Scales in nuclear matter: Chiral dynamics with pion nucleon form factors

Abstract

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from $2\pi$-exchange with excitations of virtual $\Delta(1232)$-isobars are also taken into account in our diagrammatic calculation of the energy per particle $\bar E(k_f)$. In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, $\rho_0 \simeq 0.16 $fm$^{-3}$, $\bar E_0\simeq -16 $MeV, is well reproduced with a monopole mass of $\Lambda \simeq 4\pi f_\pi \simeq 1.16 $GeV. As in the recent approach based on the universal low-momentum $NN$-potential $V_{\rm low-k}$, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion-exchange contributions to $\bar E(k_f)$ on the ''resolution'' scale $\Lambda$ can be compensated over a wide range of $\Lambda$ by counterterms with two ''running'' contact-couplings. As a further application we study the in-medium chiral condensate $<\bar q q >(\rho)$ beyond the linear density approximation. For $\rho \leq 1.5 \rho_0$ we find small corrections from the derivative $d \bar E(k_f)/d m_\pi$, which are stable against variations of the monopole regulator mass $\Lambda$.