Abstract
How long does it take to emit an electron from an atom? This question has intrigued scientists for decades. As such emission times are in the attosecond regime, the advent of attosecond metrology using ultrashort and intense lasers has retriggered strong interest on the topic from an experimental standpoint. Here, we present an approach to measure such emission delays, which does not require attosecond light pulses, and works without the presence of superimposed infrared laser fields. We instead extract the emission delay from the interference pattern generated as the emitted photoelectron is diffracted by the parent ion’s potential. Targeting core electrons in CO, we measured a 2d map of photoelectron emission delays in the molecular frame over a wide range of electron energies. The emission times depend drastically on the photoelectrons’ emission directions in the molecular frame and exhibit characteristic changes along the shape resonance of the molecule.
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Introduction
The photoelectric effect is one of the most fundamental processes used for probing atoms, molecules, and condensed matter. It has been the subject of research for more than a century and most its aspects are considered wellunderstood. The basic question of whether the emitted electron appears in the continuum instantaneously or after a short delay has been under investigation for decades. This question, however, needed to be translated into the language of wave mechanics of quantum objects. The translation of the classical concept of a time delay into quantum mechanical wave formalism was first accomplished seventy years ago by Eisenbud and Wigner (and later Smith) for scattering processes in a series of pioneering theoretical works^{1,2,3}. Their findings paved the way for the understanding of the concept of a possible photoemission delay. The emitted photoelectron wave is subject to a phase shift induced by the potential of the ionized atom or molecule. This phase shift, as compared to the phase of a wave emerging from a potentialfree region, has been termed the Wigner phase. The concept of the Wigner phase is depicted in Fig. 1. Upon encountering a potential, a plane wave Φ_{i}(x, t) = e^{ikx−iωt} changes its wavelength and as a consequence, after interacting with the potential, the phase of the plane wave is shifted by a scattering phase δ: Φ_{f}(x, t) = e^{ikx−iωt+δ} (see Fig. 1a). The photoeffect mimics that behavior as the photoelectron emerges from within the ion’s potential, adding a corresponding halfscattering phase (see Fig. 1b). In the case of molecular photoionization, the situation becomes more complex, as the potential is anisotropic. The Wigner phase acquired in such cases depends on the emission direction of the photoelectron with respect to the molecular axis (as shown in Fig. 1c). Thus, the phase shift is a particularly sensitive, purely quantum probe of even the most subtle of features of the molecular potential. The photoelectron emission time (often referred to as Wigner time delay) is given by the derivative of the electron’s phase with respect to the electron’s kinetic energy ε and is in the attosecond regime.
In the aftermath of the initial theoretical investigations, it took several decades before photoemission delays could be addressed in experiments. Several femtosecondlaserrelated techniques have been developed during the last 20 years which give experimental access to such atomic time scales. Pioneering work by Schultze et al.^{4} employed an IRlaser fieldstreaking approach to measure these ultrashort times. A broadband higherharmonic attosecond light pulse was used to ionize neon atoms and a superimposed, phaselocked strong IR pulse altered the photoelectron kinetic energy depending on the electron emission time with respect to the IR pulse. From these measurements, the authors concluded that Ne(2p) electrons are emitted with an additional delay of 21 ± 5 as (attoseconds) compared to those liberated from the Ne(2s)shell. This firstofakind work triggered strong theoretical efforts to reproduce the emission delay in the modeling of the process, which mostly yielded much shorter emission delays of only a few attoseconds (see e.g., ref. ^{5} for a review). It has been pointed out since then that the streaking laser field alters the electron emission substantially and needs to be incorporated in the models used to extract the actual naturally occurring Wigner delay. More recently, the subject of photoionization of Ne has been revisited in a followup experiment by Isinger and coworkers^{6}. The findings made there suggest that the initial measurement by Schultze et al. was (in addition) contaminated by Nesatellite states with different Wigner delays, which were finally energetically resolved in the recent investigation.
A very detailed theoretical study by Hockett and coworkers targeted Wigner delays in small molecules^{7}. Examining the emission delay in CO and N_{2} molecules, this work provided the first fully threedimensional Wigner delay maps in the molecular frame and showed the dependence of the emission delay on the electron kinetic energy, the molecular orientation with respect to the light polarization, and the molecular symmetry. Recently, pioneering work on molecules in the gas phase reported stereo Wigner delays, i.e., the difference between emission times along the direction of the carbon and the oxygen atoms of a CO molecule^{8}. By using a RABBITT scheme (Reconstruction of Attosecond Beating By Interference of Twophoton Transitions)^{9} and employing a COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) reaction microscope^{10}, the authors resolved the phasebeating of IRinduced sidebands in the electron spectrum. From these the twophoton ionization stereo Wigner delays for the Σ and Πorientations of the molecule were obtained for different kinetic energy releases (i.e., ion energies) and electron energies. Further work on chiral molecules using the same techniqu showed that the Wigner delays are enantiosensitive^{11} and studies of photoionization time delays in H_{2} showed a dependence on the dissociation process^{12}. Beautiful work by Nandi and coworkers^{13} demonstrated the power of the RABBITT approach by inspecting angularintegrated but vibrationally resolved Wigner delays providing deep insight into the photoionization process on a molecular shape resonance.
The experimental approaches mentioned so far rely all on attosecond light pulses for ionization and on a modification of the emission process by a superimposed strong laser pulse. Apart from being experimentally very challenging, by design these methods do not provide the Wigner delay of the onephoton ionization process, but an emission delay, which includes in addition contributions from the continuum–continuum transition due to the absorption of the IR photons. Relying on theoretical modeling the onephoton Wigner delay can be extracted from the measured twophoton process in the end. While the continuum–continuum contribution can be described rather trivially for atoms, in particular the angular dependence of this contribution can be very complex for the case of molecular photoemission^{14}.
In the following we present an experimental approach, which is complementary to these experimental techniques. It provides, indeed direct experimental access to the angular dependence of the Wigner delay of the onephoton molecular photoionization process. Complementary to RABBITT, however, it relies on input from theoretical modeling in order to retrieve the absolute Wigner times (i.e., our technique does not provide an angular independent offset of the delay). Using this technique we investigate core ionization of the CO molecule and extract the energy and angledependant Wigner time delay for photoionization from the photoelectron’s angular emission distribution in the molecular frame and compare the results with theoretical calculations.
Results and discussion
Our approach is related to the scheme of socalled complete experiments^{15,16}. An emitted electron (wave packet) Ψ_{ε} can be written as a coherent superposition of partial waves Ψ_{ε} = ∑a_{εℓm}Y_{ℓm} with angular momentum quantum number ℓ and magnetic quantum number m. Accordingly, if at a given photoelectron energy ε, the complex amplitudes a_{εℓm} of each partial wave Y_{ℓm} are extracted from an experiment, full information on the emitted electron and the emission process (including the angulardependent phase) can be retrieved. Furthermore, by scanning the energy of the photons employed for the ionization, the change of the phase as a function of the electron kinetic energy also becomes accessible. This energy derivative is exactly the emission angle (θ, ϕ) and electronenergy (ε)dependent Wigner delay t_{w} for which we are looking:
A natural approach in extracting the amplitudes and phases of partial waves contributing to an emitted photoelectron signal is to examine the socalled molecularframe photoelectron angular distributions (MFPADs). This is because the same scattering of the electron inside the molecular potential that leads to angledependent Wigner phases also yields a complex electron diffraction pattern, which can be recognized in the emissiondirection distribution of the electron with respect to the molecular axis. Photoelectron diffraction imaging^{17} relies, for example, on this effect and employs the measured diffraction pattern to gather insight into the molecular geometry^{18}. In pioneering work, Cherepkov et al. have demonstrated that the extraction of amplitudes and phases from measured MFPADs is indeed possible^{19} even though the fitting procedure performed there did not yield unambiguous results.
For small molecules, molecularframe angular emission distributions can nowadays be obtained routinely using synchrotron light sources for the ionization of distinct molecular orbitals resulting in photoelectrons of a welldefined kinetic energy. The molecularframe photoelectron angular distribution of an electron of a given kinetic energy represents the modulus squared of the coherent superposition of its partial waves:
For a linear molecule aligned along the polarization axis of the ionizing light, the problem becomes independent of the azimuthal emission angle ϕ. As a result, only terms with m = 0 contribute to the sum of partial waves.
An example of such an angular distribution obtained from ionizing carbon monoxide molecules is given in Fig. 2a (see methods for details on the experiment). The red line is a fit using Eq. (5) to the measured data points employing partial waves up to ℓ = 4. From the fitting results the phase, \(\arg \left[{{{\Psi }}}_{\varepsilon }(\theta )\right]\), is calculated, which is depicted in Fig. 2b. By performing the same extraction procedure on an MFPAD obtained for an adjacent photon energy and computing numerically the energy derivative, the corresponding molecularframe Wigner delays are obtained according to Eq. (1). The extracted Wigner delays and their dependence on the photoelectron emission angle is shown in Fig. 2c.
To confirm our experimental findings, we performed a modeling of the photoemission process using HartreeFock wave functions (see methods for details). The corresponding results are depicted in the middle row panels of Fig. 2 and show good agreement with the experimental findings. The two distributions shown in Fig. 2d have been computed using a relaxedcore (red line) and a frozencore (blue line) HartreeFock approach. The experimental data can be considered to lie in between the two theoretical computations, slightly favoring the latter model. The measured and computed phase \(\arg \left[{{{\Psi }}}_{\varepsilon }(\theta )\right]\) decreases monotonically as one moves from the direction in which the oxygen atom points towards the direction in which the carbon atom points. The molecularframe derivative of the phase with respect to energy, i.e., the Wigner delay, exhibits more distinct features. The computed results show a sharp maximum and a deep minimum. The minimum can be clearly observed in the experimental results as well. The maximum is less pronounced but occurs in the progression towards lower photoelectron kinetic energies (see next paragraph). The Wigner delay varies by several tens of attoseconds depending on the emission angle of the photoelectron, just as predicted by Hockett et al.^{7} for the valence ionization of CO.
We have performed additional measurements of molecularframe photoelectron angular distributions and Wigner delays in the range of the first 20 eV above the CO carbon Kthreshold by scanning the photon energy from the CKthreshold to hν = 316.3 eV. The 2D color maps shown in Fig. 3a and b depict our results of this photon energy scan as a function of electron kinetic energy and in a polar distribution of intensity, respectively. The electron energy is encoded in the radial distance from the plot’s center. Figure 3a shows the molecularframe Wigner delay map in this plotting scheme. The corresponding measured molecularframe photoelectron angular distribution is presented in Fig. 3b. This representation of the data shows that distinct features in the Wigner delay occur at the same emission angles as minima in the molecularframe photoelectron angular distribution. This behavior is in line with the predictions that drastic changes in the emission delay may occur in case of the destructive interference of partial waves due to twocenter or CohenFano interference effects^{20}. For comparison, the energydependent Wigner delay map resulting from our theoretical modeling and the map of the experimental data are shown in Fig. 3d and c as conventional color maps as functions of the molecularframe photoelectron emission angle and the electron energy. The molecular axis is aligned along the direction of the light polarization (Σorientation). In addition, we present the corresponding histograms for molecules oriented perpendicularly to the light’s polarization axis (i.e., Πorientation) in Fig. 3e and f. The range of observed Wigner delays is much smaller for the Πcase. This is expected, as a main feature of the photoemission spectrum in the presented electronenergy regime is a Σshape resonance, which is a broad resonance feature appearing only for the Σorientation with a maximum at ~8 eV^{21}. Shape resonances result from a trapping of the emerging electron wave inside a centrifugal barrier, which is present for higherangularmomentum contributions to the emitted electron wave^{22}. We clearly observe how the Wigner delay range increases as the ionization energy progresses across the resonance in the electronenergy range of 5 eV ≲ E_{e} ≲ 12 eV in Fig. 3c, d, while Fig. 3e, f do not depict this behavior. For direct comparison, we show the corresponding results obtained on the shape resonance in Fig. 2g–i. Furthermore, the average Wigner delay, when weighted with the angular emission probability, is ~130 as on top of the resonance, which agrees nicely with the resonance’s width of ~5–6 eV. The theoretical modeling (Fig. 3d) reveals a particularly strong feature at E_{e} = 9.1 eV. The color scale is cropped in order to highlight the other details of the Wigner delay map, but the feature diverges towards negative delays and then rises abruptly to large positive delays within a very small angular range close to \(\cos (\theta )=0.8\). We do not observe a corresponding feature in the measured Wigner delay map in Fig. 3c and attribute the overestimated strength to the fixed equilibrium internuclear distance of the CO molecule employed in our theoretical modeling. We estimate that those closelying negative and positive delays will compensate for each other if the nuclear motion is included. We notice, however, that in spite of the fixednuclei oneparticle HartreeFock approximation, which is known to suffer accuracy problems where shape resonances are concerned^{23}, the present theory reproduces all the features observed in the experiment. The photoelectron energy region below 3.5 eV is grayed out in the histograms. It is known that in this energy region, the photoionization is strongly affected by doubly excited states^{19}, which are not included in our theoretical model. The angular dependence observed in the experiment, however, suggests, that these doubly excited states give rise to particularly interesting modulations in the emission time, which could be the subject of future investigations. We emphasize that in the context of our paper the good agreement between theory and experiment allows for two conclusions. First, the agreement underlines the capability of the theoretical model. Second, it validates that our technique is feasible to obtain a time domain quantity from a nontimeresolving precision experiment. The theory provides the phases of the electron’s continuum wave function, thus it has direct access to the Wigner delay. The experiment infers the same quantity from measured angledependent amplitudes as function of photon energy.
In summary, we presented an experimental approach to extract photoelectron Wigner delays in the molecular frame. Contrary to previous approaches, measuring this attosecondlevel observable does not require ultrashort laser pulses or even attosecond pulses to trigger photoemission and our approach measures the native onephoton ionization process of the unperturbed molecule without any need for dressing laser fields. Furthermore, the use of lowbandwidth synchrotron radiation allows for addressing electrons in a wide range of binding energies and distinct orbitals even in larger molecules. For more complex molecules, which are not cylindrically symmetric, complete 3D Wigner delay maps can be extracted. In the future, we will address excitation energy ranges, which are dominated by electron correlation effects (as for example those of the aforementioned doubly excited states) in order to explore the role of correlation in the Wigner phase. It has been recently demonstrated that MFPADs can be measured with Xray freeelectron lasers using the same multiparticle coincidence approach employed in the present experiment^{24,25}. These measurements suggest that MFPADs (and thus 3D Wigner delay maps) from more complex molecules and processes can be obtained using Xray freeelectron laser sources and more importantly, that the temporal evolution of the MFPADs following a photoreaction will become accessible in the near future.
Methods
Theoretical methods
The total amplitude for the emission of a photoelectron with energy ε in the direction (θ, ϕ) with respect to the axis of a diatomic molecule, which forms the Euler angle β with the direction of linear polarization of the ionizing radiation, reads:
Here, \({{{{{{{{\mathcal{D}}}}}}}}}_{k0}^{1}(\beta )\) are the rotation matrices (the remaining orientation Euler angles other than β are irrelevant) and \({A}_{\varepsilon \ell mk}=\langle {{{\Psi }}}_{\varepsilon \ell m} {d}_{k}^{1} {{{\Psi }}}_{0}\rangle\) are the dipole transition amplitudes for the emission of the partial photoelectron waves^{26} with angular momentum quantum numbers ℓ and m via the absorption of a photon of polarization k, all together given in the frame of a molecule. The amplitudes A_{εℓmk} were computed by the stationary Single Center (SC) method and code^{27,28,29}, which provides an accurate theoretical description of the angleresolved photoemission spectra. The calculations were performed in the frozencore and relaxedcore HartreeFock approximations. The SC expansion of all occupied orbitals of CO was restricted to partial harmonics of ℓ_{c} ≤ 99, and for the photoelectron in the continuum, to ℓ_{ε} ≤ 49. The total transition amplitude in Eq. (3) provides access to the MFPADs and Wigner delays via:
The latter derivative was evaluated numerically using energy steps of 100 meV.
Experimental methods
The experiment was performed at beamline U49/2PGM1 of the BESSY II synchrotron^{30}. We employed a COLTRIMS reaction microscope^{10} in order to measure the momenta of the photoelectrons and the C^{+} and O^{+} ion pairs generated after Kshell ionization and subsequent Auger decay in coincidence. In brief, in the COLTRIMS apparatus, a supersonic gas jet of CO molecules is intersected with the synchrotron photon beam. Charged particles created within the interaction volume by photoionization are guided by homogeneous electric and magnetic fields to two time and positionsensitive microchannel plate detectors with delayline position readouts^{31}. In this experiment, the ion arm consisted of a 5 cm long acceleration region. The electron arm of the COLTRIMS analyzer incorporated a WileyMcLaren timefocusing scheme^{32} with 6 cm acceleration region followed by a 12 cm fieldfree drift region. The electric field was set to 13 V/cm. A superimposed homogeneous magnetic field of 4.3 Gauss confined electrons up to a kinetic energy of 22 eV within the spectrometer volume. By measuring the positions of impact and the flight times of all particles in coincidence, the initial momentum vectors are deduced. The molecularframe photoelectron angular distributions are then obtained by measuring the emission direction of the C^{+} and O^{+} ions, which are generated in a Coulomb explosion after the photoionization process and the subsequent Auger decay. It is known that the ions fragment along the initial molecular axis for an ion kinetic energy release larger than 10.2 eV^{33}. We measured the photoelectron momenta in coincidence and, in that way, obtained the relative emission angle, i.e., the emission angle in the molecular frame. We scanned the photon energy in a range between 295.3 and 316.3 eV, which creates photoelectrons with a kinetic energy between 0 and 20 eV. The scanning was performed in steps of 50 meV, and the beamline exit slit was set to 150 μm corresponding to a photon energy resolution of ~150 meV.
Data analysis
In the case that the CO molecules are oriented along the light polarization vector, a considerable simplification of Eq. (3) occurs. In particular, the orientation angle β = 0, and the summation over the polarization index reduces to the value k = 0 (with the respective rotation matrices \({{{{{{{{\mathcal{D}}}}}}}}}_{00}^{1}(0)=1\) and \({{{{{{{{\mathcal{D}}}}}}}}}_{\pm 10}^{1}(0)=0\)). As a consequence, only σpartial waves with m = 0 contribute to the C 1sphotoionization channel. Thus, the respective MFPADs can be approximated as:
In principle, the experimental MFPADs representing the Σchannel are obtained by selecting the subset of molecules that are aligned in parallel to the light polarization axis from the whole dataset recorded for randomly oriented molecules. However, in order to maximize the statistics of the measured dataset we adopted in part the socalled Ffunction formalism^{34}. The electron angular distribution I(β, θ, ϕ) after photoionization can be fully described in terms of the following F_{LN} functions by:
where, again, β is the angle between the molecular axis and the polarization axis and θ and ϕ are the polar and azimuthal angles of the outgoing photoelectron. Setting β = 0 while integrating over ϕ due to the rotational symmetry of the process is equivalent to selecting only the Σorientation. The corresponding θdependant distribution is given as:
For an isotropic ionization probability, the same angular distribution is obtained by integrating over different values of β and combining them in the following way:
Where A(θ) and B(θ) are defined as:
with the substitution \(x=\cos (\beta )\) and \(I(x,\theta )=\int\nolimits_{0}^{2\pi }I(x,\theta ,\phi )\,d\phi\).
The advantage is obvious for the experiment because now all recorded events contribute to the MFPAD of the Σstate (instead of only a small fraction) which leads to significantly better statistics.
A similar procedure can be followed for molecules oriented perpendicularly to the light polarization (β = π/2) if only that part of the MFPAD distribution is considered, which lies within the plane defined by the molecular axis and the polarization axis of the light (ϕ = 0). In this case only πpartial waves with m = ±1 emitted via absorption of photons with polarization k = ±1 contribute to the ionization (the respective rotation matrices are equal to \({{{{{{{{\mathcal{D}}}}}}}}}_{00}^{1}\left(\frac{\pi }{2}\right)=0\) and \({{{{{{{{\mathcal{D}}}}}}}}}_{\pm 10}^{1}\left(\frac{\pi }{2}\right)=\mp \frac{1}{\sqrt{2}}\)). Thereby, Eq. (3) simplifies to:
Where we used Y_{l1} = − Y_{l(−1)} for ϕ = 0 and A_{εℓ11} = A_{εℓ(−1)(−1)}.
As before, the Ffunction formalism can be used to enhance the statistics for the case of Πorientation by setting β = π/2 and ϕ = 0:
Where X(θ), Y(θ), and Z(θ) are defined as:
with \(x=\cos (\beta )\) and \(I(\theta ,\phi )=\int\nolimits_{1}^{1}I(x,\theta ,\phi )dx\).
We used the Minuit2 package of the ROOT dataanalysis framework^{35} to fit Eq. (5) and Eq. (10) to our MFPADs obtained by the Ffunction formalism in steps of 100 meV in the electron energy. For every fit the events within a range of ±1 eV were integrated. The experimentallyderived distributions are reproduced adequately when restricting the summation to spherical harmonics of ℓ ≤ 4 (as has already been previously demonstrated^{36}). The main challenge of such multiparameter fitting of the realvalued MFPAD in Eq. (5) and Eq. (10) with the complex amplitudes a_{εℓ} is a lack of uniqueness. In particular, all complex amplitudes can be extracted up to one common global phase, which is, in turn, energy dependent. As a consequence, the fitting procedure can yield random jumps of this global phase as a function of energy. We employed the following solution to this problem. First, for each energy, the isotropic contribution to the total amplitude a_{ε0} Y_{00} was set to be real. As a result, all fitted amplitudes were determined up to the unknown energydependent global phase δ_{0}(ε) of the amplitude a_{ε0}. Second, our theoretical calculations showed that the phase \(\arg \left[{{{\Psi }}}_{\varepsilon }(\theta )\right]\), as a function of the emission angle θ, depicted a monotone behavior. To fit the first dataset (of lowest electron energy), we therefore initialized the fitting algorithm with random parameters and selected a result that fulfilled that monotonicity condition. Using the fitted result obtained in that step as an input to the fitting of the next adjacent energy step, we obtained results that are consistent with our theoretical calculations. This procedure yielded reliable and stable results for many different sets of random initial parameters. We obtained the Wigner delays by using adjacent energy steps to numerically evaluate the derivative (given here, for example for Σorientation)
and found that an energy step of \(\varepsilon {\varepsilon }^{\prime}=1\) eV yielded the most stable delays while still reproducing the details of the theoretical predictions. It should be stressed, however, that Eq. (13) yields experimental Wigner delays on a relative scale, i.e., up to an unknown (but isotropic) energydependent delay, \({t}_{w}^{0}(\varepsilon )=\hslash \frac{d{\delta }_{0}(\varepsilon )}{d\varepsilon }\), provided by the amplitude a_{ε0}. This missing isotropic delay cannot be determined from the experiment but can be fixed by calibration to the theory. Here, for each photoelectron energy, we set the angleaveraged experimental Wigner delay to the respective theoretical value.
Data availability
The data that support the findings of this study are available in Zenodo with the identifier https://doi.org/10.5281/zenodo.5569677^{37}.
Code availability
The code that supports the findings of this study is available from the corresponding author upon reasonable request.
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Acknowledgements
The experimental work was supported by the Deutsche Forschungsgemeinschaft (DFG) and the Bundesministerium für Bildung und Forschung (BMBF). S.E. and D.T. were supported by DFG Priority Programme “Quantum Dynamics in Tailored Intense Fields” (Project No. DO 604/291). A.H. and K.F. are grateful for the support of the Studienstiftung des deutschen Volkes. T.J., S.G., R.D., and M.S.S. acknowledge support from the DFG via Sonderforschungsbereich 1319 (ELCH). The theoretical work was supported by the DFG Project No. DE 2366/12. We are very thankful for the outstanding support provided by the BESSY II staff as part of the Helmholtz Zentrum Berlin (HZB), in particular that of Ronny Golnak. T.J. is very grateful for initial discussion on the topic with Danielle Dowek. R.D. and T.J. thank Nikolai Cherepkov and Ricardo Díez Muiño for initial education on fitting partial waves many years ago.
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J.R., K.K., M.K., I.V.P., D.T., S.G., D.T., J.S., A.G., N.M., C.S., N.A., L.K., K.F., A.H., S.E., L.Ph.S., M.S.S., F.T., R.D., and T.J. prepared and performed the experiment. V.T.D. and J.B.W. performed the experiment. K.K., J.R., and T.J. performed the data analysis and fitting procedure. P.V.D. and N.M.N. performed the theoretical modeling. All authors contributed to the manuscript.
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Rist, J., Klyssek, K., Novikovskiy, N.M. et al. Measuring the photoelectron emission delay in the molecular frame. Nat Commun 12, 6657 (2021). https://doi.org/10.1038/s41467021269942
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DOI: https://doi.org/10.1038/s41467021269942
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