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REVIEW 4 major objections 5 minor 46 references

Diffraction patterns in attosecond photoionization time delay

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper predicts that the attosecond time delay of photoelectrons from a cubic molecule carries a diffraction pattern with ±100-attosecond fringes that should be observable in pump-probe chronoscopy.

desk verdict A credible, cleanly presented model prediction of symmetry-driven diffraction motifs in EWS photoionization delays for a cubic molecule; worth serious refereeing despite the idealized potential. read the letter →

arxiv 2412.08204 v1 pith:TI7B4MCS submitted 2024-12-11 physics.atom-ph physics.atm-clus

Sajad Azizi , Mohamed El-Amine Madjet , Zheng Li , Jan M. Rost , Himadri S. Chakraborty This is my paper · ORCID
classification physics.atom-phphysics.atm-clus
keywords Eisenbud-Wigner-SmithtimedelayattosecondphotoionizationdiffractionperfluorocubanecubicsymmetryRABBITTstreakingphotoelectronangulardistribution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper predicts that when a photon ionizes an electron from a molecule with cubic symmetry, the attosecond time delay of the emitted electron carries a diffraction pattern: a regular mesh of delays and time advances within ±100 attoseconds that is visible in both the electron energy and emission angle. This is argued for a single-active-electron model of perfluorocubane, whose delocalized LUMO sits in a cubic cage. The predicted pattern survives averaging over molecular orientations and over the azimuthal direction, so it should be observable with current ultrafast pump-probe chronoscopy (RABBITT or streaking). If true, this turns time delay into a structural probe of molecular symmetry, extending diffraction from photoelectron intensity into the time domain.

What carries the argument

The central object is the Eisenbud-Wigner-Smith time delay, the energy derivative of the phase of the photoionization amplitude, computed from the dipole matrix element in the length gauge. The argument runs on the identity $\tau(k) \sim (RI' - R'I)/\sigma$, which ties minima of the cross section to extrema of the delay and explains why deep minima (dark spots, where integer multiples of electron waves fit the diffractor size) produce time advances while shallow minima (bright spots) produce delays. A 'degree-of-squareness' parameter $s$ deforms the potential from a sphere to a cube, showing that the diffraction pattern emerges purely from the symmetry breaking. The cubic potential model of perfluorocubane provides the concrete target, and the Fourier relation between fringe spacing ($\Delta k = 3.4$ a.u.) and the cube size ($L = 1.7$ a.u.) is the quantitative fingerprint that identifies the fringes as diffraction.

What would settle it

Measure the photoelectron time delay of perfluorocubane (as anion or neutral) with RABBITT or streaking over kinetic energies from threshold to about 1 keV and look for an astroid-shaped pattern of delays and advances with fringes spaced by roughly $\Delta k = 3.4$ a.u. after orientational averaging; if no such pattern appears, or if the sign of the extrema is inverted relative to the cross-section minima, the central claim is contradicted. Alternatively, a full multielectron calculation that removes the fringes would falsify the single-active-electron model.

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Extended reading notes

Core claim

Using a cubic potential calibrated to the LUMO of perfluorocubane (ground-state energy $-2.81$ eV versus the measured $-2.8$ eV), the simulations show that the Eisenbud-Wigner-Smith delay, $\tau(k)$, develops an astroid-shaped diffraction profile in the polar angular map of photoemission. Delays appear near $\vartheta = n\pi/2$ and advances near $\vartheta = (2n+1)\pi/4$, mirroring shallow and deep minima of the cross section. The mechanism is captured by the identity $\tau \sim (RI' - R'I)/\sigma$, where $R$ and $I$ are the real and imaginary parts of the dipole matrix element and $\sigma$ the cross section: a cross-section minimum becomes an extremum of the delay, with the sign determining advance or delay. After angular and azimuthal averaging, fringes with momentum spacing $\Delta k = 3.4$ a.u. survive, and the reciprocal $2\pi/\Delta k = 1.85$ a.u. matches the cubic potential size $L = 1.7$ a.u., identifying the pattern as diffraction from the cube. The resulting temporal diffractogram shows delays and advances growing consistently to about ±100 as over an energy range up to 1 keV.

Load-bearing premise

The load-bearing premise is that a single-active-electron potential with cubic symmetry, matched only to the LUMO energy of perfluorocubane, faithfully represents the photoionization dynamics; if multielectron effects, the fluorine substituents, or deviations from ideal cubic symmetry dephase the electron waves, the predicted ±100 as patterns could wash out.

Editorial extensions

If this is right

  • Diffraction in photoionization is no longer limited to intensity: the EWS time delay itself carries regular angular and energy fringes, and these fringes are robust to orientational averaging.
  • A pump-probe measurement on a cubic molecule such as perfluorocubane should see a time-delay diffractogram with fringes spaced by about $\Delta k = 3.4$ a.u., corresponding to the molecule's size.
  • The sign of the fringe—delay versus advance—maps onto whether the emission direction hits a bright spot or a dark spot of the diffraction pattern, giving a clock-based readout of the underlying interference condition.
  • The pattern extends up to about 1 keV and grows to roughly ±100 as after azimuthal averaging, within reach of current RABBITT and streaking setups.
  • Similar symmetry-induced temporal diffraction should occur in photoionization from other molecules with stable symmetries, not just cubes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • By analogy with the paper's square-to-cube deformation, the same temporal-diffraction mechanism could apply to other Platonic or quasi-symmetric targets, and the angular location of delays versus advances could serve as a symmetry classifier for unknown molecular cages.
  • The paper does not include multielectron or correlation effects, so a natural next step would be a full multielectron calculation or measurement to test whether the ±100 as patterns survive beyond the single-active-electron model; the cubic symmetry may protect the qualitative fringes even if magnitudes shift.
  • The identity $\tau \sim (RI' - R'I)/\sigma$ suggests that any system whose cross section has sharp diffraction minima will also show time-delay extrema, so existing synchrotron measurements of structured cross sections could be re-examined for predicted delay features.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper predicts Eisenbud-Wigner-Smith (EWS) time delays in single-photon ionization from a model cubic potential intended to represent the delocalized LUMO/HOMO electron of perfluorocubane (C8F8 / C8F8⁻). The authors solve the single-active-electron Schrödinger equation in a potential of cubic symmetry, compute dipole matrix elements in the length gauge, and take the energy derivative of the phase to obtain the EWS delay. They present two-dimensional maps of cross section, phase, and time delay as functions of photoelectron kinetic energy and emission angle, showing diffraction fringes, an astroid-shaped minimum profile, and alternating positive/negative delay substructures within ±100 as. After averaging over Euler angles and the photoelectron azimuthal direction, the authors find that discernible delay/advance patterns remain, and they propose that these should be observable in RABBITT or streaking experiments. The model is calibrated only by matching the ground-state energy E0 = −2.81 eV to the LUMO energy −2.8 eV of C8F8; all potential parameters and numerical details are relegated to the Supplemental Material.

Significance. If the prediction is robust, this would be the first proposal of angular- and energy-resolved diffraction patterns in photoionization time delays for a non-spherical molecular target, and it would provide a concrete, testable target for attosecond chronoscopy on a recently synthesized molecule. The paper has clear strengths: the physical motivation is compelling, the use of a tunable sphere-to-cube shape parameter provides a clean numerical experiment, and the presentation in terms of molecular-frame diffractograms is experimentally oriented. The claim of sub-100 as delay/advance motifs that survive angular averaging is falsifiable and would be a valuable benchmark if confirmed. However, the current manuscript does not yet establish the quantitative reliability of these predictions because the model potential is unspecified in the main text, no convergence or sensitivity analysis is presented, and the only validation is a single bound-state energy.

major comments (4)
  1. [Model potential and Supplemental Material (SM [32])] The manuscript repeatedly defers the definition of the model potential, the numerical method, and supporting figures to the Supplemental Material, which is not included in the submitted manuscript. The main text states only that 'A potential with cubic symmetry is adopted' and that 'Details of the theory and computation are given in SM [32]'; no parameters such as well depth, edge sharpness, or the form of the s-parameter interpolation appear in the main text. Without the potential specification and the numerical parameters, the calculation cannot be reproduced and the quantitative values of the EWS delay cannot be assessed. The authors must provide the SM as part of the review package or move the essential potential and grid parameters into the main text.
  2. [Calibration of the model potential] The only quantitative check is the ground-state energy E0 = −2.81 eV matched to the LUMO energy −2.8 eV [30]. This fixes one combination of well depth and size but leaves the potential's spatial shape, edge diffuseness, and angular corrugation unconstrained. The EWS delay is the energy derivative of the continuum phase, and the diffraction substructure of ±100 as is controlled by the partial-wave composition of the final state, which is highly sensitive to these unconstrained features. A realistic molecular potential with smooth C–C and C–F interactions, or a final-state potential of the neutral or cationic target, could significantly dephase the partial waves and wash out the predicted delay/advance pattern. The authors should provide a sensitivity study varying the potential depth, size, and smoothness within ranges consistent with E0 and L, and show how τ(k, ϑ) changes as the cube edges are smoothed or the potential is modified.
  3. [Eq. (2)-(3) and Fig. 3] The consistency check that the fringe spacing Δk = 3.4 a.u. gives 2π/Δk = 1.85 a.u. ≈ L = 1.7 a.u. is presented as support for the diffraction interpretation. Since the model potential is a cube of size L, this relation is essentially fixed by the input geometry; it confirms the model is behaving as a diffractor but does not independently validate the model or the predicted time-delay substructure. The paper should explicitly state that this is a consistency check, not a parameter-free prediction, and that the predictive content lies in the amplitude, angular dependence, and survival after averaging of the ±100 as features.
  4. [Discussion following Eq. (3)] The statement 'a minimum in cross section will translate to an extremum in the time profile' is not a rigorous consequence of τ = (RI′ − R′I)/σ. An extremum of τ occurs when dτ/dE = 0, which is not generally equivalent to a minimum of σ; the sign of the numerator determines whether the feature is a delay or an advance, but the correlation with cross-section minima is an observed pattern, not a general theorem. The authors should temper this claim and support it with the specific numerical data of Fig. 2(c).
minor comments (5)
  1. [Fig. 2 caption and text] In the paragraph describing Fig. 2, the sentence 'Fig. 2(c) for time delay, the energy gradient of the phase in (b), mimics [36] the cross section image in (c)' should refer to panel (a), not panel (c), for the cross section.
  2. [Eq. (3)] The notation σ in Eq. (3) is not defined in the main text; it should be identified as the squared modulus of D, e.g., σ = |D|², to make the equation self-contained.
  3. [Section on degree-of-squareness parameter s] The parameter s is introduced only by reference to Fig. S3 in the SM; a one-sentence definition in the main text (for instance, how the shape interpolates between sphere and cube) would improve readability.
  4. [Abstract and introduction] The text contains a typo: 'perflurocubane' should be 'perfluorocubane' in the introduction.
  5. [Experimental outlook] The sentence 'For a free-oriented molecule, measurements will automatically incorporate angular averaging' is vague; it would be clearer to state that random molecular orientation in a gas-phase or matrix sample leads to an orientational average that the authors implement via Euler-angle averaging, and to discuss partial alignment if applicable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the cubic-symmetry diffraction patterns are computed outputs of an explicitly adopted model, not reductions of the fitted input.

full rationale

The derivation chain is self-contained and non-circular. The authors adopt a cubic-symmetry single-active-electron potential, calibrate its depth so the ground-state energy matches the C8F8 LUMO (-2.81 eV vs -2.8 eV), solve for the bound and continuum wavefunctions, form the dipole matrix element D, and compute the EWS delay as the energy derivative of its phase. The only fitted parameter is the potential depth, which fixes a relation between depth and volume but does not determine the continuum phase gradient, the angular partial-wave composition, or the diffraction fringe spacing. The observed fringe separation Δk = 3.4 a.u. is checked post hoc against the independently adopted cube size L = 1.7 a.u. (2π/Δk ≈ 1.85 a.u.), not tuned to reproduce the delay pattern. The relation between cross-section minima and time-delay extrema is explicitly derived in Eq. (3), τ ∼ (RI′−R′I)/σ, and the statement that the time-delay image mimics the cross section is attributed to prior external work [36]; the time-delay pattern is therefore presented as a computed consequence of the amplitude, not as a renamed input. The cubic symmetry of the output is indeed inherited from the cubic symmetry of the input, but the specific energy-dependent positions, astroid shape, and ±100 as magnitudes are nontrivial computational results rather than definitions. Self-citations to earlier fullerene diffraction and method papers [22–24,27,35,38,45] are not load-bearing: the present cubic-molecule result comes from the current calculation, and those citations are published, externally checkable studies rather than an unverified uniqueness claim. Model realism (potential smoothness, multielectron effects, rotational averaging) is a correctness risk, not a circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a model potential with several hand-chosen parameters (depth, size, shape) and the single-active-electron approximation. No new physical entities are introduced. The diffraction pattern is a direct consequence of the imposed cubic symmetry, so the model must be validated against more realistic calculations or experiment.

free parameters (3)
  • Model potential depth = -2.81 eV (tuned to match C8F8 LUMO at -2.8 eV)
    The depth of the cubic potential is chosen so the computed ground state energy matches the DFT LUMO energy reported in Ref. [30]. This is a calibration, not a first-principles parameter.
  • Degree-of-squareness parameter s = 1 (cubic limit)
    The paper varies s from sphere (0) to cube (1) following Ref. [33] and presents the cubic case. The value s=1 is chosen by hand from the molecular symmetry, not from data.
  • Cubic potential size L = 1.7 atomic units
    The size of the potential is set to the molecular scale; the diffraction fringe spacing (2π/Δk = 1.85 a.u.) is checked against this value as a consistency test, not used as a fit.
assumptions (4)
  • standard math Time-independent Schrödinger equation with single-active-electron Hamiltonian in length gauge (Eq. 1)
    The calculation solves one-electron quantum mechanics in a fixed model potential.
  • domain assumption Single-active-electron approximation
    The dynamics is reduced to one electron; multielectron correlation, channel coupling, and relaxation are ignored. No validation for C8F8 is provided.
  • ad hoc to paper The cubic model potential is a valid representation of the anion HOMO of perfluorocubane
    The potential is adopted to reproduce the delocalized cubic character of the orbital and the LUMO energy, but it is not derived from the molecular electronic structure.
  • domain assumption EWS delay from the dipole phase is a meaningful proxy for RABBITT/streaking measurable delays
    The paper acknowledges that probe-induced continuum-continuum delays must be added (Ref. [38]); the EWS delay is used as the principal observable.

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Cite this review

Pith. "Pith review of Diffraction patterns in attosecond photoionization time delay." pith.science (2026). https://pith.science/paper/TI7B4MCS

@misc{pith2026241208204,
  author       = {Pith},
  title        = {Pith review of: Diffraction patterns in attosecond photoionization time delay},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TI7B4MCS}},
  note         = {Machine review of arXiv:2412.08204}
}
abstract

Upon absorbing a photon, the ionized electron sails through the target force field in attoseconds to reach free space. This navigation probes details of the potential landscape that get imprinted into the phase of the ionization amplitude. The Eisenbud-Wigner-Smith (EWS) time delay, the energy derivative of this phase, provides the navigation time relative to the time of the electron's ``free'' exit. This time is influenced by the diffraction of the electron from the potential landscape, offering structural and dynamical information about interactions. If the potential has an intrinsic symmetry, a regular pattern in the time delay, including subpatterns of delays and advances, may occur from the diffraction process. The recent synthesis of a polyhedral fluorocarbon instigates the current study of photoionization from a cubic molecule. Our simulation of the EWS delay unravels rich diffraction motifs within $\pm$100 attoseconds in both energy and angular distributions. Averaging over the Euler angles from the laboratory to the molecular frame and over the photoelectron azimuthal direction indicates that the pattern should be discernible in ultrafast chronoscopy. The study benchmarks diffraction in molecular photoionization as a fundamental process which can be experimentally accessed through ultrafast time delay.

Figures

Figures reproduced from arXiv: 2412.08204 by the authors.

Figure 1
Figure 1. Contour plots for HOMO and LUMO of C8F8 and HOMO of C8F − 8 computed at the B3LYP/6-311++G(d,p) level of theory and shown with energies. The current study ratifies this expectation. Our predic￾tion of multidimensional diffraction should motivate ex￾periments to capture the resulting patterns. While the photoelectron intensity can be accessed with synchrotron lights [28, 29], the more contemporary ultrafast measure￾m… view at source ↗
Figure 2
Figure 2. Polar angular distribution images, with photoelectron kinetic energy plotted in the radial direction, of cross [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Extended energy polar angular distribution [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Cross section and time delay polar images for different choice of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Diffractograms of cross section (a) and time [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

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Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [36]

    Kheifets, Meng Han, Kiyoshi Ueda, and Hans Jakob Wörner, Relation between photoionisation cross sections and attosecond time delays, New J

    Jia-Bao Ji, Anatoli S. Kheifets, Meng Han, Kiyoshi Ueda, and Hans Jakob Wörner, Relation between photoionisation cross sections and attosecond time delays, New J. Phys. 26, 093014 (2024)

    work page 2024

  2. [32]

    See Supplemental Material at url for details of the method- ologies and computation of photoionization time delay , which includes Refs. [33–35]

    work page

  3. [30]

    Masafumi Sugiyama, Midori Akiyama, Yuki Yonezawa, Kenji Komaguchi, Masahiro Higashi, Kyoko Nozaki, and Takashi Okazoe, Electron in a cube: Synthesis and characterization of perfluorocubane as an electron acceptor , Science 377, 756– 759 (2022)

    work page 2022

  4. [1]

    Golubev, and Mohammed Th

    Dandan Hui, Husain Alqattan, Mohamed Sennary , Nikolay V . Golubev, and Mohammed Th. Hassan,Attosecond electron microscopy and diffraction, Sci. Adv. 10, eadp5805 (2024)

    work page 2024

  5. [2]

    Zilong Tang, Ramesh Jarupula, and Haiwang Yong, Pushing the limits of ultrafast diffraction: Imaging quantum coherences in isolated molecules, iScience 27, 110705 (2024)

    work page 2024

  6. [3]

    Månsson, Andrea Trabattoni, A

    Vincent Wanie, Sergey Ryabchuk, Lisa Colaizzi, Mara Galli, Erik P . Månsson, Andrea Trabattoni, A. Barzana Wahid, Johannes Hahne, Antonio Cartella, Karthik Saraswathula, Fabio Frassetto, D. Passos Lopes, Rafael Martínez Vázquez, Roberto Osellame, Luca Poletto, François Légaré, Mauro Nisoli, and Francesca Calegari, A flexible beamline combin- ing XUV attos...

    work page 2024

  7. [4]

    Francesca Calegari, Giuseppe Sansone, Salvatore Stagira, Caterina Vozzi, and Mauro Nisoli,Advances in attosecond sci- ence, J. Phys. B 49, 062001 (2016)

    work page 2016

  8. [5]

    P . M. Paul, E. S. Toma, P . Breger, G. Mullot, F . Augé, Ph. Bal- cou, H. G. Muller, and P . Agostini,Observation of a train of at- tosecond pulses from high harmonic generation, Science 292, 1689–1692 (2001)

    work page 2001

Show all 46 references
  1. [6]

    Klünder, J

    K. Klünder, J. M. Dahlström, M. Gisselbrecht, T . Fordell, M. Swoboda, D. Guénot, P . Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and Anne L’Huillier,Probing single-photon ionization on the attosecond time scale , Phys. Rev. Lett. 106, 143002 (2011)

    2011

  2. [7]

    Kienberger, E

    R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuška, V . Yakovlev, F . Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F . Krausz, Atomic transient recorder, Nature 427, 817–821 (2004)

    2004

  3. [8]

    Seiffert, Q

    L. Seiffert, Q. Liu, S. Zherebtsov, A. Trabattoni, P . Rupp, M. C. Castrovilli, M. Galli, F . Süssmann, K. Wintersperger, J. Stierle, G. Sansone, L. Poletto, F . Frassetto, I. Halfpap, V . Mondes, C. Graf, E. Rühl, F . Krausz, Mauro Nisoli, Francesca Calegari, and M. F . Kling...

    2017

  4. [9]

    Champenois, Louis F

    Taran Driver, Miles Mountney , Jun Wang, Lisa Ortmann, Andre Al-Haddad, Nora Berrah, Christoph Bostedt, Elio G. Champenois, Louis F . DiMauro, Joseph Duris, Douglas Gar- ratt, James M. Glownia, Zhaoheng Guo, Daniel Haxton, Erik Isele, Igor Ivanov, Jiabao Ji, Andrei Kamalov, Si...

    2024

  5. [10]

    Ahmadi, E

    H. Ahmadi, E. Plésiat, M. Moioli, F . Frassetto, L. Poletto, P . Decleva, C. D. Schröter, T . Pfeifer, R. Moshammer, A. Pala- cios, Fernando Martin, and Giuseppe Sansone, Attosecond photoionisation time delays reveal the anisotropy of the molec- ular potential in the recoil fr...

    2022

  6. [11]

    Xiaochun Gong, Saijoscha Heck, Denis Jelovina, Conaill Perry , Kristina Zinchenko, Robert Lucchese, and Hans Jakob Wörner,Attosecond spectroscopy of size-resolved water clusters, Nature 609, 507–511 (2022)

    2022

  7. [12]

    Adv.7, eabj8121 (2021)

    Saijoscha Heck, Denitsa Baykusheva, Meng Han, Jia-Bao Ji, Conaill Perry , and Hans Jakob Wörner,Attosecond interferom- etry of shape resonances in the recoil frame of CF4, Sci. Adv.7, eabj8121 (2021)

    2021

  8. [13]

    Saijoscha Heck, Meng Han, Denis Jelovina, Jia-Bao Ji, Conaill Perry , Xiaochun Gong, Robert Lucchese, Kiyoshi Ueda, and Hans Jakob Wörner,Two-center interference in the photoionization delays of Kr 2, Phys. Rev. Lett. 129, 133002 (2022)

    2022

  9. [14]

    thesis, Princeton University (1948)

    Leonard Eisenbud, The formal properties of nuclear collisions, Ph.D. thesis, Princeton University (1948)

    1948

  10. [15]

    Wigner,Lower limit for the energy derivative of the scattering phase shift, Phys

    Eugene P . Wigner,Lower limit for the energy derivative of the scattering phase shift, Phys. Rev. 98, 145–147 (1955)

    1955

  11. [16]

    Smith,Lifetime matrix in collision theory , Phys

    Felix T . Smith,Lifetime matrix in collision theory , Phys. Rev. 118, 349–356 (1960)

    1960

  12. [17]

    Nia, and José A

    Ambarneil Saha, Shervin S. Nia, and José A. Rodríguez,Elec- tron diffraction of 3D molecular crystals , Chem. Rev. 122, 13883–13914 (2022)

    2022

  13. [18]

    69, edited by Louis F

    Kasra Amini and Jens Biegert, Ultrafast electron diffraction imaging of gas-phase molecules, in Advances in Atomic, Molec- ular, and Optical Physics, Vol. 69, edited by Louis F . DiMauro, Hélène Perrin, and Susanne F . Yelin (Academic Press, 2020), pp. 163–231

    2020

  14. [19]

    Aguilar, Jess Tate, and Miguel José Yacamán, Advances in the electron diffraction characterization of atomic clusters and nanoparticles, Nanoscale Adv

    Arturo Ponce, Jeffery A. Aguilar, Jess Tate, and Miguel José Yacamán, Advances in the electron diffraction characterization of atomic clusters and nanoparticles, Nanoscale Adv. 3, 311– 325 (2021)

    2021

  15. [20]

    Kienzle and Laurence D

    Danielle M. Kienzle and Laurence D. Marks,Surface transmis- sion electron diffraction for SrTiO 3 surfaces, CrystEngComm 14, 7833–7839 (2012)

    2012

  16. [21]

    Gorelik, Ute Kolb, Lukáš Palatinus, Philippe Boullay , Sven Hovmöller, and Jan Pieter Abrahams, 3D Electron diffraction: The nanocrys- tallography revolution, ACS Cent

    Mauro Gemmi, Enrico Mugnaioli, Tatiana E. Gorelik, Ute Kolb, Lukáš Palatinus, Philippe Boullay , Sven Hovmöller, and Jan Pieter Abrahams, 3D Electron diffraction: The nanocrys- tallography revolution, ACS Cent. Sci. 5, 1315–1329 (2019)

    2019

  17. [22]

    Chakraborty , Mohamed E.-A

    Andy Rüdel, Rainer Hentges, Uwe Becker, Himadri S. Chakraborty , Mohamed E.-A. Madjet, and Jan M. Rost,Imag- ing delocalized electron clouds: Photoionization of C 60 in Fourier reciprocal space, Phys. Rev. Lett. 89, 125503 (2002)

    2002

  18. [23]

    McCune, Mohamed E.-A

    Matthew A. McCune, Mohamed E.-A. Madjet, and Himadri S. Chakraborty ,Reflective and collateral photoionization of an atom inside a fullerene: Confinement geometry from reciprocal spectra, Phys. Rev. A 80, 011201(R) (2009)

    2009

  19. [24]

    Anstine, Gopal Dixit, Mo- hamed El-Amine Madjet, and Himadri S

    Maia Magrakvelidze, Dylan M. Anstine, Gopal Dixit, Mo- hamed El-Amine Madjet, and Himadri S. Chakraborty , At- tosecond structures from the molecular cavity in fullerene pho- toemission time delay, Phys. Rev. A 91, 053407 (2015)

    2015

  20. [25]

    For more details, see Ref.[26]

    For example, the angular dependence of the electric dipole differential cross section for the photoionization of a spheri- cally symmetric target depends on the Legendre polynomial P2(cosθ ) by choosing the outgoing electron direction as the axis of quantization so thatθ is th...

  21. [26]

    J. W . Cooper,Photoionization from Outer Atomic Subshells. A Model Study, Phys. Rev. 128, 681–693 (1962)

    1962

  22. [27]

    Aiswarya, Rasheed Shaik, Jobin Jose, Hari R

    R. Aiswarya, Rasheed Shaik, Jobin Jose, Hari R. Varma, and Himadri S. Chakraborty , Simultaneous real and momentum space electron diffraction from a fullerene molecule, Phys. Rev. Lett. 133, 033002 (2024)

    2024

  23. [28]

    Quitián-Lara, Patrick Hemberger, John Bozek, Graham Worth, and Ingo Fischer, Photoelectron spectroscopy and dissociative photoionization of fulminic acid, HCNO, J

    Marius Gerlach, Barry Mant, Tobias Preitschopf, Emil Karaev, Dennis Mayer, Heidy M. Quitián-Lara, Patrick Hemberger, John Bozek, Graham Worth, and Ingo Fischer, Photoelectron spectroscopy and dissociative photoionization of fulminic acid, HCNO, J. Chem. Phys. 158, 134308 (2023)

    2023

  24. [29]

    Garcia, Christian Alcaraz, Jean-Christophe Loison, and Ingo Fischer, Photoelectron spectrum of the pyridyl radical , Phys

    Emil Karaev, Marius Gerlach, Katharina Theil, Gustavo A. Garcia, Christian Alcaraz, Jean-Christophe Loison, and Ingo Fischer, Photoelectron spectrum of the pyridyl radical , Phys. Chem. Chem. Phys. 26, 17042–17047 (2024)

    2024

  25. [31]

    M. J. Frisch, G. W . Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V . Barone, G. A. Peters- son, H. Nakatsuji, et al., Gaussian 16, Rev. C.01 (Gaussian, Inc., Wallingford CT , 2016)

    2016

  26. [33]

    Fernández Guasti and M

    M. Fernández Guasti and M. De La Cruz Heredia,Diffraction Pattern of a Circle /square Aperture, J. Mod. Opt. 40, 1073- 1080 (1993)

    1993

  27. [34]

    B. R. Johnson, The renormalized Numerov method applied to calculating bound states of the coupled-channel Schrödinger equation, J. Chem. Phys. 69, 4678–4688 (1978)

    1978

  28. [35]

    thesis, Technische Universität Dresden (2023)

    Sajad Azizi, Three aspects of photo-ionization in ultrashort pulses, Ph.D. thesis, Technische Universität Dresden (2023)

    2023

  29. [37]

    Xiaochun Gong, Wenyu Jiang, Jihong Tong, Junjie Qiang, Peifen Lu, Hongcheng Ni, Robert Lucchese, Kiyoshi Ueda, and Jian Wu, Asymmetric attosecond photoionization in molecular shape resonance, Phys. Rev. X 12, 011002 (2022)

    2022

  30. [38]

    Castrovilli, Mara Galli, Qingcao Liu, Erik P

    Shubhadeep Biswas, Andrea Trabattoni, Philipp Rupp, Maia Magrakvelidze, Mohamed El-Amine Madjet, Umberto De Giovannini, Mattea C. Castrovilli, Mara Galli, Qingcao Liu, Erik P . Månsson, Johannes Schötz, Vincent Wanie, François Légaré, Pawel Wnuk, Mauro Nisoli, Angel Rubio, Him...

    arXiv

  31. [39]

    Rost, Proper time delays measured by optical streaking, Phys

    Ulf Saalmann and Jan M. Rost, Proper time delays measured by optical streaking, Phys. Rev. Lett. 125, 113202 (2021)

    2021

  32. [40]

    DeVine, M.L

    J.A. DeVine, M.L. Weichman, C. Xie, M.C. Babin, M.A. John- son, J. Ma, H. Guo, and D.M. Neumark,Autodetachment from vibrationally excited vinylidene anions, J. Phys. Chem. Lett.9, 1058–1063 (2018)

    2018

  33. [41]

    Bragg, J.R.R

    A.E. Bragg, J.R.R. Verlet, A. Kammrath, O. Cheshnovsky , and 7 D.M. Neumark, Hydrated electron dynamics: From clusters to bulk, Science 306, 669–671 (2004)

    2004

  34. [42]

    Bragg, R

    A.E. Bragg, R. Wester, A.V . Davis, A. Kammrath, and D.M. Neumark, Excited-state detachment dynamics and rotational coherences of C − 2 via time-resolved photoelectron imaging , Chem. Phys. Lett. 376 767—775 (2003)

    2003

  35. [43]

    Guilherme Ferreira Martins, Thiago Sampaio Castro, and Daví Alexsandro Cardoso Ferreira, Theoretical investigation of anion perfluorocubane, J. Mol. Model. 29, 319 (2023)

    2023

  36. [44]

    Abhik Ghosh and Jeanet Conradie, The perfluoro cage effect: A search for electron-encapsulating molecules, ACS Omega 8, 4972–4975 (2023)

    2023

  37. [45]

    Chakraborty ,Attosecond time delay in valence photoionization and photorecombination of argon: A time-dependent local-density-approximation study, Phys

    Maia Magrakvelidze, Mohamed El-Amine Madjet, Gopal Dixit, Misha Ivanov, and Himadri S. Chakraborty ,Attosecond time delay in valence photoionization and photorecombination of argon: A time-dependent local-density-approximation study, Phys. Rev. A 91, 063415 (2015)

    2015

  38. [46]

    Deep Mukherjee, Upendra Harbola, and Shaul Mukamel, Ionization pathway interference in photoionization time delays in molecules, J. Phys. Chem. Lett. 15, 3866–3870 (2024)

    2024

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