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R. J. Furnstahl

Publications and source records attributed to R. J. Furnstahl.

At least 73 records · Page 4Linked to original sources
arXiv2014

Infrared extrapolations for atomic nuclei

Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon-nucleon interactions at next-to-next-to-leading order and show that the infrared component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, well above the energy minimum, the ultraviolet corrections can be suppressed while infrared extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.

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arXiv2014

Systematic expansion for infrared oscillator basis extrapolations

Recent work has demonstrated that the infrared effects of harmonic oscillator basis truncations are well approximated by imposing a partial-wave Dirichlet boundary condition at a properly identified radius L. This led to formulas for extrapolating the corresponding energy E_L and other observables to infinite L and thus infinite basis size. Here we reconsider the energy for a two-body system with a Dirichlet boundary condition at L to identify and test a consistent and systematic expansion for E_L that depends only on observables. We also generalize the energy extrapolation formula to nonzero angular momentum, and apply it to the deuteron. Formulas given previously for extrapolating the radius are derived in detail.

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arXiv2014

Universality in Similarity Renormalization Group Evolved Potential Matrix Elements and T-Matrix Equivalence

We examine how the universality of two-nucleon interactions evolved using similarity renormalization group (SRG) transformations correlates with T-matrix equivalence, with the ultimate goal of gaining insight into universality for three-nucleon forces. With sufficient running of the SRG flow equations, the low-energy matrix elements of different realistic potentials evolve to a universal form. Because these potentials are fit to low-energy data, they are (approximately) phase equivalent only up to a certain energy, and we find universality in evolved potentials up to the corresponding momentum. More generally we find universality in local energy regions, reflecting a local decoupling by the SRG. The further requirements for universality in evolved potential matrix elements are explored using two simple alternative potentials. We see evidence that in addition to predicting the same observables, common long-range potentials (i.e., explicit pion physics) is required for universality in the potential matrix elements after SRG flow. In agreement with observations made previously for Vlowk evolution, regions of universal potential matrix elements are restricted to where half-on-shell T-matrix equivalence holds.

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arXiv2014

Nuclear Theory and Science of the Facility for Rare Isotope Beams

The Facility for Rare Isotope Beams (FRIB) will be a world-leading laboratory for the study of nuclear structure, reactions and astrophysics. Experiments with intense beams of rare isotopes produced at FRIB will guide us toward a comprehensive description of nuclei, elucidate the origin of the elements in the cosmos, help provide an understanding of matter in neutron stars, and establish the scientific foundation for innovative applications of nuclear science to society. FRIB will be essential for gaining access to key regions of the nuclear chart, where the measured nuclear properties will challenge established concepts, and highlight shortcomings and needed modifications to current theory. Conversely, nuclear theory will play a critical role in providing the intellectual framework for the science at FRIB, and will provide invaluable guidance to FRIB's experimental programs. This article overviews the broad scope of the FRIB theory effort, which reaches beyond the traditional fields of nuclear structure and reactions, and nuclear astrophysics, to explore exciting interdisciplinary boundaries with other areas. \keywords{Nuclear Structure and Reactions. Nuclear Astrophysics. Fundamental Interactions. High Performance Computing. Rare Isotopes. Radioactive Beams.

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arXiv2013

High-resolution probes of low-resolution nuclei

Renormalization group (RG) methods used to soften Hamiltonians allow large-scale computational resources to be used to greater advantage in calculations of nuclear structure and reactions. These RG transformations lower the effective resolution of the nuclei, which raises questions about how to calculate and interpret high-momentum transfer probes of nuclear structure. Such experiments are conventionally explained in terms of short-range correlations, but these disappear with the evolution to low-momentum scales. We highlight the important issues and prospects in the context of recent developments in RG technology, with guidance from the analogous extraction of parton distributions.

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arXiv2013

New applications of renormalization group methods in nuclear physics

We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

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arXiv2013

Universal properties of infrared oscillator basis extrapolations

Recent work has shown that a finite harmonic oscillator basis in nuclear many-body calculations effectively imposes a hard-wall boundary condition in coordinate space, motivating infrared extrapolation formulas for the energy and other observables. Here we further refine these formulas by studying two-body models and the deuteron. We accurately determine the box size as a function of the model space parameters, and compute scattering phase shifts in the harmonic oscillator basis. We show that the energy shift can be well approximated in terms of the asymptotic normalization coefficient and the bound-state momentum, discuss higher-order corrections for weakly bound systems, and illustrate this universal property using unitarily equivalent calculations of the deuteron.

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arXiv2013

P-shell nuclei using Similarity Renormalization Group evolved three-nucleon interactions

The Similarity Renormalization Group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While in principle the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. These calculations are used to assess convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.

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arXiv2013

Neutron matter based on consistently evolved chiral three-nucleon interactions

We present the first results for the neutron matter equation of state (EOS) using nucleon-nucleon and three-nucleon chiral effective field theory interactions that are consistently evolved in the framework of the Similarity Renormalization Group (SRG). The dependence of the EOS on the SRG resolution scale is greatly reduced when induced three-nucleon forces (3NF) are included and the residual variation, which in part is from missing induced four-body interactions, is comparable to estimated many-body perturbation theory truncation errors. The relative growth with decreasing resolution of the 3NF contributions to the energy per neutron is of natural size, but it accelerates at the lowest resolutions where strong renormalization of the long-range 3NF matrix elements is also observed.

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arXiv2012

The Similarity Renormalization Group with Novel Generators

The choice of generator in the Similarity Renormalization Group (SRG) flow equation determines the evolution pattern of the Hamiltonian. The kinetic energy has been used in the generator for most prior applications to nuclear interactions, and other options have been largely unexplored. Here we show how variations of this standard choice can allow the evolution to proceed more efficiently without losing its advantages.

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arXiv2012

Local Projections of Low-Momentum Potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment.

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arXiv2012

The Renormalization Group in Nuclear Physics

Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.

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arXiv2011

Testing the density matrix expansion against ab initio calculations of trapped neutron drops

Microscopic input to a universal nuclear energy density functional can be provided through the density matrix expansion (DME), which has recently been revived and improved. Several DME implementation strategies are tested for neutron drop systems in harmonic traps by comparing to Hartree-Fock (HF) and ab initio no-core full configuration (NCFC) calculations with a model interaction (Minnesota potential). The new DME with exact treatment of Hartree contributions is found to best reproduce HF results and supplementing the functional with fit Skyrme-like contact terms shows systematic improvement toward the full NCFC results.

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arXiv2011

Operator Evolution via the Similarity Renormalization Group I: The Deuteron

Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this paper on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.

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arXiv2011

Improved nuclear matter calculations from chiral low-momentum interactions

We present new nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force contribution that includes a corrected combinatorial factor beyond Hartree-Fock that was omitted in previous nuclear matter calculations. We find realistic saturation properties using parameters fit only to few-body data, but with larger uncertainty estimates from cutoff dependence and the 3NF parametrization than in previous calculations.

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arXiv2011

Decoupling of Spurious Deep Bound States with the Similarity Renormalization Group

The Similarity Renormalization Group (SRG) is a continuous series of unitary transformations that can be implemented as a flow equation. When the relative kinetic energy ($\Trel$) is used in the SRG generator, nuclear structure calculations have shown greatly improved convergence with basis size because of the decoupling of high-energy and low-energy physics. However this generator can sometimes be problematic. A test case is provided by a study of initial interactions from chiral effective field theories with large cutoffs, which can lead to spurious deep bound states. We would like the SRG to decouple these from the physical shallow bound states. However, with $\Trel$ the high- and low-energy bound states are not decoupled in the usual sense. Replacing $\Trel$ by the momentum-space diagonal of the Hamiltonian ($H_d$) in the SRG generator does produce decoupling, such that the shallow states are in the low-momentum region and the deep bound states are at higher momentum. The flow toward universal low-momentum interactions is also restored.

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arXiv2010

Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group

In recent years, the Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The substantial contribution of both induced and initial three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. We present the most recent progress on this work, extending the calculational capability to the p-shell nuclei and showing that the hierarchy of induced many-body forces is consistent with previous estimates. Calculations over a range of the flow parameter for 6Li, including fully evolved NN+3N interactions, show moderate contributions due to induced four-body forces and display the same improved convergence properties as in lighter nuclei. A systematic analysis provides further evidence that the hierarchy of many-body forces is preserved.

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