Similarity Renormalization Group Evolution of Three-Nucleon Forces in a Hyperspherical Momentum Representation

TL;DR

This paper introduces a new hyperspherical momentum framework for SRG evolution of three-nucleon forces, ensuring unitarity and enabling clear visualization of force evolution and decoupling patterns.

Contribution

It presents a novel hyperspherical momentum approach for SRG evolution of 3NF, maintaining unitarity and improving visualization of force evolution.

Findings

Unitary evolution demonstrated for the triton with various interactions

Exact representation of the $T_{rel}$-SRG regulator in each partial wave

Clear visualization of SRG decoupling and universality patterns

Abstract

A new framework for computing the Similarity Renormalization Group (SRG) evolution of three-nucleon forces (3NF) in momentum representation is presented. The use of antisymmetric three-particle hyperspherical momentum states ensures unitary evolutions within certain basis truncations, much like antisymmetric harmonic oscillator SRG evolutions. Additionally, in each partial wave the $T_{\mbox{rel}}$-SRG regulator is exactly represented, similar to recent 3NF momentum representation evolutions. Unitary equivalence is demonstrated for the triton using several chiral two- plus three-nucleon interactions. This method allows for a clean visualization of the evolution of the three-nucleon forces, which manifests the SRG decoupling pattern and low-momentum universality.