Pith. sign in

REVIEW 3 major objections 3 minor 91 references

Trajectory effects on charge exchange and energy loss in collisions of H$^+$, He$^{2+}$, Li$^{3+}$, and Be$^{4+}$ ions with atomic hydrogen

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read Charge exchange in bare-ion collisions with atomic hydrogen is trajectory-independent, while projectile energy loss is strongly trajectory-dependent, with straight-line models overestimating low-energy stopping.

desk verdict The charge-exchange benchmark is solid, but the energy-loss trajectory claim rests on comparing two non-equivalent estimators and needs more work before it can be trusted. read the letter →

arxiv 2411.10221 v1 pith:DWYVDJCA submitted 2024-11-15 physics.atom-ph

Miranda Nichols , D. Hanstorp , R. Cabrera-Trujillo This is my paper · ORCID
classification physics.atom-ph
keywords chargeexchangeelectroncapturestoppingcrosssectionenergylosstime-dependentSchrödingerequationelectron-nucleardynamicslatticemethodbareioncollisions
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 asks whether the projectile's nuclear path matters for what happens when a bare ion (H+, He2+, Li3+, Be4+) collides with atomic hydrogen. It solves the time-dependent Schrödinger equation for the electron on a numerical lattice under two treatments of the nuclei: a straight-line trajectory and a coupled electron-nuclear dynamics in which the projectile and target move under the electron density and the nuclear repulsion. The authors find that electron-capture cross sections are essentially identical in the two treatments across the studied range and agree with the available experiments and theories, so capture can be computed reliably with straight-line paths. Energy loss behaves differently: at low collision energies the straight-line model makes the target gain more electronic energy than the projectile can physically supply, while the coupled model gives consistent electronic and nuclear stopping cross sections. If correct, this separates a cheap and reliable quantity (charge exchange) from one that requires coupled dynamics (stopping) in the low-energy regime.

What carries the argument

The machinery is a lattice solution of the time-dependent Schrödinger equation, Eq. (1), for the electron in the field of the two nuclei, with the nuclear motion advanced by Eq. (2): the projectile momentum changes under the quantum expectation value of the electron's Coulomb force plus the projectile–target repulsion. The straight-line variant fixes the projectile on $\mathbf{R}_2 = \mathbf{b} + \mathbf{v}t$, so its kinetic energy is constant by construction; the coupled variant lets both nuclei recoil. Capture probabilities come from the electron density in the projectile region $\Gamma$ (z > 15 a.u.), energy loss is split into electronic (relative-motion) and nuclear (target-recoil) parts, and stopping cross sections are the impact-parameter integrals of those energy losses weighted by $2\pi b$. The preferred capture shell is set by the energy-conservation condition $n_f = Z_p$, and the Bethe high-energy stopping formula (Eq. (8)) supplies a check on the electronic stopping.

What would settle it

A decisive test would be to run both trajectory models with the same energy-loss estimator—for example, letting the straight-line projectile decelerate along its forced path and reading its kinetic-energy loss rather than the target's energy gain in the box—and compare the resulting electronic stopping cross sections at energies below 10 keV/u for H+ on H(1s). If the two models then agree, the strong trajectory-dependence claim is not supported; if they still differ, it is confirmed. Experimentally, a merged-beam or recoil-ion measurement of projectile energy loss and target recoil for H+ + H(1s) below a few keV/u would settle the same question.

Watch

Extended reading notes

Core claim

The central claim is that within the collision-energy range studied, electron capture by bare projectile ions from hydrogen does not depend on whether the nuclei follow straight lines or fully coupled trajectories, whereas projectile energy loss depends strongly on the trajectory. The supporting evidence is that the two trajectory models produce overlapping capture cross sections for all four projectiles, in agreement with experimental data for Z=1–3 and with established theory for Z=4; but the straight-line electronic stopping cross sections deviate sharply from the coupled ones, exceed the total stopping cross section, and in the H+ case reach a low-energy maximum that violates energy conservation. The paper attributes the capture insensitivity to the adiabatic molecular pseudopotential, which depends primarily on the projectile–target separation rather than on collision kinematics. The paper concludes that a proper description of electron-nuclear dynamics is required for energy- and momentum-transfer processes, even though it is not required for charge exchange.

Load-bearing premise

The load-bearing premise is that the two models' energy-loss measurements can be compared directly even though one model measures the projectile's lost kinetic energy and the other measures the electron's energy gain inside a fixed box; if those two measurements disagree for bookkeeping reasons rather than because of the trajectory, the energy-loss conclusion would weaken.

Editorial extensions

If this is right

  • Electron-capture cross sections for H+, He2+, Li3+, and Be4+ on H(1s) can be generated with straight-line trajectories without losing accuracy in the studied energy range.
  • Straight-line electronic-stopping calculations that use the target's electronic energy gain as the stopping estimator are unreliable at low collision energies, where they can exceed the total stopping or even the projectile's available energy.
  • Coupled electron-nuclear trajectories put electronic stopping on a consistent footing at high energies and reveal that nuclear recoil stopping dominates the total stopping below roughly 1 keV/u for all four projectiles.
  • The Be4+ + H(1s) capture cross section is predicted to stay almost constant below 25 keV/u, a testable benchmark for a system with no experimental data yet.
  • The tabulated cross sections in Table I provide reference data for total, electronic, and nuclear stopping of these ions in atomic hydrogen.

Reading between the lines

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

  • A direct extension of the paper's logic is that straight-line TDDFT stopping calculations for more complex targets carry the same low-energy estimator risk studied here; redoing them with coupled ion dynamics would show how much of their low-energy stopping is a trajectory artifact.
  • Because the straight-line and coupled models measure electronic energy loss differently (target energy gain in a limited region versus projectile kinetic-energy loss), isolating true trajectory effects would require running both models with a single common estimator.
  • The same lattice wave function could be used to split electronic stopping into capture, excitation, and ionization channels; the paper does not report this partitioning.
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 / 3 minor

Summary. The paper presents lattice time-dependent Schrödinger equation calculations for H+, He2+, Li3+, and Be4+ ions colliding with atomic hydrogen in the 0.1–900 keV/u range, comparing straight-line projectile trajectories with trajectories coupled to the electron dynamics. The authors compute charge-exchange cross sections and electronic, nuclear, and total stopping cross sections. The central claims are that electron capture is trajectory-independent and agrees well with published experiments and theories for all four projectiles, while projectile energy loss is strongly trajectory-dependent, with the straight-line approximation overestimating energy loss at low energies and failing to conserve energy. The paper concludes that a proper electron-nuclear coupled description is necessary for energy and momentum transfer.

Significance. If the charge-exchange results are taken at face value, they provide a useful benchmark for Z=1–4 bare ions on H(1s) over a wide energy range, including Be4+, where no experimental data exist. The charge-exchange cross sections are validated against multiple independent experiments (McClure, Shah and Gilbody, Seim et al., Havener et al.) and against a broad set of theories (AOCC, CTMC, MOCC, LTDSE, Sturmian, QM-CCC), which is a genuine strength. The energy-loss claim, if correct, would be important for TDDFT-based stopping-power simulations and for low-energy ion-beam applications. However, the energy-loss analysis is compromised by inconsistent energy bookkeeping between the two trajectory models, as detailed in the major comments, so the paper's headline conclusion about trajectory dependence of stopping is not yet established.

major comments (3)
  1. [Sec. III.C, Eq. (7)] The straight-line electronic stopping cross section is computed from the electronic energy gain of the target in the slab −30 < z < 15 a.u., whereas the coupled Se is obtained from the projectile relative kinetic energy loss minus the target recoil energy (ΔEe = ΔET − ΔEn). These are not equivalent observables. As Fig. 2 shows, at low energies and high projectile charge a large fraction of the final electron density lies in the projectile region z > 15 a.u. (capture), and the straight-line estimator excludes exactly this channel. Because capture is the dominant inelastic channel at low energies, the difference between the two Se curves in Fig. 6 reflects the difference in bookkeeping as much as any genuine trajectory effect. The paper's central claim of "strong trajectory dependence" in energy loss therefore rests on a comparison of two non-equivalent quantities, and the claim is not supported until both estimators are defined on the same energy bookkeeping basis.
  2. [Table I] Table I lists ST and Sn for the coupled trajectories. Since the paper defines the total stopping as ST = Se + Sn (Sec. III.C), the implied electronic stopping Se = ST − Sn is negative for numerous low-energy entries: for example H+ at 0.1 keV/u gives ST = 3.276 and Sn = 7.557, implying Se = −4.281; He2+ at 0.1 keV/u gives ST = 0.196 and Sn = 15.675, implying Se = −15.479. Negative electronic stopping is unphysical and contradicts the stated decomposition. This indicates that the coupled-trajectory energy-loss results are not internally consistent at low collision energies, which is precisely the regime where the paper claims the strongest trajectory dependence. The authors must identify whether this is a numerical artifact (e.g., grid or boundary effects on the kinetic-energy estimate) or an error in the stopping definitions, and report corrected values.
  3. [Abstract and Sec. III.C] The abstract states that "the straight-line approximation overestimating energy loss at low collision energies," but Sec. III.C states the opposite for three of the four projectiles: "For He2+, Li3+, and Be4+ projectiles, the straight-line electronic stopping cross sections are smaller due to the more pronounced charge transfer process." Even for H+, the straight-line Se in Fig. 6A exceeds the total coupled ST at low energies, which the paper itself labels unphysical. The direction of any trajectory effect is therefore not systematic and the abstract overgeneralizes. The authors should qualify the claim by projectile and by stopping component, or provide a corrected analysis that resolves the sign inconsistency.
minor comments (3)
  1. [Throughout] The manuscript contains numerous typographical and rendering errors that impede readability: the title reads "coll isions"; Fig. 4 legends contain garbled text such as "Th−5 w24k ((2u3led )"; "LTSDE" appears in the text and figure; "The can be explained" omits a subject; the reference list contains corrupted strings such as "Marie Sk/suppress lodowska-Curie" and "Ko/suppress lakowska"; and several reference entries have malformed author fields.
  2. [Sec. III.C and Fig. 6] The comparison with experimental stopping data is made for H2 targets and for neutral or partially screened projectiles (H, He, Li), not for the bare-ion H(1s) systems studied here. The paper acknowledges this limitation and refers to charge-fraction corrections, but the statement that the results are "consistent with the available experimental data at high collision energies" should be softened or quantified, since the comparison is indirect.
  3. [Sec. II and Table I] The computational parameters (grid step 0.4 a.u., time step 0.01 a.u., initial distance z0 = −30 a.u.) are stated, but no convergence tests with respect to these parameters are shown. Given that the ground-state energy of hydrogen is reported as −0.490 a.u. rather than the exact −0.5 a.u., the energy-loss values, especially at low energies where small kinetic-energy differences matter, may be sensitive to these choices. A brief convergence study would strengthen the energy-loss claims.

Circularity Check

1 steps flagged · score 3.0 of 10

Charge exchange is independently benchmarked, but the claimed energy-loss trajectory dependence compares two differently defined Se estimators, making part of that claim an artifact of bookkeeping.

  1. other [Sec. III.C (Projectile energy loss), Eq. (7) and Fig. 6; straight-line Se estimator paragraph]
    "Thus, the relative energy loss is ΔEe = K_r^f − K_r^i ... For the electronic energy loss in the straight-line trajectories, the constant projectile velocity results in ΔET = 0. However, it is customary to subtract the electronic energy loss of the projectile from the electronic energy gain of the target ... By calculating the final electronic energy of the target from the final wave function in the interval −30 < z < 15 a.u. and subtracting the initial ground state energy of the target, we isolate the straight-line contribution to the electronic energy loss."

    The coupled Se is a global projectile relative-energy loss (ΔEe = ΔET − ΔEn) and thus includes energy carried by electrons captured into the projectile region. The straight-line Se is defined only as the target electronic energy gain in the slab −30 < z < 15 a.u., explicitly excluding the projectile capture region z > 15. Figure 2 shows that at low energies most final density lies in the projectile region for Z > 1, and resonant transfer is large for H+. The two estimators therefore differ by the capture-channel energy by construction. Attributing the coupled-versus-straight-line differences in Fig. 6 to 'strong trajectory dependence' confounds a genuine trajectory effect with this estimator difference.

full rationale

The charge-exchange result is self-contained: σ is computed from lattice TDSE wave functions and benchmarked against external experiments (McClure, Hvelplund/Andersen, Gealy/Van Zyl, Shah/Gilbody, Seim, Havener) and against independent AOCC, CTMC, MOCC, Sturmian, and other calculations; no parameter is fitted to these data. The Bethe comparison uses the standard I0 = 14.9 eV. END machinery is self-cited (refs 26, 28, 29, 68, 70, 87) but only as method provenance, not as a load-bearing uniqueness theorem, so no circularity arises there. The one real concern is the energy-loss comparison: the coupled and straight-line Se values use different estimators, so the claimed trajectory dependence is partly built into the estimator choice. Table I also contains coupled entries with ST < Sn, implying negative Se, which reinforces that the energy bookkeeping is not yet a reliable basis for the trajectory-dependence claim. Because the central charge-exchange claim is independently supported and no fitted parameter is renamed as a prediction, the overall circularity is modest.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central results rest on the numerical TDSE/END scheme from the authors' earlier work (refs 26-29, 68, 70): Ehrenfest mean-field nuclear forces, a uniform 0.4 a.u. lattice, Crank-Nicolson propagation, and a masking absorber. No empirical constant is fitted to target observables; the only external constants are standard (I0 = 14.9 eV in the Bethe reference). The main hidden assumptions are the sufficiency of the finite simulation window for final target momenta, the comparability of the two energy-loss estimators, and the use of H2-based experimental references for an atomic hydrogen target.

free parameters (5)
  • Grid spacing (uniform lattice step) = 0.4 a.u.
    Discretization step in all three directions; yields hydrogen ground state energy -0.490 a.u. (2% offset from -0.5 a.u.) which the authors accept as adequate. A hand-chosen convergence setting, not fitted to target data.
  • Time step = 0.01 a.u.
    Stated to balance accuracy and efficiency; no convergence study is reported.
  • Capture/excitation boundary z = 15 a.u. = 15 a.u.
    Defines the projectile region Gamma used to compute PCX = integral of electronic density; this boundary partly determines all reported capture cross sections.
  • Initial projectile distance z0 = -30 a.u.
    Sets the starting separation and the collision time t0 = 2 z0 / v0; the initial wave function is recomputed by imaginary-time propagation at each impact parameter to include polarization.
  • Impact parameter cutoff b_max = 14 a.u. with 0.4 a.u. steps
    Cross sections integrate b from 0 to 14 a.u. via Eq. (6); contributions beyond 14 a.u. are assumed negligible without an explicit test.
assumptions (6)
  • domain assumption Nuclear forces are computed with the Ehrenfest mean-field approximation (Eq. 2), a single trajectory for the full wave packet.
    Taken from ref [68]; no branching or decoherence between charge-transfer channels, an approximation most stressed at low energies where capture probabilities are large.
  • domain assumption One-electron TDSE (Eq. 1) is the full problem for H(1s) plus a bare projectile.
    Exact for the single-electron target but limits the method to bare ions; the paper notes this when discussing screened projectiles (Sec. III.C).
  • domain assumption The finite simulation window (z0 = 30 a.u., t0 = 2 z0 / v0) fully captures final target momentum and energy.
    Sec. II claims the window is 'long enough to achieve a clear separation'; no convergence test for the long-range Coulomb tail of the projectile force is shown.
  • standard math Bethe formula (Eq. 8) with I0 = 14.9 eV is the correct high-energy reference for atomic hydrogen.
    I0 taken from Bethe (1930) and Mott-Massey; used as an external benchmark line in Fig. 6.
  • domain assumption H2-target experimental stopping data and SRIM H2 curves, scaled by Z^2, approximate bare-ion stopping on atomic H.
    Fig. 6 and Sec. III.C compare Se with H2 data; the paper flags the beam charge fraction issue via ref [87] but does not quantify the molecular versus atomic target difference.
  • domain assumption Trajectory independence of charge exchange follows from an adiabatic molecular pseudo-potential that depends only on internuclear distance.
    Sec. III.B explanation; qualitative and not derived from the computed wave functions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Trajectory effects on charge exchange and energy loss in collisions of H$^+$, He$^{2+}$, Li$^{3+}$, and Be$^{4+}$ ions with atomic hydrogen." pith.science (2026). https://pith.science/paper/DWYVDJCA

@misc{pith2026241110221,
  author       = {Pith},
  title        = {Pith review of: Trajectory effects on charge exchange and energy loss in collisions of H$^+$, He$^2+$, Li$^3+$, and Be$^4+$ ions with atomic hydrogen},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DWYVDJCA}},
  note         = {Machine review of arXiv:2411.10221}
}
abstract

The charge exchange and energy loss processes provide insights into fundamental processes across physical, chemical, and engineered systems. While this field has been thoroughly investigated, a clear study on trajectory effects is lacking, particularly in the context of inelastic processes at low energies. In this work, we address this gap by solving the time-dependent Schr\"odinger equation for the electron in a numerical lattice with a coupled electron-nuclear dynamics approach as well as a straight-line trajectory approximation for the nuclei to asses trajectory effects on charge exchange and energy loss. The collision dynamics are studied using bare ion projectiles with charge $Z=$1-4 incident on atomic hydrogen in an energy range of 0.1 to 900 keV/u. We find that the charge exchange process is trajectory-independent within the energy range considered, showing excellent agreement with available experimental and theoretical data. However, projectile energy loss exhibits strong trajectory dependence, with the straight-line approximation overestimating energy loss at low collision energies due to the forced linear path. Our results for electronic stopping cross sections with electron-nuclear coupled trajectories are consistent with the available experimental data at high collision energies. At low energies, nuclear energy loss becomes prominent, driven by polarization effects induced by the ion charge on the hydrogen target. Overall, our work highlights the importance of nuclear trajectory considerations in collision dynamics and offers a foundation for further investigations of more complex systems.

Figures

Figures reproduced from arXiv: 2411.10221 by the authors.

Figure 1
Figure 1. FIG. 1. A [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Electronic density as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Electron capture probability, weighted by the impac [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Electron capture cross sections for ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Projectile electronic energy loss, weighted by the i [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Stopping cross sections for atomic hydrogen targets [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

91 extracted references · 77 canonical work pages

  1. [1]

    using an imaginary time technique for each configuration [ 70], which allows for ground state convergence. Finally, we set an absorbing -15 -10 -5 0 5 10 15 20 25 30 35 40 45 -15-10-5 0 5 10 15 -15 -10 -5 0 5 10 15 v0 b•ion ΩΓ H z (a.u.) y (a.u.) x (a.u.) -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 z (a.u.) y (a.u.) x (a.u.) -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 v0 ...

  2. [2]

    With this, Eq

    The collision time is defined as t0 = 2z0/v 0, where v0 is the initial velocity of the projectile and z0 is the initial projectile distance to the target. With this, Eq. ( 2) is solved with the fourth- order Runge-Kutta method coupled to Eq. ( 1). For the straight trajectories, we simply advance R2 according to Eq. ( 3). To prevent numerical instabilities ...

  3. [3]

    Heisenberg, Z

    W. Heisenberg, Z. Physik 39, 499 (1926)

    1926

  4. [4]

    R. C. Isler, Plasma Phys. Control. Fusion 36, 171 (1994)

    1994

  5. [5]

    where n = 4 is more extended than the other systems. B. Electron capture cross section The area under the electron capture probability curves of Fig. 3 is proportional to the electron capture cross sections, since σ = 2π ∫ bPCX db . (6) In Fig. 4, we show the electron capture cross sections as a function of the projectile collision energy for H+, He2+, Li...

    1966

  6. [6]

    Rutherford, Philos

    E. Rutherford, Philos. Mag. 21, 669 (1911)

    1911

  7. [7]

    Bohr, The Penetration of Atomic Particles Through Matter (Munksgaard, Copenhagen, 1948)

    N. Bohr, The Penetration of Atomic Particles Through Matter (Munksgaard, Copenhagen, 1948)

    1948

  8. [8]

    Dennerl, Space Sci

    K. Dennerl, Space Sci. Rev. 157, 57 (2010)

    work page 2010

Show all 91 references
  1. [9]

    R. J. Fonck, D. S. Darrow, and K. P. Jaehnig, Phys. Rev. A 29, 3288 (1984)

    1984

  2. [10]

    T. E. Cravens, Geophys. Res. Lett. 24, 105 (1997)

    1997

  3. [11]

    J. A. Carter, S. Sembay, and A. M. Read, Astron. Nachr. 333, 313 (2012)

    2012

  4. [12]

    Gaussorgues, C

    C. Gaussorgues, C. Le Sech, F. Masnou-Seeuws, R. Mc- Carroll, and A. Riera, J. Phys. B 8, 239 (1975)

    1975

  5. [13]

    Champion, M

    C. Champion, M. A. Quinto, J. M. Monti, M. E. Galassi, P. F. Weck, O. A. Foj´ on, J. Hanssen, and R. D. Rivarola, Phys. Med. Biol. 60, 7805 (2015)

    2015

  6. [14]

    H. Luna, A. L. De Barros, J. A. Wyer, S. W. Scully, J. Laconte, P. M. Garcia, G. M. Sigaud, A. C. Santos, V. Senthil, M. B. Shah, C. J. Latimer, and E. C. Mon- tenegro, Phys. Rev. A 75, 1 (2007)

    2007

  7. [15]

    B. H. Bransden, Rep. Prog. Phys 35, 949 (1972)

    1972

  8. [16]

    Hvelplund and A

    P. Hvelplund and A. Anderson, Phys. Scr. 26, 375 (1982)

    1982

  9. [17]

    Lichten, Phys

    W. Lichten, Phys. Rev. 131, 229 (1963)

    1963

  10. [18]

    G. J. Lockwood and E. Everhart, Phys. Rev. A 125, 567 (1962)

    1962

  11. [19]

    McClure, Phys

    G. McClure, Phys. Rev. 148, 148 (1996)

    1996

  12. [20]

    M. B. Shah and H. B. Gilbody, J. Phys. B 11, 121 (1978)

    1978

  13. [21]

    M. W. Gealy and B. Van Zyl, Phys. Rev. A 36, 3091 (1987)

    1987

  14. [22]

    Schwab, G

    W. Schwab, G. B. Baptista, E. Justiniano, R. Schuch, H. Vogt, and E. W. Weber, J. Phys. B 20, 2825 (1987)

    1987

  15. [23]

    C. C. Havener, R. Rejoub, P. S. Krsti´ c, and A. C. Smith, Phys. Rev. A 71, 042707 (2005)

    2005

  16. [24]

    W. Seim, A. Muller, I. Wirkner-Bott, and E. Salzborn, J. Phys. B 14, 3475 (1981)

    1981

  17. [25]

    M. M. Sant’Anna, W. S. Melo, A. C. Santos, V. L. de Je- sus, M. B. Shah, G. M. Sigaud, E. C. Montenegro, H. F. Busnengo, S. E. Corchs, R. D. Rivarola, and L. Guly´ as, Phys. Rev. A 61, 9 (2000)

    2000

  18. [26]

    Hoekstra, F

    R. Hoekstra, F. J. Heer, and R. Morgenstern, J. Phys. B 24, 4025 (1991)

    1991

  19. [27]

    A. A. Basalaev, V. V. Kuz’michev, M. N. Panov, and O. V. Smirnov, Tech. Phys. 65, 855 (2020)

    2020

  20. [28]

    Stolterfoht, R

    N. Stolterfoht, R. Cabrera-Trujillo, Y. ¨Ohrn, E. Deumens, R. Hoekstra, and J. R. Sabin, Phys. Rev. Lett 99, 2 (2007)

    2007

  21. [29]

    M. B. Shah, T. V. Goffe, and H. B. Gilbody, J. Phys. B 11, L233 (1978)

    1978

  22. [30]

    Deumens, A

    E. Deumens, A. Diz, R. Longo, and Y. ¨Ohrn, Rev. Mod. Phys. 66, 917 (1994)

    1994

  23. [31]

    B. J. Killian, R. Cabrera-Trujillo, E. Deumens, and Y. ¨Ohrn, J. Phys. B 37, 4733 (2004)

    2004

  24. [32]

    D. R. Schultz, M. R. Strayer, and J. C. Wells, Phys. Rev. Lett. 82, 3976 (1999)

    1999

  25. [33]

    Cabrera-Trujillo, J

    R. Cabrera-Trujillo, J. R. Sabin, Y. ¨Ohrn, and E. Deu- mens, Phys. Rev. Lett. 84, 5300 (2000)

    2000

  26. [34]

    H. J. Ludde and R. M. Dreizler, J. Phys. B 16, 1009 (1983)

    1983

  27. [35]

    H. J. Ludde and R. M. Dreizler, J. Phys. B 15, 2713 (1982)

    1982

  28. [36]

    Jorge, J

    A. Jorge, J. Su´ arez, C. Illescas, L. F. Errea, and L. M´ endez,Phys. Rev. A 94, 032707 (2016)

    2016

  29. [37]

    Minami, M

    T. Minami, M. S. Pindzola, T.-G. Lee, and D. R. Schultz, J. Phys. B 39, 2877 (2006)

    2006

  30. [38]

    Minami, T

    T. Minami, T. G. Lee, M. S. Pindzola, and D. R. Schultz, J. Phys. B 41, 135201 (2008)

    2008

  31. [39]

    Ko/suppress lakowska, M

    A. Ko/suppress lakowska, M. S. Pindzola, and D. R. Schultz, Phys. Rev. A 59, 2588 (1999)

    1999

  32. [40]

    Botheron and B

    P. Botheron and B. Pons, Phys. Rev. A 83, 1 (2011)

    2011

  33. [41]

    Hill, Dipti, K

    C. Hill, Dipti, K. Heinola, A. Dubois, N. Sisourat, A. Taoutioui, H. Agueny, K. T˝ ok´ esi, I. Ziaeian, C. Illescas, A. Jorge, L. M´ endez, A. S. Kadyrov, N. W. Antonio, A. M. Kotian, T. Kirchner, A. C. Leung, J. Ko, J. K. Lee, O. Marchuk, M. G. O’Mullane, E. Litherland-Smith,...

    2023

  34. [42]

    A. C. K. Leung and T. Kirchner, Atoms 10, 11 (2022)

    2022

  35. [43]

    R. E. Olson and A. Salop, Phys. Rev. A 16, 531 (1977)

    1977

  36. [44]

    Abrines and I

    R. Abrines and I. C. Percival, Proc. R. Soc. 88, 861 (1966)

    1966

  37. [45]

    D. R. Schultz, L. Meng, C. Reinhold, and R. E. Olson, Phys. Scr. 1991, 89 (1991)

    1991

  38. [46]

    Ziaeian and K

    I. Ziaeian and K. T˝ ok´ esi,Sci. Rep. 11, 1 (2021)

    2021

  39. [47]

    Jorge, C

    A. Jorge, C. Illescas, J. E. Miraglia, and M. S. Graviell e, J. Phys. B 48, 235201 (2015). 11

    2015

  40. [48]

    Fritsch and C

    W. Fritsch and C. D. Lin, Phys. Rev. A 29, 3039 (1984)

    1984

  41. [49]

    Elizaga, L

    D. Elizaga, L. F. Errea, J. D. Gorfinkiel, C. Illescas, L. M´ endez, A. Mac´ ıas, A. Riera, A. Rojas, O. J. Kro- neisen, T. Kirchner, H. J. L ¨dde, A. Henne, and R. M. Dreizler, J. Phys. B 32, 857 (1999)

    1999

  42. [50]

    A compar- ative study by Minami et al

    have been successfully applied to He 2+, Li 3+, and Be4+ projectiles for a wide range of energies. A compar- ative study by Minami et al. [34] evaluated the LTDSE, AOCC, and CTMC methods in an energy range of ∼ 1 to 1000 keV/u by comparing with experimental values for total an...

  43. [51]

    L. F. Errea, C. Illescas, L. M´ endez, B. Pons, A. Riera, and J. Su´ arez,J. Phys. B 37, 4323 (2004)

    2004

  44. [52]

    Fritsch and C

    W. Fritsch and C. D. Lin, J. Phys. B 15, L281 (1982)

    1982

  45. [53]

    Agueny, J

    H. Agueny, J. P. Hansen, A. Dubois, A. Makhoute, A. Taoutioui, and N. Sisourat, At. Data Nucl. Data Tables 129-130, 101281 (2019)

    2019

  46. [54]

    Toshima, Phys

    N. Toshima, Phys. Rev. A 50, 3940 (1994)

    1994

  47. [55]

    L. F. Errea, L. M´ endez, B. Pons, A. Riera, I. Sevila, and J. Su´ arez,Phys. Rev. A 74, 1 (2006)

    2006

  48. [56]

    L. Liu, X. Y. Li, J. G. Wang, and R. K. Janev, Phys. Plasmas 21 (2014), 10.1063/1.4886142

    2014 doi

  49. [57]

    B. H. Bransden, C. J. Noble, and J. Chandler, J. Phys. B 16, 4191 (1983)

    1983

  50. [58]

    Harel, H

    C. Harel, H. Jouin, and B. Pons, At. Data Nucl. Data Tables 68, 279 (1998)

    1998

  51. [59]

    P. S. Krsti´ c,J. Phys. B 37, L217 (2004)

    2004

  52. [60]

    T. G. Winter, Phys. Rev. A 76, 1 (2007)

    2007

  53. [61]

    R. K. Janev and G. Ivanovskis, Phys. Scr. T62, 43 (1996)

    1996

  54. [62]

    A. T. Le, C. D. Lin, L. F. Errea, L. M´ endez, A. Riera, and B. Pons, Phys. Rev. A 69, 062703 (2004)

    2004

  55. [63]

    N. W. Antonio, C. T. Plowman, I. B. Ab- durakhmanov, I. Bray, and A. S. Kadyrov, J. Phys. B 54 (2021), 10.1088/1361-6455/ac22e1

    2021 doi

  56. [64]

    I. B. Abdurakhmanov, A. S. Kadyrov, S. K. Avazbaev, and I. Bray, J. Phys. B 49, 115203 (2016)

    2016

  57. [65]

    Milojevi´ c, I

    N. Milojevi´ c, I. Manˇ cev, D. Delibaˇ si´ c, and D. Belki´ c, Phys. Rev. A 102, 012816 (2020)

    2020

  58. [66]

    Ryufuku, Phys

    H. Ryufuku, Phys. Rev. A 25, 720 (1982)

    1982

  59. [67]

    B. Ding, B. Wang, and B. Hu, Phys. Lett. A 373, 3047 (2009)

    2009

  60. [68]

    Ponomareva, E

    E. Ponomareva, E. Pitthan, R. Holeˇ n´ ak, J. Shams- Latifi, G. P. Kiely, D. Primetzhofer, and A. E. Sand, Phys. Rev. B 109, 165123 (2024)

    2024

  61. [69]

    Li, J.-m

    C.-K. Li, J.-m. Xue, X.-p. OuYang, and F.-S. Zhang, Phys. Rev. A 107, 042813 (2023)

    2023

  62. [70]

    K. A. Nichols, S. X. Hu, A. J. White, V. N. Goncharov, D. I. Mihaylov, L. A. Collins, N. R. Shaffer, and V. V. Karasiev, Phys. Rev. E 108, 035206 (2023)

    2023

  63. [71]

    S.-N. Pang, F. Wang, Y.-T. Sun, F. Mao, and X.-L. Wang, Phys. Rev. A 105, 032803 (2022)

    2022

  64. [72]

    Cabrera-Trujillo, C

    R. Cabrera-Trujillo, C. E. L. C. Roman, and C. E. Teran- Cisneros, Phys. Rev. A 108, 1 (2023)

    2023

  65. [73]

    Crank and P

    J. Crank and P. Nicolson, Math. Proc. Camb. Philos. Soc. 1, 50 (1947)

    1947

  66. [74]

    F. Anis, V. Roudnev, R. Cabrera-Trujillo, and B. D. Esry, Phys. Rev. A 73, 043414 (2006)

    2006

  67. [75]

    De Giovannini, A

    U. De Giovannini, A. H. Larsen, and A. Rubio, EPJ B 88, 56 (2015)

    2015

  68. [76]

    Bethe, Annalen der Physik 397, 325 (1930)

    H. Bethe, Annalen der Physik 397, 325 (1930)

    1930

  69. [77]

    H. A. Bethe and R. Jackiw, Intermediate Quantum Me- chanics (Benjamin / Cummings, New York, 1986)

    1986

  70. [78]

    Inokuti, Rev

    M. Inokuti, Rev. Mod. Phys. 43, 297 (1971)

    1971

  71. [79]

    J. F. Ziegler, NIM-B 219-220, 1027 (2004)

    2004

  72. [80]

    IAEA stopping power database,

    “IAEA stopping power database,” Version 2024-03

    2024

  73. [81]

    Montanari, P

    C. Montanari, P. Dimitriou, L. Marian, A. Mendez, J. Peralta, and F. Bivort-Haiek, NIM-B 551, 165336 (2024)

    2024

  74. [82]

    Schieferm¨ uller, R

    A. Schieferm¨ uller, R. Golser, R. Stohl, and D. Semrad, Phys. Rev. A 48, 4467 (1993)

    1993

  75. [83]

    Børgesen and H

    P. Børgesen and H. Sørensen, Nucl. Instr. and Meth. 200, 571 (1982)

    1982

  76. [84]

    F.Besenbacher, H.H.Andersen and H.Knudsen, Mat

    P. F.Besenbacher, H.H.Andersen and H.Knudsen, Mat. Fys. Medd. Dan. Vid. Selsk. 40 (1979)

    1979

  77. [85]

    Reiter, N

    G. Reiter, N. Kniest, E. Pfaff, and G. Clausnitzer, NIM-B 44, 399 (1990)

    1990

  78. [86]

    Baumgart, H

    H. Baumgart, H. Berg, E. Huttel, E. Pfaff, G. Reiter, and G. Clausnitzer, Nucl. Instrum. Methods Phys. Res. 215, 319 (1983)

    1983

  79. [87]

    Andersen, F

    H.H. Andersen, F. Besenbacher, and H. Knudsen, Nucl. Instr. and Meth. 149, 121 (1978)

    1978

  80. [88]

    Y.A.Teplova, V.S.Nikolaev and L.N.Fateeva, Sov

    I. Y.A.Teplova, V.S.Nikolaev and L.N.Fateeva, Sov. Phys. JETP 15, 31 (1962)

    1962

  81. [89]

    Allison and C

    S. Allison and C. Littlejohn, Phys. Rev. 104, 959 (1956)

    1956

  82. [90]

    N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Clarendon Press, Oxford, 1965) p. 3rd ed

    1965

  83. [91]

    Cabrera-Trujillo, Physica Scripta 98, 125401 (2023)

    R. Cabrera-Trujillo, Physica Scripta 98, 125401 (2023)

    2023

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.