Electronic transition dipole moment and radiative lifetime calculations of sodium dimer ion-pair states

Ro-vibrational level dependence of the radiative lifetime of the Na241Σg + shelf state

We report on calculations-using the LEVEL and BCONT programs by Le Roy, the latter of which is a version modified by B. McGeehan-of the dependence of the radiative lifetime of the Na₂ sodium dimer 4¹Σ_g ⁺ shelf-state on the initial vibrational and rotational level for corresponding quantum numbers of 0 ≤ v ≤ 75 and 0 ≤ J ≤ 90, respectively. We also present experimental lifetime values for 43 < v < 64, averaged over J = 19 and 21, obtained by a delayed pump-probe method using a previously described molecular beam and time-of-flight apparatus. Our calculated results are based on all possible dipole allowed transitions (to the 2¹Σ_u ⁺, 1(B)¹Π_u, and 1(A)¹Σ_u ⁺ electronic states) terminating into bound as well as free final states. The shelf of the initial electronic state is a consequence of configuration interaction with the lowest Na⁺-Na^- ion-pair potential and occurs, for the rotationless molecule, at the vibrational level v = 52. From the 4¹Σ_g ⁺ vibrational ground state to the shelf, the calculated lifetimes increase monotonically by a factor of about 3.8. Beyond around v = 52, depending on rotational excitation, the lifetimes decrease, settling to a value intermediate to the maximum and the minimum at v = 0. Within error bars and in the range available, our experimental data are compatible with these findings. In addition, our calculations reveal unusual and pronounced oscillatory variation of the lifetime with rotational quantum numbers for fixed vibrational levels above-but not below-the shelf. We discuss our findings in terms of the appropriate transition dipole moments and wavefunctions and provide a detailed comparison to recent lifetime calculations of sodium dimer ion-pair states [Sanli et al., J. Chem. Phys. 143, 104304 (2015)].

Time-resolved double-resonance spectroscopy: Lifetime measurement of the 6 1 Σ g + ( 7,31 ) electronic state of molecular sodium

We report on the lifetime measurement of the 6   1 Σ g + ( 7,31 ) state of Na₂ molecules, produced in a heat-pipe oven, using a time-resolved spectroscopic technique. The 6   1 Σ g + ( 7,31 ) level was populated by two-step two-color double resonance excitation via the intermediate A   1 Σ u + ( 8,30 ) state. The excitation scheme was done using two synchronized pulsed dye lasers pumped by a Nd:YAG laser operating at the second harmonics. The fluorescence emitted upon decay to the final state was measured using a time-correlated photon counting technique, as a function of argon pressure. From this, the radiative lifetime was extracted by extrapolating the plot to collision-free zero pressure. We also report the calculated radiative lifetimes of the N a 2   6   1 Σ g + ro-vibrational levels in the range of v = 0-200 with J = 1 and J = 31 using the LEVEL program for bound-bound and the BCONT program for bound-free transitions. Our calculations reveal the importance of the bound-free transitions on the lifetime calculations and a large difference of about a factor of three between the J = 1 and J = 31 for the v = 40 and v = 100, respectively, due to the wavefunction alternating between having predominantly inner and outer well amplitude.

Vibrationally resolved lifetimes of the 21Σu+ state of Na2

Lifetimes of partially resolved ro-vibrational levels of the Na₂ 2¹Σ_u⁺ double well state have been measured for the first time. Ground state sodium dimer molecules in a molecular beam are resonantly excited by the doubled output of a 10 ns pulsed dye laser in the range 333-357 nm. After being allowed to decay for a predetermined time interval, the surviving excited molecules are ionized by 532 nm photons from a delayed Nd:YAG laser and detected in a linear time-of-flight mass spectrometer. By appropriate tuning of the excitation laser and systematic variation of the probe laser delay, lifetimes are obtained for vibrational levels in the range from 22 to 57. At zero rotation, the three lowest vibrational quantum numbers that we have explored (22, 25, and 28) correspond to wavefunctions whose probability densities are appreciable only in the inner well. Levels with larger quantum numbers are located above the barrier, which, for the rotation-free case, lies between quantum numbers 33 and 34. Because of the congested nature of the excitation spectrum and the experimental resolution of about 0.2 cm^-1 available to us, our experimental results are only partially quantum state resolved. Nevertheless, we can discern a decrease in lifetime from about 50 to 40 ns for the inner well levels and a slight increase in lifetime with increasing quantum number for levels above the potential barrier. We have also performed lifetime calculations based on the LEVEL and BCONT programs made available by Le Roy, the latter of which was modified by McGeehan. When limited to bound-bound transitions, theoretical lifetimes for levels above the barrier are systematically larger than experimental values by a factor of almost two. With the addition of bound-free transitions, agreement between experiment and theory is, for the most part, within the experimental uncertainties.