Analysis of the Rydberg character of the5d7dD21state of barium

The $5d7d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ state of barium is configuration mixed with the 6snd Rydberg series. This work examines the larger-$r$ behavior of the Rydberg character of the mixed-state wave function by projecting it experimentally onto a series of known Rydberg states, $6P_{\frac{1}{2}}\mathrm{nd}$, $J=3\mathrm{}$. Results agree with calculations based on the quantum-defect characterization of the wave function. This work also presents an analytical approximation to the radial-wave-function overlap integral between Rydberg states of arbitrary energy.