# Precision measurement of the ionization energy and quantum defects of 39K I

## TL;DR

This study precisely measures the ionization energy and quantum defects of 39K Rydberg states using laser and millimeter-wave spectroscopy, providing improved atomic data and insights into fine-structure and core polarizabilities.

## Contribution

It offers the most accurate ionization threshold and quantum defect values for 39K, along with detailed fine-structure analysis and core polarizability estimates, advancing atomic physics knowledge.

## Key findings

- Improved ionization threshold of 39K at 35009.8139710(22) cm-1.
- Confirmed inverted fine structure for n >= 32 in the d series.
- Fine-structure splittings consistent with hydrogenic predictions for g series.

## Abstract

We present absolute-frequency measurements in ultracold 39K samples of the transitions from the ground state to np Rydberg states. A global nonlinear regression of the np1/2 and np3/2 term values yields an improved wave number of 35009.8139710(22)(sys)(3)(stat) cm-1 for the first ionization threshold of 39K and the quantum defects of the np1/2 and np3/2 series. In addition, we report the frequencies of selected one-photon transitions n's <- np3/2, n'd <- np3/2, n'f <- nd and n'g <- nf and two-photon transitions nf <- np determined by millimeter-wave spectroscopy. By combining the results from the laser and millimeter-wave spectroscopic experiments, we obtain improved values for the quantum defects of the s1/2, d3/2, d5/2, f and g states. For the d series, the inverted fine structure was confirmed for n >= 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 >= 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 and quadrupole polarizabilities of the K+ ion core. Additionally, the hyperfine splitting of the 4s1/2 ground state of 39K was determined to be 461.719700(5) MHz using radio-frequency spectroscopy and Ramsey-type interferometry.