Implicit vs Explicit Renormalization and Effective Interactions

Abstract

Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the out coming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei about 200MeV. This amounts to a great simplification in the determination of the effective interaction parameters.

6 pages, 4 figures. Discussion on One pion exchange added

References in corpus (5)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Shell-model calculations and realistic effective interactions
• Low-momentum interactions with smooth cutoffs
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Block Diagonalization using SRG Flow Equations

Cited by in corpus (11)

• Error analysis of nuclear forces and effective interactions
• Counting states and the Hadron Resonance Gas: Does X(3872) count?
• Fixed points of the Similarity Renormalization Group and the Nuclear Many-Body Problem
• Is the X(3872) a bound state ?
• Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid
• On the precise measurement of the $X(3872)$ mass and its counting rate
• The infrared limit of the Similarity Renormalization Group evolution and Levinson's theorem
• The BCS pairing gap in the on-shell limit of the Similarity Renormalization Group
• Phase transition in the SRG flow of nuclear interactions
• $\pi \pi$ scattering from a similarity renormalization group perspective
• On-shell transition of SRG and nuclear systems