Renormalization group evolution of optical potentials: explorations using a toy model

TL;DR

This paper investigates the application of the similarity renormalization group (SRG) to optical potentials within a simplified one-dimensional model, revealing how SRG decoupling improves perturbative approaches and affects nonlocality in reaction theory.

Contribution

It introduces the first study of SRG evolution of optical potentials using a toy model, demonstrating benefits for reaction-structure consistency and perturbative methods.

Findings

SRG decoupling enhances perturbative approximations

Induced SRG nonlocality compares to optical potential nonlocality

Low RG resolution improves reaction modeling

Abstract

To take full advantage of experimental facilities such as FRIB for applications to nuclear astrophysics, nuclear structure, and explorations of neutrinos and fundamental symmetries, we need a better understanding of the interplay of reaction and structure theory. The renormalization group (RG) is the natural tool for maintaining a consistent treatment of reaction and structure. Here we make a first study of RG for optical potentials, which are important ingredients for direct reactions. To simplify the analysis, we use a pedagogical one-dimensional model and evolve toward low RG resolution using the similarity RG (or SRG). We show how SRG decoupling at low resolution carries over to the optical potential and enhances perturbative approximations, and how induced SRG nonlocality compares to the nonlocality of the optical potential. We discuss the results in the larger context of consistent SRG evolution of operators and wave functions in the analysis of direct reactions.