ar X iv : n uc l - th / 9 90 70 78 v 2 7 O ct 1 99 9 Saturation from nuclear pion dynamics

We construct an equation-of-state for nuclear matter based on the chiral Lagrangian. The relevant scales are discussed and an effective chiral power expansion scheme, which is constructed to work around the nuclear saturation density, is presented. A realistic equation-of-state is obtained by adjusting one free parameter, when the leading and subleading terms in the expansion are included. The saturation mechanism is due to correlations induced by the one-pion-exchange interaction. Furthermore , we find a substantial deviation from the Fermi-gas estimate of the quark condensate in nuclear matter already at the saturation density. For more than four decades, one of the basic problems of nuclear physics has been to find a microscopic understanding of the nuclear equation-of-state in terms of the free nucleon-nucleon interaction [1–3]. The present status is that a quantitative description of nuclear matter can be achieved in a non-relativistic approach only by invoking a three-body force [5], or alternatively with the lowest-order term in the relativistic Brueckner approach [4]. A drawback of the latter, is the lack of a systematic expansion scheme. Thus, it has so far not been possible to obtain a reliable estimate for the corrections to the leading term. Such calculations are based on the traditional semi-phenomenological approach to the nucleon-nucleon interaction, represented by e.g. the Urbana-Argonne [6] and Bonn [7] potentials. During the last few years, a novel approach to the nucleon-nucleon interaction , based on chiral perturbation theory (χPT), has started to emerge. A key element in χPT is the power counting, which relies on a separation of scales. This allows one to organize a systematic approximation scheme. In the nuclear many-body problem, new scales enter, which requires a modification of the expansion scheme developed for the nucleon-nucleon interaction in free space. In this letter we identify the new scales and present an effective chi-ral perturbation theory, appropriate for the nuclear many-body problem. We employ this scheme to construct a nuclear equation-of-state and compute the quark condensate in nuclear matter.