pith. sign in

arxiv: 1907.00634 · v1 · pith:IEA2ECMUnew · submitted 2019-07-01 · ⚛️ physics.atom-ph

Antiproton--hydrogen collisions calculation by Coulomb wave function discrete variable method

Zorigt Gombosuren , Khenmedekh Lochin , Aldarmaa Chuluunbaatar This is my paper

Pith reviewed 2026-05-25 11:39 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords antiproton-hydrogen collisionsionization cross sectionstime-dependent Schrödinger equationCoulomb wave function discrete variable methoddifferential cross sectionsnonrelativistic collisionselectron ejection
0
0 comments X

The pith

Differential cross sections for antiproton-hydrogen ionization are computed by numerically solving the time-dependent Schrödinger equation and agree with relativistic results.

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

The paper shows how to compute ionization in nonrelativistic collisions of antiprotons and protons with hydrogen atoms. The time-dependent Schrödinger equation is solved for the electron using a discrete-variable representation built from Coulomb waves, while the projectile travels classically on a straight line at constant speed. Ionization amplitudes follow from projecting the final wave function onto continuum states of the hydrogen electron. Differential cross sections are then extracted as functions of impact energy, scattering angle, and electron ejection parameters, and these match results from relativistic calculations.

Core claim

Nonrelativistic collision of proton and antiproton with hydrogen atom is described by solving time-dependent Schrödinger equation numerically. Coulomb wave function discrete variable method is used to calculate electron wave function evolution, while projectile is defined classically, moving along straight line trajectories with constant velocity. The ionization amplitude is calculated by projection of the wave function into continuum wave function of the hydrogen electron. The differential cross sections are calculated depending on projectile impact energy, scattering angle and electron ejection energy and angles, and results are in good agreement with relativistic calculation results.

What carries the argument

Coulomb wave function discrete variable method (CWDVR) to evolve the electron wave function in the time-dependent Schrödinger equation, combined with classical straight-line constant-velocity motion of the projectile.

If this is right

  • Differential cross sections are obtained as functions of projectile impact energy, scattering angle, and electron ejection energy and angles.
  • The nonrelativistic results agree with those from relativistic calculations.
  • Ionization amplitudes are extracted by projecting the evolved wave function onto hydrogen continuum states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same numerical scheme could be applied to other light-ion atom collisions where the straight-line approximation holds.
  • Disagreement with future experiments at higher energies would indicate the need to relax the classical-trajectory assumption.
  • The computed cross sections supply reference data for testing when relativistic corrections become necessary.

Load-bearing premise

The projectile moves classically along a straight line at constant velocity.

What would settle it

An experimental measurement of the differential cross section at a chosen impact energy, scattering angle, and electron ejection angle and energy that deviates from the values obtained by this calculation.

Figures

Figures reproduced from arXiv: 1907.00634 by Aldarmaa Chuluunbaatar, Khenmedekh Lochin, Zorigt Gombosuren.

Figure 8
Figure 8. Figure 8: DDCS dependent on ejection energy and angle. Antiproton energy is 30 keV, 200 keV and ejection energy 5 eV. Results of McGovern [5], WP-CCC [9] and QM-CCC [7] [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
read the original abstract

Nonrelativistic collision of proton and antiproton with hydrogen atom described by solving time-dependent Schrodinger equation numerically. Coulomb wave function discrete variable method (CWDVR) had been used to calculate electron wave function evolution, while projectile defined classically, moving along the straight line trajectories with constant velocity. The ionization amplitude calculated by projection of the wave function into continuum wave function of the hydrogen electron. The differential cross sections calculated depending on projectile impact energy, scattering angle and electron ejection energy and angles. Our results in good agreement with the relativistic calculation results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript describes a numerical solution of the time-dependent Schrödinger equation for non-relativistic antiproton–hydrogen collisions using the Coulomb wave function discrete variable representation (CWDVR). The projectile is treated classically on straight-line constant-velocity trajectories; the ionization amplitude is obtained by projecting the evolved wave function onto hydrogen continuum states; differential cross sections are reported as functions of projectile impact energy, scattering angle, and electron ejection energy/angles, with claimed agreement to independent relativistic calculations.

Significance. If the numerical implementation is sound, the work supplies a non-relativistic benchmark for ionization in exotic-atom collisions and a practical CWDVR implementation that could be compared against other time-dependent methods. The reported agreement with relativistic results would constitute a useful cross-check, though the absence of any convergence data or uncertainty estimates in the abstract limits the immediate utility of that comparison.

major comments (1)
  1. [Abstract] Abstract: the projectile is stated to move on straight-line trajectories at constant velocity. This fixes the deflection angle at zero for every impact parameter, so no non-trivial differential cross section versus projectile scattering angle can be obtained from the stated dynamics. No deflection function, eikonal phase, or curved-trajectory correction is mentioned that would map impact parameter to angle; without that step the central claim that differential cross sections depend on scattering angle is unsupported.
minor comments (2)
  1. No error bars, convergence tests with respect to basis size or time step, or explicit comparison tables are referenced, weakening the assertion of agreement with relativistic calculations.
  2. The precise definition of the continuum projection operator and the normalization of the resulting amplitudes should be stated explicitly (ideally with an equation) to allow independent verification.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and for identifying the inconsistency in the abstract. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the projectile is stated to move on straight-line trajectories at constant velocity. This fixes the deflection angle at zero for every impact parameter, so no non-trivial differential cross section versus projectile scattering angle can be obtained from the stated dynamics. No deflection function, eikonal phase, or curved-trajectory correction is mentioned that would map impact parameter to angle; without that step the central claim that differential cross sections depend on scattering angle is unsupported.

    Authors: We agree that the straight-line constant-velocity classical trajectory for the projectile implies zero deflection for all impact parameters, and that no deflection function, eikonal phase, or trajectory correction is described in the manuscript. Consequently the abstract's claim that differential cross sections are obtained as a function of projectile scattering angle is not supported by the stated dynamics. The calculations are performed on a grid of impact parameters, with the resulting ionization amplitudes projected onto electron continuum states; the reported differential cross sections are therefore functions of impact parameter (together with electron ejection energy and angles) rather than projectile scattering angle. We will revise the abstract to remove the reference to projectile scattering angle and to state the results explicitly in terms of impact parameter. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained against external benchmarks

full rationale

The paper solves the TDSE numerically via CWDVR for the electron with a classical straight-line constant-velocity projectile, computes ionization amplitudes by projection onto continuum states, and reports differential cross sections. No equations or steps reduce by construction to fitted inputs, self-definitions, or self-citation chains. The claimed agreement with independent relativistic calculations is external. No load-bearing premise collapses to a prior author result or ansatz smuggled via citation. The method and observables are independent; any limitation from the straight-line assumption is a separate methodological question, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, limiting visibility into parameters and assumptions; the visible premises are the classical straight-line trajectory and the nonrelativistic treatment.

axioms (2)
  • domain assumption The projectile moves classically along straight line trajectories with constant velocity.
    Explicitly stated in the abstract as the definition of the projectile motion.
  • domain assumption A nonrelativistic description suffices for the electron dynamics.
    The paper frames the entire calculation as nonrelativistic.

pith-pipeline@v0.9.0 · 5628 in / 1308 out tokens · 37689 ms · 2026-05-25T11:39:49.318058+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    Jones and D

    S. Jones and D. H. Madison, Phys. Rev. A 65, (2002) 052727

    work page 2002

  2. [2]

    A. B. Voitkiv and J. Ullrich, Phys. Rev. A 67, (2003) 062703

    work page 2003

  3. [3]

    Igarashi, S

    A. Igarashi, S. Nakazaki, and A. Ohsaki, Phys. Rev. A, Vol 61, (2000) 062712

    work page 2000

  4. [4]

    Xiao-Min Tong, Tsutomu Watanabe, Daiji Kato and Shunsuke Ohtani . Phys. Rev. A , volume 64, (2001) 022711. Figure 11. SDCS dependent on ejection angle. When antiproton energy is 200keV. Results of Igarashi [3], WP -CCC [9] and present CWDVR. Figure 12. SDCS dependent on ejection energy. Results of QM- CCC [7], WP-CC [9], CP [5], and present CWDVR. Journal...

    work page 2001

  5. [5]

    McGovern, D

    M. McGovern, D. Assafr ao, J. R. Mohallem, C. T. Whelan, and H. R. J. Walters, Phys. Rev. A 79, (2009) 042707

    work page 2009

  6. [6]

    McGovern, D

    M. McGovern, D. Assafrao, J. R. Mohallem, C. T. Whelan, and H. R. J. Walters, Phys. Rev. A 81, (2010) 032708

    work page 2010

  7. [7]

    I. B. Abdurakhmanov, A. S. Kadyrov, I. Bray, and A. T. Stelbovics, J. Phys. B: At. Mol. Opt. Phys. 44, (2011) 165203

    work page 2011

  8. [8]

    M. F. Ciappina, T.G. Lee, M. S. Pindzola, and J. Colgan, Phys. Rev. A 88, (2013) 042714

    work page 2013

  9. [9]

    I. B. Abdurakhmanov, A. S. Kadyrov, and I. Bray, Phys. Rev. A 94, (2016) 022703

    work page 2016

  10. [10]

    A. I. Bondarev, Y. S. Kozhedub, I. I. Tupitsyn, V. M. Shabaev, and G. Plunien . Phys. Rev. A 95, (2017) 052709

    work page 2017

  11. [11]

    Liang-You and Starace

    Peng. Liang-You and Starace. Anthony F, The journal of chemical physics 125, (2006) 154311

    work page 2006

  12. [12]

    Suzuki, J

    M. Suzuki, J. Math. Phys. 26 (1985) 601; Phys. Lett. A 146 (1990) 6

    work page 1985

  13. [13]

    A. I. Bondarev· Y. S. Kozhedub· I. I. Tupitsyn · V. M. Shabaev · G. Plunien and·Th. St ohlker, Hyperfine Interact (2019) 240:60

    work page 2019

  14. [14]

    Xiao Min Tong, Shih I Chu Chemical Physics 217 (1997) 119-130

    work page 1997

  15. [15]

    Zorigt, L

    G. Zorigt, L. Khenmedekh, Ch. Aldarmaa, IJMA - 10(5), (2019) 19-23

    work page 2019