Vibration-dependent photoelectron angular distributions and branching ratios observed across the Cooper-minimum region of bromobenzene

Ivan Powis,David M P Holland,Minna Patanen,Catalin Miron,Egill Antonsson,Christophe Nicolas

doi:10.1103/physreva.96.013413

Ivan Powis, David M P Holland + Show 4 more

Open Access

https://doi.org/10.1103/physreva.96.013413

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Abstract

Vibrational state-resolved photoelectron anisotropy parameters, $\ensuremath{\beta}$, for the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}{\phantom{\rule{0.16em}{0ex}}}^{2}{B}_{1}$, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}\phantom{\rule{0.16em}{0ex}}{}^{2}{B}_{2}$, and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}{\phantom{\rule{0.28em}{0ex}}}^{2}{B}_{1}$ state ionizations of bromobenzene have been recorded at photon energies ranging from 20.5 to 94 eV, thus spanning the region of the expected bromine Cooper minimum (CM). The $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}$ state displays no CM and its $\ensuremath{\beta}$ value is also independent of vibrational level, in accord with the Franck-Condon approximation. The $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}$ state $\ensuremath{\beta}$ values display the CM to differing degrees, but both show a vibrational dependence that extends to energies well below the obvious CM dip. Calculations are presented that replicate these observations. We thus demonstrate a wide-ranging Franck-Condon approximation breakdown detected in the $\ensuremath{\beta}$ anisotropy parameter in the absence of any resonance. Measured and calculated vibrational branching ratios for these states are also presented. Although the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$ state branching ratios remain constant, in accord with Franck-Condon expectations, the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}$ and (especially) the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{C}$ state ratios display weak, quasilinear variations across the studied range of photon energy, but with no apparent correlation with the CM position.

Highlights

The concept of the Cooper minimum is long established in the context of valence photoionization cross-section studies, but is receiving fresh attention in the investigation of high harmonic generation (HHG) [1]
The vibrational invariance of the β parameters and an energy invariance of the branching ratios are as expected in the Franck-Condon approximation
At the heart of our study has been the measurement of vibrationally resolved angular distribution β parameters and relative cross sections across a very wide photon energy range

Summary

Introduction

The concept of the Cooper minimum is long established in the context of valence photoionization cross-section studies, but is receiving fresh attention in the investigation of high harmonic generation (HHG) [1]. As the electron energy increases, and the outgoing waves contract toward the core, the overlap integral in a given channel can change sign, the relevant matrix element passing through a zero At this point there will be a corresponding minimum in the total photoionization cross section. The atomic photoelectron angular distribution can be even more strongly influenced by a Cooper minimum (CM) than is the cross section This is readily understood in the atomic-like picture; for photoionization of a 3p electron there will be outgoing s and d waves, and as 3p → kd amplitude gets canceled at the CM, the isotropic s wave alone remains to dominate, with the β anisotropy parameter dipping to zero. The observed minima of cross section and β parameter may not exactly coincide [3]

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Conclusion