Saturation of nuclear matter in effective field theory

The two-nucleon interaction derived in chiral effective field theory is used to investigate the saturation properties of symmetric nuclear matter at next-to-leading order. Pauli blocking effects in the two-pion exchange diagrams are shown to produce an effective attraction in nuclear matter. PACS. 21.65.-f Nuclear matter – 21.65.Mn Equation of state of nuclear matter – 21.30.-x Forces in hadronic systems Within the last two decades, effective field theory has provided new methods for nuclear structure investigations. Two-, threeand four-nucleon interactions based on the most general chiral effective pion-nucleon Lagrangian have been developed based onWeinberg’s power counting scheme. The phase shifts of the nucleon-nucleon interaction below the pion production threshold are reproduced with a precision that is comparable with the one achieved by modern phenomenological two-nucleon potentials, when pushing the expansion to the order NLO, see Refs.[1,2]. These forces together with three-nucleon forces at NLO have been applied to a cornucopia of reactions. In particular, various three-nucleon scattering observables have been analyzed at low and intermediate energies showing, in general, a good agreement with the data. The binding energies of He and He have been reproduced successfully once the leading three-nucleon force is included. Within the framework of the no-core shell model, the chiral forces have been used to study nuclei with A = 7, 10 . . .13 systems, in particular the sensitivity to the three-nucleon force, see [3,4] for more details. Recent progress in these fields is reviewed in Ref. [5]. Given these successes, the question arises whether effective field theory can contribute to the solution of the nuclear matter problem. First groundbreaking attempts in this direction have been done by the Munich group, see e.g. Refs. [6,7] (and references therein). In the present communication, we apply the NLO version of the chiral nucleon-nucleon interaction to symmetric nuclear matter. This differs from the Munich approach which concentrates on the development of a chiral effective interaction to be used exclusively in the nuclear medium without link to the two-nucleon interaction in the vacuum. In Ref.[8], nuclear matter has been studied with a lowmomentum two-nucleon force Vlow−k derived from the Ar1 Throughout, we use the abbreviation LO for leading order, NLO for next-to-leading order and so on. gonne v18 potential via renormalization group techniques. It was found that the low-momentum interactions can be used in second order perturbation theory to describe nuclear matter, provided Pauli blocking effects due to the medium are properly included. This finding suggests that a resummation of the ladder diagrams, as it is mandatory in Brueckner theory, can be avoided. Recently, the simplified version AV 6 of the Argonne potential has been used in a quantum Monte Carlo study of symmetric nuclear matter [9]. For Fermi momenta less than kF = 1.33 fm , the binding energies obtained for nuclear matter are not smaller than the ones calculated within the Fermi hypernetted chain approach or the Brueckner Hartree-Fock method [10]. This fact is interpreted as evidence for the inadequacy of three-nucleon interaction models for all densities [9]. Both the two-nucleon potential derived from effective field theory and Vlow−k derived from any of the highprecision NN potentials can be characterized by the fact that the large momentum components of the interaction are removed, in contrast to meson-exchange potentials. The chiral potential differs from phenomenological ones, such as v18, by its power counting scheme which allows systematic improvements. In Ref.[13], the pion-nucleon vertices are systematically taken from the chiral expansion of the pion-nucleon interaction. The two-nucleon interaction is generated by eliminating the pion-two-nucleon states via the FST-Okubo projection method [11,12]. The two-pion exchange diagrams relevant for the discussion of nuclear matter properties are shown in Fig.1 for the order NLO. The Weinberg-Tomozawa term generates a class of triangle diagrams (c) characterized by one internal nucleon line. Moreover, there are diagrams with two internal nucleon lines, such as the crossed-box two-pion exchange graph (a). Notice that the class of box two-pion exchange diagrams (b) in Fig.1 is not two-nucleon reducible and therefore has to be iterated when solving the Schrödinger 2 P. Saviankou et al.: Saturation of nuclear matter in effective field theory