Abstract
To incorporate the \ensuremath{\Delta} isobar in the relativistic Dirac-Brueckner model we develop a formalism that treats the \ensuremath{\Delta} analogously to the nucleon. That is, we introduce scalar and vector components of the \ensuremath{\Delta} self-energy and define effective quantities for the \ensuremath{\Delta} similar to the ones for the nucleon. Using this formalism and based on one-boson-exchange interactions, we present a parameter-free calculation of the equation of state of nuclear matter. We list results for the effective quantities of both the nucleon and the \ensuremath{\Delta}. The main result we find is that in our model the properties of the nucleon in nuclear matter seem hardly affected by the inclusion of the \ensuremath{\Delta}. Also the medium dependence of the properties of the \ensuremath{\Delta} turns out to be quite small. Finally we investigate the momentum dependence of the mean field of the \ensuremath{\Delta}.
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