Applications of the Similarity Renormalization Group to the Nuclear Interaction

E.D.Jurgenson

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Applications of the Similarity Renormalization Group to the Nuclear Interaction

E.D.Jurgenson

Nuclear Theory · Submitted 15 Dec 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.87 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.95 · mentions code or data availability 0.02.

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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 key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the inter-nucleon 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. To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces. The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. Building on one-dimensional results we performed the first practical evolution of three-dimensional many-body forces within the No-Core Shell Model basis. Results for the 3H binding energy are consistent with previous calculations involving momentum-space evolution of only two-body forces, and validate expectations from calculations in the one-dimensional oscillator basis. When applied to 4He calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force. The radius of light nuclei is also explored in the three-dimensional basis.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.55	0.33	0.21	asserted 0.99
s1	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 inter-nucleon interaction.	background 0.63	0.18	0.19	asserted 1.00
s2	We examine decoupling quantitatively for two-body observables and few-body binding energies.	contribution 0.93	0.91	0.05	asserted 0.83
s3	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.	result 0.77	0.87	0.28	asserted 1.00
s4	To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces.	method 0.96	0.81	0.04	asserted 0.99
s5	The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations.	method 1.00	0.88	0.03	asserted 1.00
s6	Building on one-dimensional results we performed the first practical evolution of three-dimensional many-body forces within the No-Core Shell Model basis.	contribution 0.98	0.96	0.13	asserted 1.00
s7	Results for the 3H binding energy are consistent with previous calculations involving momentum-space evolution of only two-body forces, and validate expectations from calculations in the one-dimensional oscillator basis.	result 0.83	0.82	0.12	hedged possibility 0.59
s8	When applied to 4He calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force.	result 1.00	0.94	0.15	asserted 1.00
s9	The radius of light nuclei is also explored in the three-dimensional basis.	contribution 0.88	0.87	0.04	asserted 0.81

What kind of paper the classifier reports this is: simulation study 0.73 · evidence from simulation or computation 1.00.

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Original 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 key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the inter-nucleon 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. To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces. The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. Building on one-dimensional results we performed the first practical evolution of three-dimensional many-body forces within the No-Core Shell Model basis. Results for the 3H binding energy are consistent with previous calculations involving momentum-space evolution of only two-body forces, and validate expectations from calculations in the one-dimensional oscillator basis. When applied to 4He calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force. The radius of light nuclei is also explored in the three-dimensional basis.

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2 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as support 1 paper

This analysis is supported by studies in one-dimensional models that showed purely attractive initial potentials to have monotonically decreasing binding energy [ref] .

Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group · Evolution of Many-Body Forces · 1.00

What it cites · 59 sentences without a confident label

Contests 1 paper

Unfortunately, it turned out that the breakdown scale in this approach is too low to be of practical use in nuclear structure, though new variations have been proposed [ref] .

Perturbative nuclear physics · Plans for Future Investigations · contest 0.71

Builds on 1 paper

Here we develop a one-dimensional analog to the single-particle basis in the spirit of Ref. [ref] and compare the results with our Jacobi basis calculations.

No-core shell-model calculations with starting- energy-independent multi-valued effective interactions · Lab Frame in One and Three Dimensions · 0.93

Uses the method or tool of 6 papers

The SRG evolution equation for the three-particle sector in the notation of Ref. [ref] is

Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model · Diagrammatic Analysis of Many-Body Force Evolution · 0.88
The computation of $Q_d$ and $r_d$ from the wavefunction uses [ref] ,

Low-momentum interactions with smooth cutoffs · Decoupling and Deuteron Observables · 0.96
[ref], we can replace $P H_s P$ and $Q H_s Q$ by their eigenvalues $E_p$ and $E_q$ in the SRG equations, yielding [ref]

Light-cone Hamiltonian flow for positronium · Block Diagonalization · 0.81

Uses data or values from 1 paper

The initial ($λ= ∞$) NN potential used here is the 500 MeV N$^3$LO interaction from Ref. [ref] .

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory · Convergence in the Oscillator Basis · 0.91

Compares with 2 papers

The same pattern has been observed for NN potentials in three dimensions [ref] and remains qualitatively the same when parameters in the potential are varied (e.g., see the right plot in Fig. [ref]).

Convergence in the no-core shell model with low-momentum two-nucleon interactions · Three-body Results · 0.91
This is small compared to the rough estimate in Ref. [ref] that the contribution from the long-ranged part of the N$^3$LO four-nucleon force to $^4$He binding is of order a few hundred keV.

A first estimation of chiral four-nucleon force effects in 4He · Induced Many-Body Forces · 0.97

Cites as support 2 papers

This decoupling explains the greatly improved convergence with basis size seen in the NCSM for corresponding $λ$ values [ref] .

Convergence in the no-core shell model with low-momentum two-nucleon interactions · Decoupling and Few-Body Energies with the NCSM · 0.98
Convergence is even faster for lower $λ$ values [ref] , ensuring a useful range for the analysis of few-body systems.

Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group · Convergence in $$: $G =$ · 0.96

Cites as background 10 papers

Renormalization Group (RG) methods that evolve NN interactions with a sharp or smooth cutoff in relative momentum, known generically as $$, usually rely on equations based on the half-on-shell invariance of the two-nucleon T matrix [ref] .

Low-momentum interactions with smooth cutoffs · Block Diagonalization · 0.88
Renormalization Group (RG) methods that evolve NN interactions with a sharp or smooth cutoff in relative momentum, known generically as $$, usually rely on equations based on the half-on-shell invariance of the two-nucleon T matrix [ref] .

Model-independent low momentum nucleon interaction from phase shift equivalence · Block Diagonalization · 0.88
The majority of work in this area is contained in Ref. [ref] , but some preliminary work was done for few-body systems using a simple operator for the momentum distribution in the wavefunction of few-body systems [ref] :

Recent observation of short range nucleon correlations in nuclei and their implications for the structure of nuclei and neutron stars · Evolving Individual Operators: A Study of Cutoff Behavior · 0.92

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