Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

  • N. KaiserEmail author
Regular Article - Theoretical Physics


A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by considering the effective range correction in the s-wave interaction and a (spin-independent) p-wave contact-interaction. A two-component recursion generates the in-medium T-matrix at any order when off-shell terms spoil the factorization of multi-loop diagrams. The resummation to all orders is achieved in the form of a geometrical series for the particle-particle ladders, and through an arctangent-function for the combined particle-particle and hole-hole ladders. One finds that the effective range correction changes the results in the limit of large scattering length considerably, with the effect that the Bertsch parameter ξ n nearly doubles. Applications to the equation of state of neutron matter at low density are also discussed. For the p-wave contact-interaction the resummation to all orders is facilitated by decomposing tensorial loop-integrals with a transversal and a longitudinal projector. The enhanced attraction provided by the p-wave ladder series has its origin mainly in the coherent sum of Hartree and Fock contributions.


Scattering Length Geometrical Series Ladder Diagram Neutron Matter Unitary Limit 
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  1. 1.
    W. Zwerger (Editor), BCS-BEC Crossover and Unitary Fermi Gas, in Lect. Notes Phys. 836 (Springer, 2012).Google Scholar
  2. 2.
    M. McNeil Forbes, S. Gandolfi, A. Gezerlis, Phys. Rev. Lett. 106, 235303 (2011).ADSCrossRefGoogle Scholar
  3. 3.
    M. McNeil Forbes, S. Gandolfi, A. Gezerlis, cond-mat/1205.4815.Google Scholar
  4. 4.
    M.J.H. Ku, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Nature Phys. 8, 366 (2012).ADSCrossRefGoogle Scholar
  5. 5.
    Y. Nishida, D.T. Son, Phys. Rev. Lett. 97, 050403 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    S. Gandolfi et al., Phys. Rev. C 79, 054005 (2009).ADSCrossRefGoogle Scholar
  7. 7.
    A. Gezerlis, J. Carlson, Phys. Rev. C 81, 025803 (2011).ADSCrossRefGoogle Scholar
  8. 8.
    N. Kaiser, Nucl. Phys. A 860, 41 (2005) and references therein.ADSCrossRefGoogle Scholar
  9. 9.
    H.W. Hammer, R.J. Furnstahl, Nucl. Phys. A 678, 277 (2000).ADSCrossRefGoogle Scholar
  10. 10.
    J.V. Steele, nucl-th/0010066 (the middle term in eq. (eq:16) needs to be corrected and multiplied by a factor 2).Google Scholar
  11. 11.
    T. Schäfer, C.W. Kao, S.R. Cotanch, Nucl. Phys. A 762, 82 (2005).ADSCrossRefGoogle Scholar
  12. 12.
    W. Zwerger, private communication.Google Scholar
  13. 13.
    A. Schwenk, C.J. Pethick, Phys. Rev. Lett. 95, 160401 (2005).ADSCrossRefGoogle Scholar
  14. 14.
    A. Lacour, J.A. Oller, U.G. Meißner, Ann. Phys. (NY) 326, 241 (2011) and references therein.ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    A. Gezerlis, Phys. Rev. C 83, 065801 (2011).ADSCrossRefGoogle Scholar
  16. 16.
    A. Gezerlis, R. Sharma, Phys. Rev. C 85, 015806 (2012).ADSCrossRefGoogle Scholar
  17. 17.
    S. Gandolfi et al., Phys. Rev. Lett. 101, 132501 (2008).ADSCrossRefGoogle Scholar
  18. 18.
    Q. Chen et al., Phys. Rev. C 77, 054002 (2006).ADSCrossRefGoogle Scholar
  19. 19.
    A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998).ADSCrossRefGoogle Scholar
  20. 20.
    I. Tews, T. Krüger, K. Hebeler, A. Schwenk, nucl-th/1206.0025.Google Scholar
  21. 21.
    H.W. Hammer, D. Lee, Ann. Phys. (NY) 325, 2212 (2010).MathSciNetADSCrossRefzbMATHGoogle Scholar
  22. 22.
    S. Schulteß, Resummations and Chiral Dynamics of Nuclear Matter, diploma thesis, TU München (2012).Google Scholar
  23. 23.
    S. Fritsch, N. Kaiser, Eur. Phys. J. A 21, 117 (2004).ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Physik-Department T39Technische Universität MünchenGarchingGermany

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