Nuclear energy density functional from chiral pion-nucleon dynamics revisited

Abstract

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1\pi$-exchange, iterated $1\pi$-exchange, and irreducible $2\pi$-exchange with intermediate $\Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^{\ast }(\rho )$ entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength $F_{\nabla }(\rho )$ of the $(\vec{\nabla }\rho {)}^2$ surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region ${\rho }_0/2<\rho <{\rho }_0$. The spin-orbit coupling strength $F_{so}(\rho )$ receives contributions from iterated $1\pi$-exchange (of the ``wrong sign'') and from three-nucleon interactions mediated by $2\pi$-exchange with virtual $\Delta$-excitation (of the ``correct sign''). In the region around ${\rho }_0/2\simeq 0.08$fm${}^{-3}$ where the spin-orbit interaction in nuclei gains most of its weight these two components tend to cancel, thus leaving all room for the short-range spin-orbit interaction. The strength function $F_J(\rho )$ multiplying the square of the spin-orbit density comes out much larger than in phenomenological Skyrme forces and it has a pronounced density dependence.

18 pages, 7 figures, submitted to Nuclear Physics A

References in corpus (7)

• The Skyrme Interaction in finite nuclei and nuclear matter
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. IX: Constraint of pairing force to ${}^1{S}_0$ neutron-matter gap
• Toward ab initio density functional theory for nuclei
• Density Matrix Expansion for Low-Momentum Interactions
• The relativistic self-energy in nuclear dynamics
• Note on spin-orbit interactions in nuclei and hypernuclei
• Quasi-particle interaction in nuclear matter from chiral pion-nucleon dynamics

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• Proton elastic scattering on calcium isotopes from chiral nuclear optical potentials
• Ab Initio Derivation of Model Energy Density Functionals
• Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions
• Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• First applications of Fayans functional to deformed nuclei
• Sloppy nuclear energy density functionals: effective model reduction
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
• Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials
• Addressing spectroscopic quality of covariant density functional theory
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• Comparing different density-matrix expansions for long-range pion exchange
• Chiral nuclear dynamics with three-body forces
• Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure