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.