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The attosecond technology provides a powerful tool for studying the ultrafast dynamics of electrons during the strong-field ionization of atoms and molecules. This technology relies on quantitative theoretical models to invert the ultrafast time-domain information of the system during the ionization process from the photoelectron spectrum obtained through experimental measurements. One of the key issues in constructing quantitative strong-field theoretical models is the theoretical description of the Coulomb effect. Compared with the single-center Coulomb potential of atoms, molecules have multi-center coulomb potential. This fundamental geometric structure feature leads to many new effects of molecules in the external field, such as orientation effect, charge resonance effect, intrinsic dipole effect and vibration effect. Therefore, it can be expected that the tunneling ionization process of molecules contains more phenomena than that of atoms, which is worthy of in-depth study by experiments and theories. Particularly for stretched molecular ions, such as H2+, those exhibiting charge resonance effects in external fields, the distinction between near-nucleus and far-nucleus Coulomb effects, which is of great significance for constructing quantitative theoretical models, becomes more complex, providing a platform for testing the applicability of quantitative theoretical models.
This work systematically compares the predictions of different theoretical models for the attoclock characteristic observables in molecular systems with large internuclear distances. Through comparative analysis, it is found that the recently proposed semiclassical response time theory, which incorporates near-nucleus Coulomb corrections, shows better agreement with numerical experimental results than the developed strong-field approximation models that consider far-nucleus Coulomb corrections. The semiclassical response time theory establishes a theoretical framework for describing strong-field ultrafast ionization dynamics of stretched molecular systems by considering dual-center Coulomb potential corrections and excited-state contributions. Specifically, it approximates the complex four-body interactions (electron-laser-dual nuclei) in stretched molecular systems into three-body interactions (electron-laser-dressed-up barrier-proximal nucleus), while incorporating the influence of the other nucleus on the potential barrier as a correction term for the tunnel-exit position. This framework highlights the significant impact of quantum-property-dominated near-nucleus Coulomb effects on molecular tunneling ionization. Furthermore, the theory provides an explicit formula for the response time determined by fundamental laser and molecular parameters. By calculating this response time, the theory deduces the values of attoclock observables, enabling a clear discussion of ionization time delays in stretched molecular tunneling ionization and revealing that such delays reflect the timescale of strong four-body interactions among the laser, electron, and molecular nuclei. In contrast, the developed strong-field approximation model that simultaneously accounts for excited-state effects and numerically solves Newtonian equations to describe far-nucleus Coulomb effects cannot fully describe the above-mentioned four-body interaction, making it difficult to quantitatively describe the complex tunneling ionization dynamics under the combined action of coulomb and excited states. Additionally, since this model cannot clearly define the ionization time, the related ionization time delay issues cannot be well discussed. Computational results demonstrate that the semi-classical response time theoretical model has improved both in terms of calculation accuracy and efficiency, thereby verifying the applicability of this theoretical model in the research process of molecular ultrafast ionization dynamics.
Moreover, for H2+ with intermediate internuclear distances, the charge resonance effect induces a significant ionization enhancement effect. We present relevant numerical experimental attoclock results and prospect the potential application of the response time theory in such systems. We also envision the extension of this theory to strong-field tunneling ionization in polar molecules, multi-center linear molecules, planar and three-dimensional molecules, and oriented molecules, where interference and Coulomb-acceleration effects compete. -
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