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

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)].