Stark shifts of potassium and rubidium $D1$ lines have been measured with high precision by Miller et al. [Phys. Rev. A 49, 5128 (1994)]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the $4p_j\text{−}3d_{j^{\prime }}$ transitions in K and the $5p_j\text{−}4d_{j^{\prime }}$ transitions in Rb to high precision. The $4p_{1/2}\text{−}3d_{3/2}$ and $5p_{1/2}\text{−}4d_{3/2}$ transitions contribute on the order of 90% to the respective polarizabilities of the $n{p}_{1/2}$ states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the $np\text{−}\left(n-1\right)d$ matrix elements and their uncertainties. We compare these values with our all-order calculations of the $np\text{−}\left(n-1\right)d$ matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving $nd$ states. Such matrix elements are of special interest for many applications, such as determination of “magic” wavelengths in alkali-metal atoms for state-insensitive cooling and trapping, and determination of blackbody radiation shifts in optical frequency standards with ions.

• Received 31 August 2007

DOI:https://doi.org/10.1103/PhysRevA.76.052516