The Effect of the Δ (1236)-Resonance in Nuclear Matter

Abstract

The effect of the resonant ⊿ (1236)-states in nuclear matter, is studied within the framework of the exp(S)-formalism [1, 2]. Treating the Schrödinger-Equation of the ground state of an A-particle fermion system with the help of the exp (S)-formalism one obtains a system of A coupled equations which all together are equivalent to the A particle Schrödinger equation. Neglecting three- and more particle forces as well as more particle effects the ground state of the A -particle system is described by the coupled system of one particle and two-particle-equations. Considering the special conditions of nuclear matter the one particle equations turn out to be trivial while the two particle equations reduce to a generalized Bethe-Goldstone-equation. After decomposition of these equations into partial waves we obtain a computable set of coupled integro-differential equations. These equations are fully selfconsistently solved including all partial waves up to total spin J = 2. Numerical calculation shows that the effects produced by ⊿-⊿-partial waves are comparable to those produced by N -⊿-partial waves. Transitions from the N-N channels to N-⊿ or ⊿-⊿ channels are caused by nonrelativistic potentials obtained from the static limit of meson theory. The N-N-interaction is described by a Reid-potential which is modified in order to reproduce the two particle dates (N-N phase shifts, deuteron).