Pion condensation and realistic nucleon-nucleon interactions

  • Amand Faessler
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 138)


The general ideas behind Pion Condensation are discussed and the Pion p-wave selfenergy is calculated in nuclear matter taking into account the effects of the nucleon particle-hole and Δ-isobar nucleon-hole states. The residual particle-hole interaction is derived from the Brueckner reaction-matrix using a realistic nucleon-nucleon interaction. This reaction matrix depends on starting energy, nuclear matter density and three momentum variables. The transition potentials between NN−1-ΔN−1 states and the ΔN−1-ΔN−1 states are described by the exchange of π and ϱ mesons with the correlations between the nucleons properly included. The resulting selfenergies are analized within the commonly used model of constant interaction strengths. This analysis yields effective interaction strengths weakly depending on the momentum of the Pion field and on the nuclear density. The particle-hole interaction described by the Brueckner reaction matrix, including the Δ-isobars yields pion condensation at twice the empirical nuclear matter density. The inclusion of the higher order terms in the particle-hole interaction (induced ph-interaction), however, shifts this density up to about 6 times the empirical nuclear matter density. Finally, the influence of the Δ-isobars and the transition potential with the π and ϱ mesons exchange is studied on pion condensation in 16O. Although the calculation in finite nuclei with realistic forces is yet to be done the results of the model calculation show that it is essential to include Δ-isobars and ϱ-meson exchange. In the model presented here these two effects shift down the critical density for pion condensation from 8ϱO to 3ϱO.


Nuclear Matter Slater Determinant Nuclear Matter Density Pion Momentum Finite Nucleus 
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  1. 1.
    A.B. Migdal, ZhETF 61 (1971) 2210; Nucl. Phys. A210 (1973) 421Google Scholar
  2. 2a.
    R.F. Sawyer, Phys. Rev. Lett. 29 (1972) 386Google Scholar
  3. 2b.
    D.J. Scalapino, Phys. Rev. Let. 29 (1972) 386Google Scholar
  4. 2c.
    R.F. Sawyer, D.J. Scalapino, Phys. Rev. D7 (1973) 953Google Scholar
  5. 3.
    G.E. Brown, W. Weise, Phys.Rep. 27C (1976) 2Google Scholar
  6. 4.
    S.O. Bäckman, W. Weise, in “Mesons and Nuclei”, ed. M. Rho, D.H. Wilkinson (North-Holland, Amsterdam 1979) p. 1095Google Scholar
  7. 5a.
    V. Ruck, G. Gyulassy, W. Greiner, Z. Physik A277 (1976) 391Google Scholar
  8. 5b.
    M. Gyulassy, W. Greiner, Ann. Phys. 109 (1977) 485Google Scholar
  9. 6.
    W.H. Dickhoff, A. Faessler, J. Meyer-ter-Vehn, H. Müther, to be publishedGoogle Scholar
  10. 7.
    R.K. Tripathi, A. Faessler, K. Shimizu, to be published as a short note in Z. Phys.Google Scholar
  11. 8.
    R.V. Reid, Ann. Pys. (N.Y.) 50 (1968) 411Google Scholar
  12. 9.
    K. Holinde, R. Machleidt, Nucl. Phys. A280 (1977) 429.Google Scholar
  13. 10.
    J. Meyer-ter-Vehn, Z. Phys. A287 (1978) 241Google Scholar
  14. 11.
    G. Do Dang, Phys. Rev. Lett. 43 (1979) 1708.Google Scholar
  15. 12.
    J. Speth, G.E. Brown, private communicationGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Amand Faessler
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenWest-Germany

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