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Relativistic eikonal description of A(p,pN) reactions

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B. Van Overmeire, W. Cosyn, P. Lava, J. Ryckebusch

Nuclear Theory · Submitted 6 Mar 2006 · 56 references

Pith's verdict: A useful model paper whose central factorization identity does not hold for non-coplanar kinematics; the tested coplanar data may survive, but the wide-applicability claim is not established.

T0 · AI review

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arXiv IDnucl-th/0603013 (version 3)
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CitationB. Van Overmeire, J. Ryckebusch, P. Lava, W. Cosyn. "Relativistic eikonal description of A(p,pN) reactions." arXiv:nucl-th/0603013 (2006). https://pith.science/paper/7SK5U5TZ
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The paper

The paper claims

The paper proposes a relativistic, factorized eikonal framework for quasielastic proton knockout and shows that optical-potential distortion reproduces measured cross-section shapes from 250 MeV to 1 GeV.

The reading

This paper aims to establish that one relativistic eikonal framework can describe quasielastic proton-knockout reactions, A(p,pN), across a wide energy range by separating the hard knockout from the soft initial- and final-state interactions. The cross section is written in factorized form: a free on-shell proton-proton cross section times a distorted momentum distribution, with all distortion effects collected in an IFSI factor. Using optical potentials inside the eikonal phases, the calculations reproduce the shape of the 1 GeV data on 12C, 16O, and 40Ca as well as the 250 MeV 4He(p,2p) data. If the claim holds, the model offers a practical way to extract nuclear-structure information from knockout experiments in an energy range where partial-wave distorted-wave calculations become cumbersome.

What carries the argument

The central object is the IFSI factor $S_{\mathrm{IFSI}}(\mathbf{r}) = \hat{S}_{k_1} \hat{S}_{k_2} \hat{S}_{p_1}$, a product of three eikonal phase factors attached to the incoming and two outgoing protons. In the optical-potential version each factor is an exponential of an integral of the central optical potential along the proton's trajectory, with the integration truncated at the hard-collision point; in the Glauber version each factor becomes a product of $1 - \Gamma(\mathbf{b}-\mathbf{b}_j)\theta(z-z_j)$ over spectator nucleons. This factor is inserted into the distorted momentum-space wave function $\phi^D(\mathbf{p}_m) = \int e^{-i\mathbf{p}_m\cdot\mathbf{r}}\phi(\mathbf{r}) S_{\mathrm{IFSI}}(\mathbf{r})\,d\mathbf{r}$, whose squared modulus defines the distorted momentum distribution in the factorized cross section. The free on-shell proton-proton cross section enters through the replacement of the off-shell quasielastic amplitude by the measured free cross section.

Extended reading notes

Core claim

The central claim is that the quasielastic A(p,pN) differential cross section factorizes into a free proton-proton cross section and a distorted momentum distribution, with initial- and final-state interactions entering only through the IFSI factor $S_{\mathrm{IFSI}}(\mathbf{r})$ that multiplies the bound-nucleon wave function before Fourier transformation. The paper constructs this factor from relativistic eikonal phases generated by optical potentials (the ROMEA variant) and, alternatively, from Glauber profile functions (the RMSGA variant). It then shows that the optical-potential version reproduces the shape of measured cross sections in two kinematically different experiments, one at 1 GeV and one at 250 MeV. The authors take this agreement as support for the model's applicability over a wide energy range.

Load-bearing premise

The framework assumes that optical potentials fitted to elastic proton-nucleus scattering, together with the free on-shell proton-proton cross section, correctly describe the inelastic knockout distortion, and that spin-orbit and negative-energy contributions can be dropped.

Editorial extensions

If this is right

  • The same factorized formula, with optical-potential eikonal phases, can model A(p,2p) and A(p,pn) cross sections from roughly 250 MeV to 1 GeV, so knockout spectroscopy does not have to switch reaction models across this range.
  • Because IFSI attenuate the cross section and shift the apparent missing momentum in a level- and target-dependent way, extracting bound-state momentum distributions requires the model's distortion corrections rather than a plane-wave reading of the data.
  • The surface-peaked character of the reaction is a distortion effect: measured cross sections sample only about 12 per cent of the central density for Fermi-level knockout, which limits how directly deep-hole states can be probed.
  • The Glauber version overestimates distortion when the ejected nucleon is slow (around 100 MeV) because of its linear-trajectory and frozen-spectator assumptions; optical potentials are the appropriate choice in that regime, while Glauber remains useful for higher-energy applications such as nuclear transparency.

Reading between the lines

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

  • One could turn the IFSI factor directly into a nuclear-transparency prediction, since the attenuation of the plane-wave cross section is essentially the squared IFSI factor averaged over the bound-state density; the paper flags this direction but does not compute it.
  • Because the model drops the spin-orbit part of the optical potential and the negative-energy projection, it makes no prediction for spin-dependent distortions; a measurement of the analyzing power in A(p,2p) would show where that omission becomes visible.
  • The same eikonal IFSI construction could be attached to other exclusive hard vertices, such as (p,p pi) or electron-induced knockout, by replacing the hard collision factor while keeping the distortion factor unchanged.
Original abstract

The authors present a relativistic and cross-section factorized framework for computing quasielastic A(p,pN) observables at intermediate and high energies. The model is based on the eikonal approximation and can accomodate both optical potentials and the Glauber method for dealing with the initial- and final-state interactions (IFSI). At lower nucleon energies, the optical-potential philosophy is preferred, whereas at higher energies the Glauber method is more natural. This versatility in dealing with the IFSI allows one to describe A(p,pN) reactions in a wide energy range. Most results presented here use optical potentials as this approach is argued to be the optimum choice for the kinematics of the experiments considered in the present paper. The properties of the IFSI factor, a function wherein the entire effect of the IFSI is contained, are studied in detail. The predictions of the presented framework are compared with two kinematically different experiments. First, differential cross sections for quasielastic proton scattering at 1 GeV off 12C, 16O, and 40Ca target nuclei are computed and compared to data from PNPI. Second, the formalism is applied to the analysis of a 4He(p,2p) experiment at 250 MeV. The optical-potential calculations are found to be in good agreement with the data from both experiments, showing the reliability of the adopted model in a wide energy range.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,595 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.66 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The authors present a relativistic and cross-section factorized framework for computing quasielastic A(p,pN) observables at intermediate and high energies. The model is based on the eikonal approximation and can accomodate both optical potentials and the Glauber method for dealing with the initial- and final-state interactions (IFSI). At lower nucleon energies, the optical-potential philosophy is preferred, whereas at higher energies the Glauber method is more natural. This versatility in dealing with the IFSI allows one to describe A(p,pN) reactions in a wide energy range. Most results presented here use optical potentials as this approach is argued to be the optimum choice for the kinematics of the experiments considered in the present paper. The properties of the IFSI factor, a function wherein the entire effect of the IFSI is contained, are studied in detail. The predictions of the presented framework are compared with two kinematically different experiments. First, differential cross sections for quasielastic proton scattering at 1 GeV off 12C, 16O, and 40Ca target nuclei are computed and compared to data from PNPI. Second, the formalism is applied to the analysis of a 4He(p,2p) experiment at 250 MeV. The optical-potential calculations are found to be in good agreement with the data from both experiments, showing the reliability of the adopted model in a wide energy range.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The authors present a relativistic and cross-section factorized framework for computing quasielastic A(p,pN) observables at intermediate and high energies. contribution 0.99 0.93 0.12 asserted 1.00
s1 The model is based on the eikonal approximation and can accomodate both optical potentials and the Glauber method for dealing with the initial- and final-state interactions (IFSI). method 0.99 0.55 0.04 asserted 0.80
s2 At lower nucleon energies, the optical-potential philosophy is preferred, whereas at higher energies the Glauber method is more natural. method 0.64 0.21 0.04 asserted 0.86
s3 This versatility in dealing with the IFSI allows one to describe A(p,pN) reactions in a wide energy range. contribution 0.43 0.42 0.10 asserted 0.75
s4 Most results presented here use optical potentials as this approach is argued to be the optimum choice for the kinematics of the experiments considered in the present paper. method 0.90 0.79 0.07 asserted 0.88
s5 The properties of the IFSI factor, a function wherein the entire effect of the IFSI is contained, are studied in detail. contribution 0.86 0.87 0.04 asserted 0.98
s6 The predictions of the presented framework are compared with two kinematically different experiments. method 0.51 0.89 0.04 asserted 0.99
s7 First, differential cross sections for quasielastic proton scattering at 1 GeV off 12C, 16O, and 40Ca target nuclei are computed and compared to data from PNPI. contribution 0.54 0.90 0.03 asserted 0.98
s8 Second, the formalism is applied to the analysis of a 4He(p,2p) experiment at 250 MeV. contribution 0.68 0.91 0.03 asserted 0.99
s9 The optical-potential calculations are found to be in good agreement with the data from both experiments, showing the reliability of the adopted model in a wide energy range. result 0.51 0.94 0.79 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.85 · evidence from simulation or computation 0.81.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: Schematic representation of the
Figure 2. FIG. 2: Geometry of the scattering process. The vectors
Figure 3. FIG. 3: (Color online) The radial and polar-angle dependenc
Figure 4. FIG. 4: (Color online) As in Fig. 3 but now for the imaginary pa
Figure 5. FIG. 5: The radial dependence of the real part of the IFSI fact
Figure 6. FIG. 6: (Color online) The polar- and azimuthal-angle depen
Figure 7. FIG. 7: Contribution to the
Figure 8. FIG. 8: The sensitivity of the real part of the complete IFSI fa
Figure 9. FIG. 9: (Color online) As in Fig. 3 but now using the RMSGA meth
Figure 10. FIG. 10: Differential cross section for the
Figure 11. FIG. 11: As in Fig. 10 but for the
Figure 12. FIG. 12: As in Fig. 10 but for the
Figure 13. FIG. 13: The
Figure 14. FIG. 14: Differential cross section for the

Figures reproduced from arXiv:nucl-th/0603013 by the authors.

References
How the literature uses it

2 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

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Cites it as background 1 paper

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