Coupled-cluster calculations of nucleonic matter

Abstract

Background: The equation of state (EoS) of nucleonic matter is central for the understanding of bulk nuclear properties, the physics of neutron star crusts, and the energy release in supernova explosions. Because nuclear matter exhibits a finely tuned saturation point, its EoS also constrains nuclear interactions.Purpose: This work presents coupled-cluster calculations of infinite nucleonic matter using modern interactions from chiral effective field theory (EFT). It assesses the role of correlations beyond particle-particle and hole-hole ladders, and the role of three-nucleon forces (3NFs) in nuclear matter calculations with chiral interactions.Methods: This work employs the optimized nucleon-nucleon ($NN$) potential NNLO${}_{\mathrm{opt}}$ at next-to-next-to leading order, and presents coupled-cluster computations of the EoS for symmetric nuclear matter and neutron matter. The coupled-cluster method employs up to selected triples clusters and the single-particle space consists of a momentum-space lattice. We compare our results with benchmark calculations and control finite-size effects and shell oscillations via twist-averaged boundary conditions.Results: We provide several benchmarks to validate the formalism and show that our results exhibit a good convergence toward the thermodynamic limit. Our calculations agree well with recent coupled-cluster results based on a partial wave expansion and particle-particle and hole-hole ladders. For neutron matter at low densities, and for simple potential models, our calculations agree with results from quantum Monte Carlo computations. While neutron matter with interactions from chiral EFT is perturbative, symmetric nuclear matter requires nonperturbative approaches. Correlations beyond the standard particle-particle ladder approximation yield non-negligible contributions. The saturation point of symmetric nuclear matter is sensitive to the employed 3NFs and the employed regularization scheme. 3NFs with nonlocal cutoffs exhibit a considerably improved convergence than their local cousins. We are unable to find values for the parameters of the short-range part of the local 3NF that simultaneously yield acceptable values for the saturation point in symmetric nuclear matter and the binding energies of light nuclei.Conclusions: Coupled-cluster calculations with nuclear interactions from chiral EFT yield nonperturbative results for the EoS of nucleonic matter. Finite-size effects and effects of truncations can be controlled. For the optimization of chiral forces, it might be useful to include the saturation point of symmetric nuclear matter.