Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

TL;DR

This paper calculates the isovector surface and spin-orbit terms of the nuclear energy density functional using chiral pion-nucleon dynamics, providing parameter-free predictions that surpass phenomenological models and are relevant for neutron-rich nuclei.

Contribution

It extends previous work by systematically computing isovector terms from chiral perturbation theory, including various pion-exchange processes and Pauli-blocking effects, with improved density-matrix expansion.

Findings

Strength functions are significantly larger than Skyrme forces.

Parameter-free predictions based on long-range pion-exchange dynamics.

Results are relevant for nuclear structure in neutron-rich systems.

Abstract

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: $(\vec \nabla \rho_p- \vec \nabla \rho_n)^2 G_d(\rho)+ (\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec J_p-\vec J_n) G_{so(\rho)+(\vec J_p-\vec J_n)^2 G_J(\rho)$ pertaining to different proton and neutron densities. 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. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(\rho)$, $G_{so}(\rho)$ and $G_J(\rho)$ which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.