Exact calculation of three-body contact interaction to second order

Abstract

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle $\bar{E}(k_f)$ are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to $\bar{E}(k_f)\sim k_f^{10}$ with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.

9 pages, 6 figures, to be published in European Journal A

References in corpus (4)

• Improved nuclear matter calculations from chiral low-momentum interactions
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Subleading contributions to the chiral three-nucleon force I: long-range terms
• Resummation of fermionic in-medium ladder diagrams to all orders

Cited by in corpus (14)

• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• Chiral Effective Field Theory and the High-Density Nuclear Equation of State
• Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT
• Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach
• Towards order-by-order calculations of the nuclear and neutron matter equations of state in chiral effective field theory
• Nuclear chiral dynamics and thermodynamics
• Towards grounding nuclear physics in QCD
• Regulator Artifacts in Uniform Matter for Chiral Interactions
• Density-dependent effective baryon-baryon interaction from chiral three-baryon forces
• Microscopically constrained mean field models from chiral nuclear thermodynamics
• Implementing chiral three-body forces in terms of medium-dependent two-body forces
• Exact solution of the Brueckner-Bethe-Goldstone equation with three-body forces in nuclear matter
• Estimates and power counting in uniform matter with softened interactions
• Partial restoration of chiral symmetry in hot and dense neutron matter