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

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.

13 pages, 9 figures, plus Supplementary Material

References in corpus (17)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Systematics of intermediate-energy single-nucleon removal cross sections
• Optical potential from first principles
• Updated systematics of intermediate-energy single-nucleon removal cross sections
• Operator Evolution via the Similarity Renormalization Group I: The Deuteron
• Convergence of the Born Series with Low-Momentum Interactions
• Novel applications of the dispersive optical model
• Block Diagonalization using SRG Flow Equations
• Weinberg eigenvalues for chiral nucleon-nucleon interactions
• Short-range correlation physics at low RG resolution
• Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces
• Scale dependence of deuteron electrodisintegration
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• Weinberg Eigenvalues and Pairing with Low-Momentum Potentials
• Elastic nucleon-nucleus scattering as a direct probe of correlations beyond the independent-particle model
• Operator evolution from the similarity renormalization group and the Magnus expansion
• The quasi-deuteron model at low RG resolution

Cited by in corpus (3)

• High-resolution momentum distributions from low-resolution wave functions
• Perspectives on few-body cluster structures in exotic nuclei
• A Vision for the Science of Rare Isotopes