Hyperfine Structure and Lifetimes of the4P322and5P322States ofK39

The hyperfine constants of the $4{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of ${\mathrm{K}}^{39}$ have been measured using the optical level-crossing method. The results are: $a\left(4\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=2.0\mathrm{}\pm 0.1$ Mc/sec; $b\left(4\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=2.9\mathrm{}\pm 0.2$ Mc/sec; $a\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=1.95\mathrm{}\pm 0.05$ Mc/sec; $b\left(5\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=0.92\mathrm{}\pm 0.1$ Mc/sec. These hfs constants are accurately proportional to the fine structure intervals to within 1%. These data, and the results from previous measurements on the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states, yield values for the ratio $\frac{a\left(P_{\frac{1}{2}}\right)}{a\left(P_{\frac{3}{2}}\right)}$ in good agreement with measurements on other alkali atoms. The calculated quadrupole moment is $Q=(0.053\mathrm{}\pm 0.008)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$, including Sternheimer corrections. The life-times of these states were determined to be: $\tau \left(4\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=26.0\mathrm{}\pm 0.5$ nsec and $\tau \left(5\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=140.8\mathrm{}\pm 1.0$ nsec.