Abstract
Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V_med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of V_med from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range $2\pi$-exchange term, a mid-range $1\pi$-exchange component and a short-range contact term. Several applications of V_med to the equation of state of cold nuclear and neutron matter, the nucleon single-particle potential in nuclear matter, and the nuclear quasiparticle interaction are discussed. We also explore differences in using local vs. nonlocal regulating functions on 3N forces and make direct comparisons to exact results at low order in perturbation theory expansions for the equation of state and single-particle potential. We end with a discussion and numerical calculation of the in-medium NN potential V_med from the next-to-next-to-next-to-leading order (N3LO) chiral 3N force, which consists of a series of long-range and short-range terms.
Highlights
Three-nucleon forces are essential to any microscopic description of nuclear many-body systems, from the structure and reactions of finite nuclei [1,2,3,4] to the equation of state and transport properties of dense matter encountered in core-collapse supernovae and neutron stars [2, 5,6,7,8,9,10,11,12,13]
It has been challenging [5] to obtain nuclear two- and three-body forces that simultaneously fit well the properties of finite nuclei and nuclear matter, but in recent years, much progress has been achieved within the framework of chiral effective field theory [23,24,25,26,27] to construct three-body forces consistent with the employed two-body force, all within a systematic power series expansion involving the ratio of the physical scale Q to the chiral symmetry breaking scale χ ∼ 1 GeV
Due to the large number of contributions to Vmed at N3LO, we only show selected results for individual topologies
Summary
Three-nucleon forces are essential to any microscopic description of nuclear many-body systems, from the structure and reactions of finite nuclei [1,2,3,4] to the equation of state and transport properties of dense matter encountered in core-collapse supernovae and neutron stars [2, 5,6,7,8,9,10,11,12,13]. Three-body forces have been shown to be especially relevant for understanding the properties of neutron-rich nuclei out to the drip line [16, 18, 21, 22] In the past, it has been challenging [5] to obtain nuclear two- and three-body forces that simultaneously fit well the properties of finite nuclei and nuclear matter, but in recent years, much progress has been achieved within the framework of chiral effective field theory [23,24,25,26,27] to construct three-body forces consistent with the employed two-body force, all within a systematic power series expansion involving the ratio of the physical scale Q to the chiral symmetry breaking scale χ ∼ 1 GeV. We find that local regulators introduce large artifacts compared to nonlocal regulators when the same value of the cutoff scale is used in both cases
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