We present absolute-frequency measurements in ultracold ${}^{39}\mathrm{K}$ samples of the transitions from the $4s_{1/2}$ ground state to $n{p}_{1/2}$ and $n{p}_{3/2}$ Rydberg states. A global nonlinear regression of the $n{p}_{1/2}$ and $n{p}_{3/2}$ term values yields an improved wave number of 35009.8139710(22)${}_{\mathrm{sys}}{\left(3\right)}_{\mathrm{stat}}{\mathrm{cm}}^{-1}$ for the first ionization threshold of ${}^{39}\mathrm{K}$ and the quantum defects of the $n{p}_{1/2}$ and $n{p}_{3/2}$ series. In addition, we report the frequencies of selected one-photon transitions $n^{\prime }{s}_{1/2}\leftarrow n{p}_{3/2}, n^{\prime }{d}_j\leftarrow n{p}_{3/2}, n^{\prime }{f}_{j^{\prime }}\leftarrow n{d}_j$, and $n^{\prime }{g}_{j^{\prime }}\leftarrow n{f}_j$ and two-photon transitions $n{f}_{j^{\prime }}\leftarrow n{p}_j$ determined by millimeter-wave spectroscopy, where $j$ is the total angular-momentum quantum number. By combining the results from the laser and millimeter-wave spectroscopic experiments, we obtain improved values for the quantum defects of the $s_{1/2}, d_{3/2}, d_{5/2}, f_j$, and $g_j$ states. For the $d_j$ series, the inverted fine structure was confirmed for $n\ge 32$. The fine-structure splitting of the $f$ series is less than 100 kHz at $n=31$, significantly smaller than the hydrogenic splitting, and the fine structure of the $g$ series is regular for $n\ge 30$, with a fine-structure splitting compatible with the hydrogenic prediction. From the measured quantum defects of the $f$ and $g$ series we derive an estimate for the static dipole ${\alpha }_{\mathrm{d}}$ and quadrupole ${\alpha }_{\mathrm{q}}$ polarizabilities of the ${\mathrm{K}}^{+}$ ion core. Additionally, the hyperfine splitting of the $4s_{1/2}$ ground state of ${}^{39}\mathrm{K}$ was determined to be 461.719700(5) MHz using radio-frequency spectroscopy and Ramsey-type interferometry.

• Received 9 April 2019

DOI:https://doi.org/10.1103/PhysRevA.100.012501