Precise frequency measurements of the D-lines and fine-structure   interval in K
  We use a diode laser locked to a Rb transition as the frequency reference along with a scanning Michelson interferometer to make precise measurements on the $D_1$ and $D_2$ lines of potassium. The Rb reference frequency is known with sub-MHz accuracy. We obtain the following values for the energy levels: 12 985.169 60(13)(15) cm$^{-1}$ for the $4P_{1/2}$ state ($D_1$ line); 13 042.875 95(14)(15) cm$^{-1}$ for the $4P_{3/2}$ state ($D_2$ line); and 57.706 35(19)(15) cm$^{-1}$ for the $4P_{3/2}-4P_{1/2}$ fine-structure interval. The leading source of systematic error cancels in the determination of the interval. The errors represent about an order of magnitude improvement over tabulated values. 
Ayan Banerjee, Dipankar Das, and Vasant Natarajan