Strong Quantum Level Dependence of Na$_{\mathrm{2}}$ (4$^{\mathrm{1}}\Sigma_{\mathrm{g}}^{\mathrm{+}})$ Lifetimes.

Radiative lifetimes of Na$_{\mathrm{2\thinspace }}$ro-vibrational levels of the 4$\Sigma_{\mathrm{g}}^{\mathrm{+}}$ shelf state have been calculated in a continuation of our previous work [R. Anunciado \textit{et al.}, J. Chem. Phys. \textbf{145}, 174306 (2016)] to investigate the importance of bound-free transitions for radiative lifetimes. The lifetime calculations are performed for selected vibrational levels from 0 to 75 and rotational levels, J$=$1, 20, 40, 60, and 80 and for rotational levels from 0 to 90 in vibrational levels v $=$ 49, 50 and 51. We find that radiative lifetimes vary significantly with vibrational level, particularly around the shelf. In addition, we observe a strong, unusual, oscillatory radiative lifetime dependence on rotational quantum number. Another aspect we want to emphasize is the significance of including the bound-free transitions into the calculation which reduces the lifetime noticeably compared to the results of recent work that did not include this channel [A. Sanli \textit{et al}., J. Chem. Phys. \textbf{143}, 104304 (2015)]. The lifetimes of individual ro-vibrational levels of the 4$^{\mathrm{1}}\Sigma_{\mathrm{g}}^{\mathrm{+}}$ shelf state were calculated using the LEVEL 8.2 and BCONT programs by Robert Le Roy, the latter in a version modified by Brett McGeehan.