Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Temperature and mean axial momentum vs. laser intensity of electrons released from O$_2$ by an 800 nm ultrashort pulsed laser

T0 review · 3 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A two-parameter correction to strong-field ionization yields the thermalized temperature and mean axial momentum of O2 electrons vs peak intensity, best in the Keldysh range 0.82-1.30.

desk verdict A useful, honestly-scoped semi-empirical model giving filament simulators an initial electron temperature and a genuinely new axial-momentum estimate—but the momentum estimate leans on an unvalidated cos²φ angular ansatz and should be treated as uncertain until checked. read the letter →

arxiv 2509.10986 v2 pith:CYCKFATB submitted 2025-09-13 physics.plasm-ph physics.atom-phphysics.optics

Edward L. Ruden This is my paper · ORCID
classification physics.plasm-phphysics.atom-phphysics.optics
keywords strong-fieldionizationelectronrescatteringabove-thresholdlaserfilamenttemperatureaxialmomentumO2semi-empiricalmodel
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 builds a semi-empirical model that turns published electron kinetic-energy spectra of O2 ionized by 800 nm laser pulses into two practical outputs: the temperature T the released electrons would have once thermalized, and their average momentum along the laser direction . It starts from a nonadiabatic strong-field approximation and fixes two known mismatches with data—an unobserved low-energy surge and a missing high-energy plateau—by imposing a spectral ceiling and an energy rescaling, interpreted as the effects of electron recombination and rescatter off the parent ion. Rescatter kinematics then converts the fitted spectrum, together with an assumed cos^2 angular emission profile, into as a function of peak intensity. The result is designed to supply initial conditions for electrodynamic fluid simulations of air filaments, where both the electron temperature and the axial current matter for predicting microwave emission.

What carries the argument

The engine is a nonadiabatic strong-field approximation (SFA0) that computes, for each intracycle ionization time, the most probable ionization path, the post-optical transverse momentum p_fr, and—as a second-order correction—the axial momentum p_fz = p_fr^2/(2mc) from the laser's magnetic field. Two empirical patches turn SFA0 into SFA2: a ceiling at U_c = 1.60 eV (calling the result SFA1) and an energy rescaling by ζ = 2.067. For the axial average, the paper assumes the post-optical angular distribution Φ_φ = Φ_x cos^2 φ, with the temperature at angle φ stitched between T_x and T* by Eq. 15.2; this converts the angle-averaged temperature measurements into the dominant momentum term ⟨p_2fz⟩

What would settle it

Measure the angle-resolved photoelectron spectrum of O2 at 800 nm for peak intensities near 100 TW/cm2 (γ0≈1). If the emission pattern at post-optical energies of a few eV has an angular width much broader or narrower than cos^2 φ, or shows a second lobe perpendicular to the polarization, the predicted mean axial momentum—especially the dominant term ⟨p_2fz⟩_a = k_B(18T_x+45T_*)/(70c)—would shift by tens of percent. A direct check of the full prediction is to compare the implied axial current from a filament with the observed time-integrated microwave emission.

Watch

Extended reading notes

Core claim

The paper's central claim is that the post-optical state of electrons from O2 can be captured by a two-parameter deformation of the standard strong-field approximation: a ceiling at 1.60 eV suppresses the spurious low-energy surge, and a factor 2.067 stretches the spectrum to match the measured 4π-averaged temperature. Given that fitted spectrum, classical kinematics of an electron returning to and rescattering off its parent ion—plus the magnetic-field term p_z = p_r^2/(2mc) for each electron—determine the mean axial momentum <p_fz> without additional free parameters. The model is most dependable for Keldysh parameter γ0 between 0.82 and 1.30, where T is an interpolation between good data p

Load-bearing premise

The entire axial-momentum estimate rests on the assumed post-optical angular distribution of ionized electrons being proportional to cos^2 of the angle from the polarization axis, with no emission perpendicular to the laser's field direction—a shape the paper adopts from visual inspection of published angular spectra rather than from a fit.

Editorial extensions

If this is right

  • If the model is correct, air-filament simulations can initialize electrons with both a temperature and an axial drift velocity, enabling direct computation of the axial current that produces the observed microwave and THz emission.
  • For O2 at 800 nm, the predicted T vs I0 curve is credible between γ0=0.82 and 1.30; in this window the mean axial momentum ⟨p_fz⟩ is a derived quantity, not a fitted one, so it carries the same empirical support as the temperature data.
  • The rescatter mechanism explains the high-energy plateau and the missing low-energy surge in one stroke: electrons born near the peak of the field return to the parent ion and either recombine (removing low-energy electrons) or scatter to high energies (creating the plateau and boosting axial momentum).
  • The circular-polarization case is worked out within SFA0 but cannot yet be constrained by data; the linear-polarization results stand alone until angle- and energy-resolved spectra for ε=1 appear.
  • The framework is transferable: the same rescatter kinematics, with the same two fitting parameters re-determined, could be applied to other gases (e.g., N2) and other wavelengths where angular spectra exist.

Reading between the lines

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

  • Because the cos^2 φ angular profile is the load-bearing shape assumption, a direct measurement of the angle-resolved spectrum for O2 at γ0 ≈ 1 would either validate or correct the ⟨p_fz⟩ prediction; the closed-form result ⟨p_2fz⟩_a = k_B(18T_x+45T_*)/(70c) makes the sensitivity easy to compute.
  • The paper leaves implicit that the same two-parameter model, with the identity p_fz = p_fr^2/(2mc), also predicts the radial variation of the axial momentum across a focused beam profile; a spatially resolved simulation could test against the observed ring-like radiation patterns.
  • The suggested identification of the very-low-energy surge (seen at γ0 ≈ 3.8) with electrons that fail to return to the parent ion is testable at even lower intensities, where the return condition U_f > U_f,min should produce a sharp onset of spectral suppression.
  • One could extend the rescatter-kick integration to include a molecular-orientation dependence of the ionization rate (ignored in the paper) and ask whether the added angular structure changes ⟨p_fz⟩ by more than the current uncertainty.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents a semi-empirical strong-field-approximation model for the thermalized temperature T and mean axial momentum <p_fz> of electrons released from O2 by 800 nm pulses, as functions of peak intensity I0. The SFA0 model of Appendix A provides kinetic-energy spectra and momentum components; two phenomenological parameters (a low-energy ceiling U_c and an energy rescaling ζ) are introduced to match published angle-resolved spectra and temperatures. The resulting T2 is an interpolation between T* at γ0=0.82 and 1.30. A classical rescatter model with an angular distribution Φφ∝cos²φ is then used to convert the temperature model into <p_fz>, with a correction α for the spatiotemporal pulse profile. The intended use is initial conditions for fluid simulations of air filaments.

Significance. If the model is accepted as a semi-empirical interpolation, it fills a practical gap: providing order-of-magnitude initial conditions for T and axial momentum for filament simulations, with a detailed and transparent derivation (Appendix A) and honest scoping of the temperature curve's validity range. The paper does not overclaim knowledge where data are absent, and it explicitly identifies the multiphoton regime as outside the model. However, the axial-momentum leg rests on an unvalidated angular-distribution ansatz and on an unquantified recombination weighting, so the deliverable needs additional sensitivity analysis before it can be used reliably. The paper includes no code, but the algebraic derivations are sufficiently detailed to be checked.

major comments (3)
  1. [Section III, Eqs. (12)–(16) and (19)–(20)] The angular distribution Φφ=Φx cos²φ and the associated Tφ ansatz in Eq. (15.2) are chosen by visual inspection of Okunishi et al., not fitted. This ansatz controls the dominant term <p_{2fz}>_a (Eq. 16) and the rescatter integral <p_{2fz}>_b (Eqs. 19–20). A different but compatible angular profile would shift <p_fz> by tens of percent, and no uncertainty estimate is given. Please fit the angular model to the angle-resolved data with residuals, or report a sensitivity scan (e.g., Φφ∝cos^{2n}φ, n=1,2,3). The T_+ check in Eq. (18) constrains only one moment and is insufficient.
  2. [Section II, Fig. 2 and text after Eq. (17)] U_c=1.60 eV and ζ=2.067 are chosen so that T2 matches T* at γ0=0.82 and 1.30; T2 is therefore an interpolation between two data points, not an independent prediction. The paper states this, but the abstract and title present a full T(I0) curve without uncertainty. Add explicit interpolation/extrapolation regions and error bands, and qualify the abstract's scope claim. This is central because the stated purpose is to provide initial conditions for simulations, which require error estimates.
  3. [Section III, Eq. (20)] The τ0 weighting in Eq. (20) uses the bare SF A0 rate W, although the paper argues that recombination suppresses low-energy electrons and alters the effective W. The resulting bias in <p_{2fz}>_b is unquantified; at γ0=1 this term is 0.80×10^-27 kg m/s versus 1.66×10^-27 for <p_{2fz}>_a, so a 20–30% error in Eq. (20) materially changes the total. A bracketing calculation using a recombination-truncated W would establish robustness of the final <p_fz>.
minor comments (6)
  1. [Appendix A.5] 'Lou's method' should be 'Luo's method'.
  2. [References] Reference [2] is cited as 'ArXiv:pending.pending'; update to a complete citation.
  3. [Eq. (4.5)] 'cos2 (τ0(U))' should read 'cos²(τ0(U))'.
  4. [Table 1] Define the superscripts * and † in the table caption; the prose defines them but the table is not self-contained.
  5. [Fig. 2 caption] Specify the axis labels and the scaling factors for U_{2fz} and U_{0fz} explicitly in the caption.
  6. [Throughout] The surname 'K loda' should be 'Kloda'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is openly semi-empirical; the two-point T fit is disclosed and <p_fz> is an independent kinematic estimate.

full rationale

The paper presents a semi-empirical model, not a first-principles prediction. The two adjustable parameters (U_c and ζ) are explicitly fitted to empirical spectra, and the paper itself states that T2 in 0.82≤γ0≤1.30 is 'simply an interpolation between data points' (Sec. II). This is a disclosed calibration, not a hidden reduction of the claimed deliverable to its input. The axial momentum estimate is not fitted to momentum data; it is computed from the calibrated temperatures and an explicit angular distribution ansatz (Φφ∝cos²φ) motivated by Okunishi et al. data. Even if that ansatz is uncertain, it is an additional modeling assumption, not a circular reuse of the target quantity. The self-citations to [1] and [2] are contextual and are not load-bearing for the central calculation; the paper does not rely on a uniqueness theorem or on prior author-derived inputs to force the result. Any algebraic inconsistency in Eq. 16 relative to Eq. 12 is a correctness or typographical concern, not a circularity. Overall, the derivation chain is transparent about which parts are empirical fits and which parts are kinematic estimates.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The model rests on the SFA framework (from Li/Luo), the assumption that two empirical parameters can absorb recombination/rescatter effects, an idealized angular distribution, and several approximations (power-law ionization, linear variation of momentum with intensity) used for pulse averaging. No new physical entities are introduced.

free parameters (4)
  • U_c (SFA1 ceiling energy) = 1.60 eV
    Chosen to suppress the low-energy surge in S0(U) and match published spectra; stated in Sec. II.
  • zeta (SFA2 energy rescaling factor) = 2.067
    Chosen to match T_2 to T_star at gamma0 = 0.82 and 1.30; stated in Sec. II.
  • T_x transition coefficients = 3.10 eV, -0.362 eV per unit gamma0
    Eq. 17; coefficients chosen for continuity between T_1 at gamma0=0.74 and T_2 at gamma0=1.40.
  • mu(gamma0) (ionization power-law exponent) = 4.43 at gamma0=1
    Taken from Guo et al. data; used in Eq. 25 for the alpha(gamma0) pulse-average correction.
assumptions (7)
  • domain assumption Li/Luo strong field approximation based on the most probable tunnel path gives a valid zero-order description of O2 ionization and electron acceleration.
    SFA0 is taken as the baseline throughout; Appx. A reformulates it.
  • domain assumption The plasma is weakly ionized (n << n0), so the free electron density satisfies dn/dt0 = n0 W.
    Stated in the introduction; needed for the ionization rate interpretation.
  • standard math The laser pulse envelope is slowly varying relative to the optical cycle, so E can be treated as constant intracycle.
    Used to separate intracycle dynamics; standard for USPL.
  • ad hoc to paper Electrons released by tunneling start with axial momentum p_z(ts) = -U0/c, a ground-state property ensuring p0z -> 0 as E -> 0.
    Eq. A24; this choice fixes p0z and p_fz; it is a physical hypothesis, not derived from data.
  • ad hoc to paper Two fitting parameters U_c and zeta fully represent the spectral effects of electron recombination with and rescatter off the parent ion.
    Sec. II; this is the key modeling assumption connecting SFA1/SFA2 to the data.
  • ad hoc to paper The angular distribution of post-optical electrons is Phi_phi = Phi_x cos^2 phi (Phi_y = 0), and T_phi is the linear mix in Eq. 15.2.
    Sec. III, Eqs. 13-15; inferred visually from Okunishi et al. plots.
  • domain assumption For pulse averaging, <W>_gamma follows a local power law in I with exponent mu, and <p_2fz>_bgamma varies linearly with I over the pulse.
    Sec. III, Eqs. 21-25; used to compute the alpha(gamma0) correction.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Temperature and mean axial momentum vs. laser intensity of electrons released from O$_2$ by an 800 nm ultrashort pulsed laser." pith.science (2026). https://pith.science/paper/CYCKFATB

@misc{pith2026250910986,
  author       = {Pith},
  title        = {Pith review of: Temperature and mean axial momentum vs. laser intensity of electrons released from O$_2$ by an 800 nm ultrashort pulsed laser},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CYCKFATB}},
  note         = {Machine review of arXiv:2509.10986}
}
abstract

A semi-empirical model is presented for the thermalized temperature $T$ and mean momentum in the direction of laser propagation <$p_{fz}$> of electrons released from O$_{2}$ after the passage of a focused $800$ nm ultrashort pulsed laser pulse vs. peak laser intensity $I_{0}$ to provide initial conditions for electrodynamic fluid simulations. For this, theoretical kinetic energy spectra in different directions are modified with two adjustable parameters representing the effects of electron rescatter off its parent ion during the optical cycle subsequent to ionization. The classical kinematics of rescatter, in conjunction with the spectral fits, is used to estimate <$p_{fz}$>.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ultrashort pulsed laser atmospheric filament properties and microwave radiation inferred from S-band guided wave interaction and self-emission

    physics.plasm-ph 2026-07 unverdicted novelty 6.0 of 10

    Waveguide attenuation plus self-emission yield filament σ, R, and Q(z) across pressures; inversion with ionization models gives I0, T, densities and a radiation-consistent upper bound ν_max ≪ Ohmic ν.

Reference graph

Works this paper leans on

48 extracted references · 1 linked inside Pith · cited by 1 Pith paper

  1. [1]

    rep- resenting the average of intrinsic propertyQ γ (I) of an entire pulse in the vicinity ofI ′ 0 =I 0 may be approxi- mated by Q(I ′

  2. [2]

    24) in order to convert (the now known)Q(I) intoQ γ (I)

    =Q(I 0) + Q(I 0) ∂I0 (I ′ 0 −I 0) (26) one finds that, Q(I 0) Qγ0 (I0) =α[Q(I 0), I0, µ(γ0)] (27) A complication of reverse procedure’s derivation is that α−1 (γ) now appears in the integrand of theQ γ (I) in- tegration (corresponding to the numerator of Eq. 24) in order to convert (the now known)Q(I) intoQ γ (I). This requires that we approximateα(γ) =α(...

  3. [3]

    Li”) and Luo, et al. [13] (“Luo

    SF A forG This appendix presents a reformulation of and expan- sion on the strong field approximation (SF A) of Li, et al. [12] (referred to here as “Li”) and Luo, et al. [13] (“Luo”), based on the most probable tunnel path for molecular ionization and subsequent electron accelera- tion. The vector potentialAand electric fieldEto which an O2 molecule is e...

  4. [4]

    Gas pressure dependence of mi- crowave pulses generated by laser-produced filament plasmas,

    A. Englesbe, J. Elle, R. Reid, A. Lucero, H. Pohle, M. Domonkos, S. Kalmykov, K. Krushelnick, and A. Schmitt-Sody, “Gas pressure dependence of mi- crowave pulses generated by laser-produced filament plasmas,” Optics Letters43, 4953–4956 (2018)

    2018

  5. [5]

    A9, so we base our most probable path on the ex- trema ofGalone

    Most probableG Although prefactorC, likeG, also depends ont i, it does to a much lesser degree than the exponential term in Eq. A9, so we base our most probable path on the ex- trema ofGalone. Fig. A1a shows that the critical (mini- mum) value ofG, which we identify asG=G c att i=t ic, occurs at a local differential extremum forε= 1. Fig- ure A1b, however...

  6. [6]

    residual momentum

    Most probable post-optical and residual momenta The most probable value ofpfr is found by substituting τic into the expression forξof Eq. A10.3, and into theη expressions in Eqs. A12.ξandηso determined are then substituted into Eq. A11.3 and Eq. A11.5. The results are, ε= 1:p fx =p fr sinτ 0 pfy =−p fr cosτ 0 pfr = √2mU0 γ coshτ ic − p sinh2 τic −γ 2 ε= 0...

  7. [7]

    The saddle equation (Eq

    Comparison to Luo’s most probable path method The method for determining the most probable ioniza- tion path in this paper is a two-step process. The saddle equation (Eq. A7) providestwoequations (its real and imaginary parts) that must be satisfied to constrainthree dynamic variables:p fx ,p fy , andt i. These equations are used to derivep fx andp fy tha...

    2024

  8. [8]

    Ionization rate vs. laser intensity deter- mined from ion count vs. peak intensity due to neu- tral gas exposure to an 800 nm ultrashort pulsed laser,

    E. L. Ruden, “Ionization rate vs. laser intensity deter- mined from ion count vs. peak intensity due to neu- tral gas exposure to an 800 nm ultrashort pulsed laser,” (2025). ArXiv:2508.07500 [physics.atom-ph]

    arXiv 2025

Show all 48 references
  1. [9]

    Ultrashort pulsed laser atmospheric filament intrin- sic properties and microwave emission inferred from S- 15 band guided wave interaction and self-emission,

    E. L. Ruden, J. E. Wymer, J. A. Elle, A. C. Englesbe, A. P. Lucero, E. A. Thornton, and A. Schmitt-Sody, “Ultrashort pulsed laser atmospheric filament intrin- sic properties and microwave emission inferred from S- 15 band guided wave interaction and self-emission,” (2025). ArX...

    2025

  2. [10]

    Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients,

    E. N. Pusateri, H. E. Morris, E. M. Nelson, and W. Ji, “Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients,” J. Geophys. Res. Atmos.120, 7300–7315 (2015)

    2015

  3. [11]

    Ionization in the field of a strong elec- tromagnetic wave,

    L. V. Keldysh, “Ionization in the field of a strong elec- tromagnetic wave,” Soviet Physics JETP20, 1307–1314 (1965)

    1965

  4. [12]

    Ultrabroadband microwave radiation from near- and mid-infrared laser-produced plasmas in air,

    A. Englesbe, J. Elle, R. Schwartz, T. Garrett, D. Wood- bury, D. Jang, K. Kim, H. Milchberg, R. Reid, A. Lucero, D. Gordon, R. Phillips, S. Kalmykov, and A. Schmitt- Sody, “Ultrabroadband microwave radiation from near- and mid-infrared laser-produced plasmas in air,” Phys. Rev...

    2021

  5. [13]

    Forward THz radiation emission by femtosecond filamentation in gases: theory and ex- periment,

    C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and ex- periment,” New J. of Phys.10, 013015 (2008)

    2008

  6. [14]

    High-power, high-intensity laser propagation and interactions,

    P. Sprangle and B. Hafizi, “High-power, high-intensity laser propagation and interactions,” Phys. Plasmas21, 055402 (2014)

    2014

  7. [15]

    Generation of ra- dio frequency radiation by femtosecond filaments,

    T. Garrett, J. Elle, M. White, R. Reid, A. Englesbe, R. Phillips, P. Mardahl, E. Thornton, J. Wymer, A. Jan- icek, O. Sale, and A. Schmitt-Sody, “Generation of ra- dio frequency radiation by femtosecond filaments,” Phys. Rev. E104, L063201 (2021)

    2021

  8. [16]

    Ultrashort laser pulses and electromag- netic pulse generation in air and on dielectric surfaces,

    P. Sprangle, J. R. Pe˜ nano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromag- netic pulse generation in air and on dielectric surfaces,” Phys. Rev. E69, 066415 (2004)

    2004

  9. [17]

    Sin- gle and double ionization of diatomic molecules in strong laser fields,

    C. Guo, M. Li, J. P. Nibarger, and G. N. Gibson, “Sin- gle and double ionization of diatomic molecules in strong laser fields,” Phys. Rev. A58, R4271–R4274 (1998)

    1998

  10. [18]

    Busuladˇ zi´ c, A.ˇCerki´ c, A

    M. Busuladˇ zi´ c, A.ˇCerki´ c, A. Gazibegovi´ c-Busuladˇ zi´ c, E. Hasovi´ c, and D. B. Miloˇ sevi´ c, “Molecular-orientation- dependent interference and plateau structures in strong- field ionization of a diatomic molecule by a corotating bichromatic elliptically polarized l...

    2018

  11. [19]

    Experimen- tal verification of the nonadiabatic effect in strong-field ionization with elliptical polarization,

    Min Li, Ming-Ming Liu, Ji-Wei Geng, Meng Han, Xufei Sun, Yun Shao, Yongkai Deng, Chengyin Wu, Liang-You Peng, Qihuang Gong, and Yunquan Liu, “Experimen- tal verification of the nonadiabatic effect in strong-field ionization with elliptical polarization,” Phys. Rev. A95, 053425 (2017)

    2017

  12. [20]

    Exit mo- mentum and instantaneous ionization rate of nonadia- batic tunneling ionization in elliptically polarized laser fields,

    Siqiang Luo, Min Li, Wenhai Xie, Kun Liu, Yudi Feng, Baojie Du, Yueming Zhou, and Peixiang Lu, “Exit mo- mentum and instantaneous ionization rate of nonadia- batic tunneling ionization in elliptically polarized laser fields,” Phys. Rev. A99, 053422 (2019)

    2019

  13. [21]

    The plateau in above-threshold ionization: the keystone of rescattering physics,

    W. Becker, S. P. Goreslavski, D. B. Miloˇ sevi´ c, and G. G. Paulus, “The plateau in above-threshold ionization: the keystone of rescattering physics,” J. Phys. B: At. Mol. Opt. Phys.51, 162002 (2018)

    2018

  14. [22]

    Angle-resolved high- order above-threshold ionization spectra for N 2 and O 2: measurements and the strong-field approximation,

    M. Okunishi, R. Itaya, K. Shimada, G. Pr¨ umper, K. Ueda, M. Busuladˇ zi´ c, A. Gazibegovi´ c-Busuladˇ zi´ c, D. B. Miloˇ sevi´ c, and W. Becker, “Angle-resolved high- order above-threshold ionization spectra for N 2 and O 2: measurements and the strong-field approximation,” J...

    2008

  15. [23]

    The effects of dissociative recombination in multiphoton ionization of O 2,

    A. Talebpour, C.-Y. Chien, and S. L. Chin, “The effects of dissociative recombination in multiphoton ionization of O 2,” J. Phys. B: At. Mol. Opt. Phys.29, L677–L680 (1996)

    1996

  16. [24]

    Dissociative recombination and excitation of O+ 2 : Cross sections, product yields and implications for studies of ionospheric airglows,

    R. Peverall, S. Ros´ en, J. R. Peterson, M. Larsson, A. Al-Khalili, L. Vikor, J. Semaniak, R. Bobbenkamp, A. Le Padellec, A. N. Maurellis, and W. J. van der Zande, “Dissociative recombination and excitation of O+ 2 : Cross sections, product yields and implications for studies ...

    2001

  17. [25]

    Probing molecular symmetry effects in the ionization of N 2 and O 2 by intense laser fields,

    M. M. Okunishi, K. Shimada, G. Pr¨ umper, D. Mathura, and K. Ueda, “Probing molecular symmetry effects in the ionization of N 2 and O 2 by intense laser fields,” The J. of Chem. Phys.127, 064310 (2007)

    2007

  18. [26]

    Spatial-temporal con- trol of interferences of multiple tunneling photoelectron wave packets,

    Min Li, Ji-Wei Geng, Ming-Ming Liu, Xu Zheng, Qi- huang Gong, and Yunquan Liu, “Spatial-temporal con- trol of interferences of multiple tunneling photoelectron wave packets,” Phys. Rev. A92, 013416 (2015)

    2015

  19. [27]

    Ef- fect of quantum interference on tunneling photoioniza- tion rates of N2 and O2 molecules,

    K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Ef- fect of quantum interference on tunneling photoioniza- tion rates of N2 and O2 molecules,” J. Chem. Phys.122, 104312 (2005)

    2005

  20. [28]

    Sup- pressed molecular ionization for a class of diatomics in intense femtosecond laser fields,

    J. J. Muth-B¨ ohm, A. Becker, and F. F. H. M., “Sup- pressed molecular ionization for a class of diatomics in intense femtosecond laser fields,” Phys. Rev. Lett.85, 2280–2283 (2000)

    2000

  21. [29]

    Tunnel ion- ization of diatomic atmospheric gases (N 2, O 2) by laser radiation,

    I. V. Kopytin, A. S. Kornev, and B. A. Zon, “Tunnel ion- ization of diatomic atmospheric gases (N 2, O 2) by laser radiation,” Laser Phys.29, 095301 (2019)

    2019

  22. [30]

    Strong-field photoionization of O 2 at intermediate light intensity,

    T. K loda, A. Matsuda, H. O. Karlsson, M. Elshakry, P. Linusson, J. H. Eland, R. Feifel, and T. Hansson, “Strong-field photoionization of O 2 at intermediate light intensity,” Phys. Rev. A82, 033431 (2010)

    2010

  23. [31]

    Analysis of two- dimensional photoelectron momentum spectra and the effect of the long-range Coulomb potential in single ion- ization of atoms by intense lasers,

    Zhangjin Chen, T. Morishita, Anh-Thu Le, M. Wicken- hauser, X. M. Tong, and C. D. Lin, “Analysis of two- dimensional photoelectron momentum spectra and the effect of the long-range Coulomb potential in single ion- ization of atoms by intense lasers,” Phys. Rev. A74, 053405 (2006)

    2006

  24. [32]

    A. E. Siegman,Lasers(University Science Books, Mill Valley, CA, 1986)

    1986

  25. [33]

    Co- incidence imaging of photoelectrons and photo-ions of molecules in strong laser fields,

    Cong Wu, Chengyin Wu, Yudong Yang, Zhifeng Wu, Xi- anrong Liu, Xiguo Xie, Hong Liu, Yongkai Deng, Yun- quan Liu, Hongbing Jiang, and Qihuang Gong, “Co- incidence imaging of photoelectrons and photo-ions of molecules in strong laser fields,” J. Mod. Opt.60, 1388– 1394 (2013)

    2013

  26. [34]

    Revealing orbital dependent quantum interference of O 2 underlying channel resolved strong-field spectro- scopies,

    Jiaqi Yu, Xitao Yu, Xinning Zhao, Zhongyu Yin, Xiaokai Li, Pan Ma, Chuncheng Wang, Sizuo Luo, and Dajun Ding, “Revealing orbital dependent quantum interference of O 2 underlying channel resolved strong-field spectro- scopies,” J. Phys. B: At. Mol. Opt. Phys.53, 085601 (2020)

    2020

  27. [35]

    Dif- ferential study on molecular suppressed ionization in in- tense linearly and circularly polarized laser fields,

    Yongkai Deng, Yunquan Liu, Xianrong Liu, Hong Liu, Yudong Yang, Chengyin Wu, and Qihuang Gong, “Dif- ferential study on molecular suppressed ionization in in- tense linearly and circularly polarized laser fields,” Phys. Rev. A84, 065405 (2011)

    2011

  28. [36]

    The misuse of colour in science communication,

    F. Crameri, G. Shephard, and P. Heron, “The misuse of colour in science communication,” Nat. Commun.11, 5444 (2020). 16

    2020

  29. [37]

    Ionization potential of O 2,

    J. Samson and R. Cairns, “Ionization potential of O 2,” J. Opt. Soc. Amer.56, 769–775 (1966)

    1966

  30. [38]

    tunnel time

    on this expression gives us the Lorentz plus Coulomb force due to the remaining atomic structure acting on the electron, d dt ∂L ∂˙ x − ∂L ∂x = 0p=m˙ x d dt p=e ∂A ∂t − h e m p×(∇ ×A) +e∂ϕ ∂x i (A3) These expressions are used by the SF A to classically de- scribe the motion of...

    2005

  31. [39]

    Tun- neling electron recaptured by an atomic ion or a molec- ular ion,

    Xiguo Xie, Cong Wu, Hong Liu, Min Li, Yongkai Deng, Yunquan Liu, Qihuang Gong, and Chengyin Wu, “Tun- neling electron recaptured by an atomic ion or a molec- ular ion,” Phys. Rev. A88, 065401 (2013)

    2013

  32. [40]

    Counting the elec- trons in a multiphoton ionization by elastic scattering of microwaves,

    A. Sharma, M. N. Slipchenko, M. N. Shneider, X. Wang, K. A. Rahman, and A. Shashurin, “Counting the elec- trons in a multiphoton ionization by elastic scattering of microwaves,” Scientific Reports8, 1–10 (2018)

    2018

  33. [41]

    L. D. Landau and E. M. Liftshitz,The Classical Theory of Fields(Pergamon Press, New York, NY, 1975), 4th ed

    1975

  34. [42]

    Thid´ e,Electromagnetic Field Theory(Dover, Garden City, NY, 2011), 2nd ed

    B. Thid´ e,Electromagnetic Field Theory(Dover, Garden City, NY, 2011), 2nd ed

    2011

  35. [43]

    R. P. Feynman,Quantum Electrodynamics (Advanced Book Classics)(CRC Press, Boca Raton, FL, 1971)

    1971

  36. [44]

    Imaginary-time method in quantum me- chanics and field theory,

    V. S. Popov, “Imaginary-time method in quantum me- chanics and field theory,” Phys. At. Nucl.68, 686–708 (2005)

    2005

  37. [45]

    L. D. Landau and E. M. Liftshitz,Mechanics(Pergamon Press, New York, NY, 1976), 3rd ed

    1976

  38. [46]

    Measurement and control of plasma oscil- lations in femtosecond filaments,

    B. Zhou, A. Houard, Y. Liu, B. Prade, A. Mysyrow- icz, A. Couairon, P. Mora, C. Smeenk, L. Arissian, and P. Corkum, “Measurement and control of plasma oscil- lations in femtosecond filaments,” Phys. Rev. Lett.106, 255002 (2011)

    2011

  39. [47]

    Ionization of atoms in an alternating electrical field. iii,

    A. Perelomov and V. Popov, “Ionization of atoms in an alternating electrical field. iii,” Sov. Phys. JETP25, 336– 343 (1967)

    1967

  40. [48]

    J. V. Uspensky,Theory of Equations(McGraw-Hill, New York, NY, 1948)

    1948

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.