 40 ns. The J' 5 level has a longer fluorescence lifetime than the other rotational levels. This is explained by the fact that the JIA+ (v' = 2, J' 5) nonadiabatic wave function g has appreciable contributions from the long-lived GK (v = 6) ('rCK6 47 ns) and EF (v 29) (TEF29 772 ns) adiabatic states as seen in Table IV. T for J' = 2--5 levels are given in Table III  The fluorescence lifetimes for the EFIE (v' = 27) state show a consi.derable J' dependence. The shorter lifetimes observed for the J' = 3 and 4 levels are consistent with the nonadiabatic wave functions coupled with the short-lived I (v = 2) adiabatic state. The experimental lifetimes for the EFX (v' = 27, J' = 0 and 1) levels agree better with rDWl than with rtw2. The EF1E (v'= 26) state A remarkable rotational dependence of rxp is observed for the EF / E g (v'= 26) state. The short lifetimes of the J' 1 4 levels are ascribed to the large contributions of the I (v 2) adiabatic state to their nonadiabatic wave functions. This strong interaction for J' > 1 levels is understood qualitatively by the fact that the EFIE (v' = 26) and 111-1 + (v' 2) states are located nearby each other as seen in Figure 2. g The repulsion between J' 1 levels shifts the EFIE (v' 26, J' = 1) level downward to below J' = 0 as already mentioned in III.1. Chien et al. 29 have obtained somewhat longer lifetime (rCDV = 48.5 + 3.0 ns) for J' = 1 level than our value. Their value was derived from the Hanle effect measurements without correcting for the hyperfine effects.
The EFE (v' 26 and also 25) states have large nonradiative decay rates. Consequently, rDW2 is calculated to be considerably shorter than rWl. Therefore, row2 reproduces our experimental fluorescence lifetime for the EFIE (v' = 26, J'= 0) level much better than rDW.
The EFIE (v'= 25) state The lifetime for the EFIE (v' = 25, J' = 3) is much shorter than those for other J', although a notable rotational dependence of the lifetimes is not expected from their nonadiabatic wavefunctions listed in Table IV. The lifetimes measured at J' 0 and 1 levels are -30% longer than the values of "rotwl. For a more precise comparison the following two factors must be taken into account as mentioned by Quadrelli et al.: (i) The neglect of the nonadiabatic couplings with the higher electronic states derived from the ns and nd Rydberg series and from the doubly excited 1E / g configurations. (ii) The remaining convergence errors in the calculations of the clamped-nuclei electronic energies.