Influence of virtual Δ states on the saturation properties of nuclear matter

Phys. Rev. C 13, 1720 – Published 1 April 1976
B. D. Day and F. Coester


The effect of virtual Δ(1236) states on the saturation properties of nuclear matter is studied within the framework of lowest-order Brueckner theory. The Δ is treated as a stable elementary particle. Transitions from the nucleon-nucleon (NN) channel to the nucleon-Δ (N Δ) channel are caused by a nonrelativistic potential obtained from the static limit of meson theory. The coupled-channel potentials are constrained to fit the NN phase shifts. Saturation curves are calculated for the couplings S01(NN)D05(N Δ) and P13(NN)P15(N Δ), and the effects of other N Δ couplings to nucleon-nucleon P and D waves are estimated. Calculations are done using both the Reid soft-core and Ueda-Green potentials for NN partial waves not coupled to the N Δ channel. The N Δ coupling does not change the usual tendency of the calculated saturation points to lie in a narrow band in the energy-density plane that does not contain the empirical saturation point. This result is illuminated by a rough approximation to the Pauli and dispersion effects. We have also used this approximation to estimate the loss of binding due to N Δ coupling in those channels not treated by detailed calculation. Combining all our results, we find that at the empirical density (1) the inclusion of N Δ coupling in nucleon-nucleon S, P, and D waves reduced the binding energy by about 3.3, 3.2, and 0.8 MeV, respectively, and (2) each particle spends about 3.7% of its time as a Δ. All these figures vary roughly quadratically with the πN Δ coupling constant and increase rapidly with density. The size of the shift in energy depends strongly on the suppression of the short-range part of the two-body wave function, but our approximate formulas indicate that the tendency of the calculated saturation points to remain in a narrow band is independent of the short-range behavior of the two-body interaction, i.e., it is model-independent.

NUCLEAR STRUCTURE Effect of Δ(1236) on saturation of nuclear matter studied in lowest-order Brueckner-Bethe-Goldstone theory.


  • Received 22 December 1975
  • Published in the issue dated April 1976

© 1976 The American Physical Society

Authors & Affiliations

B. D. Day and F. Coester

  • Argonne National Laboratory, Argonne, Illinois 60439

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