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

TL;DR

This study combines experimental spectroscopy and advanced theoretical calculations to analyze the structure and electron dynamics of doubly-excited planetary states in strontium, revealing strong electron correlations and validating the frozen-planet approximation.

Contribution

It provides the first detailed experimental and theoretical analysis of Sr's doubly-excited planetary states near the $7d$ and $8p$ thresholds, highlighting electron correlation effects.

Findings

Good agreement between experiment and theory for energy levels

Visualization of strongly-correlated electron motion

Validation of the frozen-planet approximation in electron dynamics

Abstract

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.