  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.
