Reducible chiral four-body interactions in nuclear matter

  • N. Kaiser
  • R. Milkus
Regular Article - Theoretical Physics


The method of unitary transformations generates five classes of leading-order reducible chiral four-nucleon interactions which involve pion exchanges and a spin-spin contact term. Their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter are evaluated in detail. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can be reduced to easily manageable one- or two-parameter integrals. One finds substantial compensations among the different contributions arising from 2-ring and 1-ring diagrams. Altogether, the net attraction generated by the chiral four-nucleon interaction does not exceed values of -1.3 MeV for densities \( \rho < 2\rho_{0}\).


Nuclear Matter Unitary Transformation Neutron Density Fermi Sphere Identical Vertex 
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  1. 1.
    E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006) and references thereinCrossRefADSGoogle Scholar
  2. 2.
    E. Epelbaum, H.-W. Hammer, Ulf-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009)CrossRefADSGoogle Scholar
  3. 3.
    S.K. Bogner, R.J. Furnstahl, A. Schwenk, Prog. Part. Nucl. Phys. 65, 94 (2010)CrossRefADSGoogle Scholar
  4. 4.
    S.K. Bogner, R.J. Furnstahl, A. Nogga, A. Schwenk, Nucl. Phys. A 763, 59 (2005)CrossRefADSGoogle Scholar
  5. 5.
    A. Nogga, S.K. Bogner, A. Schwenk, Phys. Rev. C 70, 061002 (2004)CrossRefADSGoogle Scholar
  6. 6.
    K. Hebeler et al., Phys. Rev. C 83, 031301 (2011)CrossRefADSGoogle Scholar
  7. 7.
    V. Bernard, E. Epelbaum, H. Krebs, Ulf-G. Meißner, Phys. Rev. C 77, 064004 (2008)CrossRefADSGoogle Scholar
  8. 8.
    I. Tews, T. Krüger, K. Hebeler, A. Schwenk, Phys. Rev. Lett. 110, 032504 (2013)CrossRefADSGoogle Scholar
  9. 9.
    T. Krüger, I. Tews, K. Hebeler, A. Schwenk, Phys. Rev. C 88, 025802 (2013)CrossRefADSGoogle Scholar
  10. 10.
    N. Kaiser, Eur. Phys. J. A 48, 135 (2012)CrossRefADSGoogle Scholar
  11. 11.
    E. Epelbaum, Phys. Lett. B 639, 456 (2006)CrossRefADSGoogle Scholar
  12. 12.
    E. Epelbaum, Eur. Phys. J. A 34, 197 (2007)CrossRefADSGoogle Scholar
  13. 13.
    T. Krüger, TU Darmstadt, private communications.Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Physik-Department T39Technische Universität MünchenGarchingGermany

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