Is nuclear matter perturbative with low-momentum interactions?

Abstract

The nonperturbative nature of inter-nucleon interactions is explored by varying the momentum cutoff of a two-nucleon potential. Conventional force models, which have large cutoffs, are nonperturbative because of strong short-range repulsion, the iterated tensor interaction, and the presence of bound or nearly-bound states. But for low-momentum interactions with cutoffs around 2 fm −1 , the softened potential combined with Pauli blocking leads to corrections in nuclear matter in the particleparticle channel that are well converged at second order in the potential, suggesting that perturbation theory can be used in place of Brueckner resummations. Calculations of nuclear matter using the low-momentum two-nucleon force V low k with a corresponding leading-order three-nucleon (3N) force from chiral effective field theory (EFT) exhibit nuclear binding in the Hartree-Fock approximation, and become less cutoff dependent with the inclusion of the dominant second-order contributions. The role of the 3N force is essential to obtain saturation, and the contribution to the total potential energy is compatible with EFT power-counting estimates.

Relativistic nuclear energy density functional constrained by low-energy QCD

“…The applicability of a perturbative expansion scheme for nuclear matter with low-momentum interactions, which is the basic hypothesis behind our approach, is discussed in Ref. [75]. Further studies towards foundations along these lines are presently being pursued.…”

Cluster formation and the virial equation of state of low-density nuclear matter

“…Microscopic calculations start from NN and three-nucleon interactions that reproduce NN scattering and selected few-nucleon data. In addition to the conventional variational [13,14] and Brueckner [15,16] calculations, renormalization-group methods coupled with effective field theory provide new insights to nuclear forces and the possibility of a perturbative and thus systematic approach to nuclear matter with theoretical error estimates [17,18]. However, all wave functions that are typically used only include two-nucleon correlations and omit four-nucleon correlations that could be important to describe alpha particle formation at low densities.…”

Properties of nuclear matter within the JISP16NNinteraction

“…However, as it was shown in Refs. [22][23][24], in the case of soft N N interactions, a perturbative approach can be successfully used for nuclear matter calculations. In particular, the authors of Refs.…”

“…In particular, the authors of Refs. [22,23] demonstrated that the dominant particle-particle channel contributions become perturbative in nuclear matter calculations using so-called low-momentum N N interactions (V low−k ) obtained by renormalization group methods [25,26] from Argonne AV 18 and chiral effective field theory N 3 LO N N interactions.…”

“…have a similar falloff when renormalized to a corresponding scale which lends support to our adoption of the perturbative approach of Refs. [22,23].…”