Experimental determination of highly excitedFlevels in potassium by three-photon absorption spectroscopy

Three-photon absorption spectroscopy allows determination of the $\mathrm{nf}{}_{}{}^2{}_{}{}^{}F_{\frac{5}{2},\frac{7}{2}}^0{}_{}{}^{}$ energy levels of alkali metals ($\Delta L=+3\mathrm{}$). The $3d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ levels of KI were selectively excited using a narrow-band dye laser. The $3d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}\to \mathrm{nf}{}_{}{}^2{}_{}{}^{}F_{\frac{5}{2},\frac{7}{2}}^0{}_{}{}^{}$ absorption lines were observed in the background spectrum of another dye laser, and the $\mathrm{nf}{}_{}{}^2{}_{}{}^{}F_{\frac{5}{2},\frac{7}{2}}^0{}_{}{}^{}$ energy levels were deduced, from $n=10\mathrm{}$ to $n=14\mathrm{}$ inclusive, with an accuracy better than 0.1 ${\mathrm{cm}}^{-1\mathrm{}}$. Previously, an experiment was performed for the $7f{}_{}{}^2{}_{}{}^{}F_{\frac{5}{2},\frac{7}{2}}^0{}_{}{}^{}$ levels in order to verify the method. Shifts and systematic errors were entirely negligible. For all lines, the relative intensities of the absorbed doublet peaks are in good agreement with the estimates of the $4s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 3d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ probabilities.