Thallium Oscillator Strengths and6dD322State hfs

The lifetime of the $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of thallium has been measured by the optical-double-resonance technique, with the result $\tau =7.4\mathrm{}\pm 0.3\times {10}^{-9\mathrm{}}$ sec, and by the level-crossing technique, with the result $\tau =7.6\mathrm{}\pm 0.2\times {10}^{-9\mathrm{}}$ sec. The intensity ratio of the $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-6\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-6\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ lines radiated by an optically pumped thallium beam was measured to establish the oscillator-strength ratio for these two transitions. The result is $\frac{A_{5350}}{A_{3776}}=1.16\mathrm{}\pm 0.05$. The lifetime and hfs of the thallium $6{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ state were measured by the level-crossing technique. The results are $\tau =6.2\mathrm{}\pm 1\times {10}^{-9\mathrm{}}$ sec and $\frac{\mathrm{}\left|a\right|\mathrm{}}{h}=41\mathrm{}\pm 2\times {10}^6$ sec. (The ${\mathrm{Tl}}^{205}$ and ${\mathrm{Tl}}^{203}$ hfs were not resolved in the experiment.) A table of thallium oscillator strengths has been constructed from our results and from some of the oscillator-strength ratios reported in the literature. The values in the table are compared to those in the remainder of the literature in order to collect and comment on equivalent values from other experiments. The oscillator-strength values in the table are also compared to the predictions of Bates and Damgaard's and Vainshtein's approximation methods. It was found that when ${n_p}^{*}<2\mathrm{}$, the $s-p$ transition probabilities calculated by extrapolating the tables of Bates and Damgaard are quite different from the values directly calculated using their theory. The directly calculated Bates-Damgaard values are in much better agreement with the experimental results (the average difference is 17% for 20 thallium transition). Vainshtein's calculated $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ to