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Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method

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Th. A. Rijken

Nuclear Theory · Submitted 19 Sep 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schr\"{o}dinger equations.

how it is stated · asserted 1.00 read the record →

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arXiv ID1409.5593 (version 1)
Pith IDE6NPUV4D, Pith's permanent record of this paper and its review
CitationTh. A. Rijken. "Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method." arXiv:1409.5593 (2014). https://pith.science/paper/E6NPUV4D
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,947 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.25 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.95 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \neq p_i$. The mass parameters in the exponentials of the Gaussian base-functions are fixed using the geometric progression recipe of Hiyama-Kamimura. The fitting of the expansion coefficients is linearly and very fast. Application to nucleon-nucleon is given in detail for the recent Extended-soft-core model ESC08c. The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schr\"{o}dinger equations.

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 In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). contribution 0.56 0.93 0.07 asserted 0.99
s1 This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \neq p_i$. method 0.81 0.55 0.08 asserted 0.94
s2 The mass parameters in the exponentials of the Gaussian base-functions are fixed using the geometric progression recipe of Hiyama-Kamimura. method 1.00 0.66 0.03 asserted 1.00
s3 The fitting of the expansion coefficients is linearly and very fast. method 0.71 0.82 0.06 asserted 1.00
s4 Application to nucleon-nucleon is given in detail for the recent Extended-soft-core model ESC08c. contribution 0.81 0.86 0.07 asserted 0.98
s5 The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schr\"{o}dinger equations. result 1.00 0.91 0.68 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.92.

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not examined
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  • references and citing sentences
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  • 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

The paper
Original abstract

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \neq p_i$. The mass parameters in the exponentials of the Gaussian base-functions are fixed using the geometric progression recipe of Hiyama-Kamimura. The fitting of the expansion coefficients is linearly and very fast. Application to nucleon-nucleon is given in detail for the recent Extended-soft-core model ESC08c. The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schr\"{o}dinger equations.

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