The two-pion-exchange three-nucleon potential and nuclear matter

S. A. Coon, M. D. Scadron, P. C. McNamee, Bruce R Barrett, D. W E Blatt, B. H J McKellar

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Abstract

We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be - 1.90 ± 0.2 MeV.

Original languageEnglish (US)
Pages (from-to)242-278
Number of pages37
JournalNuclear Physics, Section A
Volume317
Issue number1
DOIs
StatePublished - Apr 2 1979

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nucleon potential
pions
binding energy
current algebra
isobars
nuclear structure
subtraction
scattering amplitude
extrapolation
formalism
energy
scattering

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Coon, S. A., Scadron, M. D., McNamee, P. C., Barrett, B. R., Blatt, D. W. E., & McKellar, B. H. J. (1979). The two-pion-exchange three-nucleon potential and nuclear matter. Nuclear Physics, Section A, 317(1), 242-278. https://doi.org/10.1016/0375-9474(79)90462-7

The two-pion-exchange three-nucleon potential and nuclear matter. / Coon, S. A.; Scadron, M. D.; McNamee, P. C.; Barrett, Bruce R; Blatt, D. W E; McKellar, B. H J.

In: Nuclear Physics, Section A, Vol. 317, No. 1, 02.04.1979, p. 242-278.

Research output: Contribution to journalArticle

Coon, SA, Scadron, MD, McNamee, PC, Barrett, BR, Blatt, DWE & McKellar, BHJ 1979, 'The two-pion-exchange three-nucleon potential and nuclear matter', Nuclear Physics, Section A, vol. 317, no. 1, pp. 242-278. https://doi.org/10.1016/0375-9474(79)90462-7
Coon, S. A. ; Scadron, M. D. ; McNamee, P. C. ; Barrett, Bruce R ; Blatt, D. W E ; McKellar, B. H J. / The two-pion-exchange three-nucleon potential and nuclear matter. In: Nuclear Physics, Section A. 1979 ; Vol. 317, No. 1. pp. 242-278.
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AB - We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be - 1.90 ± 0.2 MeV.

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