Accurate determination of the electric-dipole matrix elements in K and Rb from the Stark shift measurements

Stark shifts of the rubidium and potassium D1 lines have been measured with high precision by Miller {\it et al} [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the $4p_{j}-3d_{j^{\prime}}$ transitions in K and for the $5p_{j}-4d_{j^{\prime}}$ transitions in Rb to high precision. These transitions contribute on the order of 90\% to the respective polarizabilities of the $np_{1/2}$ 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 to determine the $np-(n-1)d$ matrix elements and their uncertainties. We also compare these values with our all-order calculations 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 the ``magic'' wavelengths in alkali-metal atoms for state- insensitive cooling and trapping and determination of blackbody radiation shifts in optical frequency standards with ions. \\ \noindent [1] K.\ E.\ Miller and D.\ Krause and L.\ R.\ Hunter, Phys.\ Rev.\ A 49, 5128 (1994)