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 $V_{\mathrm{low}-\mathrm{k}}$, 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 $\rho \le 1.5{\rho }_0$ 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 $\Lambda$.

Comments: 13 pages, 6 figures