  Stark shifts of potassium and rubidium D1 lines have been measured with high
precision by Miller 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' transitions in K and for the 5p_j-4d_j'
transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2
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 us to determine
the np-(n-1)d matrix elements and their uncertainties. We compare these values
with our all-order calculations of the np-(n-1)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.
