Applications of the Similarity Renormalization Group to the Nuclear Interaction

Abstract

The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The SRG proves to be versatile and robust in its treatment of these interactions and opens the door to a deeper understanding of the renormalization process.Chiral Effective Field Theory (χEFT) provides a consistent and rigorous parametrization of the inter-nucleon interaction. While already softer than other available potentials, transformation via the Similarity Renormalization Group (SRG) brings numerous computational benefits. The hierarchy of many-body forces inherent in χEFT's are also treated consistently by the SRG's simple formalism. The SRG is a natural partner to this modern program of formulating the nuclear interaction.The key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the internucleon interaction. We examine decoupling quantitatively for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small.As implemented here, the SRG provides freedom to choose the form of its transformations and can be tailored to a given application. We explore the impacts of

Fixed points of the SRG evolution and the on-shell limit of the nuclear force

“…[52], as an attempt to determine a priory the final ordering of the spectrum induced by the SRG evolution in the infrared limit. As we will see, the perturbative analysis is well-succeeded in predicting the ordering of the spectrum only in the case of the Wilson generator, although the results for both generators are consistent with the analytical proof of diagonalization of the SRG evolved hamiltonian presented in Refs [7,40].…”

“…For a translational invariant system, i.e. V s ≡ V rel s , we can separate the CM and consider only the SRG evolution of the hamiltonian for the relative motion, H rel s = T rel + V rel s , since the CM kinetic energy T cm does not contribute [40]. For simplicity, in what follows we will drop the superscript "rel".…”

Evolving nuclear many-body forces with the similarity renormalization group

“…Note that all this information is not lost but merely reorganized into NNN terms, and when we keep those terms we regain the unitary result. This analysis is supported by studies in one-dimensional models that showed purely attractive initial potentials to have monotonically decreasing binding energy [13,21].…”

“…These maxima, in the momentum and coordinate space representations, will be correlated with the high and low-momentum cutoffs respectively. These cutoffs have the large N max behavior: [21]…”