Vibrational State Resolved Lifetimes of the Na$_{\mathrm{2}}$ 2$^{\mathrm{1}}\Sigma_{\mathrm{u}}^{\mathrm{+~}}$Double Well-State.

Lifetimes of individual Na$_{\mathrm{2}}$ ro-vibrational levels of the 2$^{\mathrm{1}}\Sigma_{\mathrm{u}}^{\mathrm{+}}$ double well-state have been measured using a delayed photoionization technique. Ground state Na$_{\mathrm{2}}$ produced in a molecular beam is excited resonantly by the doubled output of a pulsed dye laser in the range 333 -- 357 nm and then ionized by a 532 nm photon from a time-delayed Nd:YAG laser. By appropriate excitation laser tuning and systematic variation of the probe laser delay, ro-vibrational level resolved lifetimes are obtained for v$=$25-49. The double well state lifetime values are found to decrease from about 50 ns at v$=$25 to about 40 ns near the barrier at around v$=$33 and then to increase back to about 50 ns at the highest observed level of v$=$ 49. We have also performed lifetime calculations using the Leve8 and Bcont programs by Leroy$^{\mathrm{1}}$, the latter in a version modified by Brett McGeehan. We find that including only bound-bound transitions, the theoretical lifetime values are too large by a factor of up to 2. Inclusion of pertinent bound-free transitions improves the agreement noticeably. $^{\mathrm{1\thinspace }}$R. J. Le Roy, LEVEL 8.0: \textit{A Computer Program for Solving the Radial Schr\"{o}dinger Equation for Bound and Quasibound Levels}, University of Waterloo Chemical Physics Research Report CP-663 (2007); see \underline {http://leroy.uwaterloo.ca/programs/}..