Chiral four-body interactions in nuclear matter

Abstract

An exploratory study of chiral four-nucleon interactions in nuclear and neutron matter is performed. The leading-order terms arising from pion-exchange in combination with the chiral $4\pi$-vertex and the chiral NN$3\pi$-vertex are found to be very small. Their attractive contribution to the energy per particle stays below $0.6$MeV in magnitude for densities up to $\rho =0.4$fm${}^{-3}$. We consider also the four-nucleon interaction induced by pion-exchange and twofold $\Delta$-isobar excitation of nucleons. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can either be solved analytically or reduced to easily manageable one- or two-parameter integrals. After summing the individually large contributions from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at nuclear matter saturation density ${\rho }_0=0.16$fm${}^{-3}$ a moderate contribution of $2.35$MeV to the energy per particle. The curve $\bar{E}(\rho )$ rises rapidly with density, approximately with the third power of $\rho$. In pure neutron matter the analogous chiral four-body interactions lead, at the same density ${\rho }_n$, to a repulsive contribution that is about half as strong. The present calculation indicates that long-range multi-nucleon forces, in particular those provided by the strongly coupled $\pi N\Delta$-system with its small mass-gap of $293$MeV, can still play an appreciable role for the equation of state of nuclear and neutron matter.

19 pages, 15 figures, to be published in Eur. Phys. J. A

References in corpus (6)

• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• Subleading contributions to the chiral three-nucleon force I: long-range terms
• Four-nucleon force using the method of unitary transformation
• Four-nucleon system with $\Delta$-isobar excitation
• Neutron matter with chiral EFT interactions: Perturbative and first QMC calculations

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• Energy density functional for nuclei and neutron stars
• New applications of renormalization group methods in nuclear physics
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• Chiral EFT based nuclear forces: Achievements and challenges
• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• Microscopic calculations based on chiral two- and three-nucleon forces for proton- and ${}^4$He-nucleus scattering
• Historical perspective and future prospects for nuclear interactions
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Neutron matter based on consistently evolved chiral three-nucleon interactions
• Can chiral EFT give us satisfaction?
• GW170817 constraints analyzed with Gogny forces and momentum-dependent interactions
• Massive Neutron Stars with a Color Superconducting Quark Matter Core
• Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory
• Reducible chiral four-body interactions in nuclear matter
• Isospin-Asymmetry Dependence of the Thermodynamic Nuclear Equation of State in Many-Body Perturbation Theory
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions