Structure and electron dynamics of planetary states of Sr below the Sr$^+$ $7d$ and $8p$ thresholds

In a combined experimental and theoretical study we investigate the $7dnl$ and $8pnl$ ($n\ge 11$, $l=9-12$) doubly-excited planetary states of Sr. The experimental spectrum was obtained using a five-photon resonant excitation scheme. The method of configuration interaction with exterior complex scaling was used to compute the energy-level structure and dynamics of the two highly excited electrons from first principles. Good quantitative agreement was obtained with the spectra we recorded, and the theoretical calculations shed light on their complex structure and the signatures of electron correlations therein. The two-electron probability densities we calculated reveal the strongly-correlated angular motion of the two electrons in the $7dnl$ and $8pnl$ planetary states, and confirm quantitatively the predictions of the frozen-planet approximation describing electron dynamics as the polarization of the fast inner electron by the electric field of the outer "frozen" electron.