arXiv subjects

Robert Roth

Publications and source records attributed to Robert Roth.

At least 55 records · Page 3Linked to original sources

arXiv2016

Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States

We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.

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arXiv2015

Importance-Truncated Large-Scale Shell Model

We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapolations based on the energy variance. We apply the importance-truncated shell model for the study of 56-Ni in the pf valence space and of 60-Zn and 64-Ge in the pfg9/2 space. We demonstrate the efficiency and accuracy of the approach, which pave the way for future shell-model calculations in larger valence spaces with valence-space interactions derived in ab initio approaches.

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arXiv2015

Ab Initio No Core Shell Model - Recent Results and Further Prospects

There has been significant recent progress in solving the long-standing problems of how nuclear shell structure and collective motion emerge from underlying microscopic inter-nucleon interactions. We review a selection of recent significant results within the ab initio No Core Shell Model (NCSM) closely tied to three major factors enabling this progress: (1) improved nuclear interactions that accurately describe the experimental two-nucleon and three-nucleon interaction data; (2) advances in algorithms to simulate the quantum many-body problem with strong interactions; and (3) continued rapid development of high-performance computers now capable of performing $20 \times 10^{15}$ floating point operations per second. We also comment on prospects for further developments.

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arXiv2014

Accelerating Ab Initio Nuclear Physics Calculations with GPUs

This paper describes some applications of GPU acceleration in ab initio nuclear structure calculations. Specifically, we discuss GPU acceleration of the software package MFDn, a parallel nuclear structure eigensolver. We modify the matrix construction stage to run partly on the GPU. On the Titan supercomputer at the Oak Ridge Leadership Computing Facility, this produces a speedup of approximately 2.2x - 2.7x for the matrix construction stage and 1.2x - 1.4x for the entire run.

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arXiv2014

Continuum and Three-Nucleon Force Effects on 9Be Energy Levels

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of p- and lower-sd-shell nuclei. As first application we concentrate on energy levels of the 9Be system for which all excited states lie above the n-8Be threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the 1/2+ resonance energy, which is of astrophysical interest, in good agreement with experiment.

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arXiv2014

Ab Initio Description of p-Shell Hypernuclei

We present the first ab initio calculations for p-shell single-Lambda hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit $Λ$ and $Σ^+$, $Σ^0$, $Σ^-$ hyperons including $Λ$-$Σ$ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two- and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-shell hypernuclei and apply it to p-shell hypernuclei, in particular to $^7_Λ$Li, $^9_Λ$Be and $^{13}_Λ$C. We show that the chiral hyperon-nucleon interactions provide ground-state and excitation energies that agree with experiment within the cutoff dependence. At the same time we demonstrate that hypernuclear spectroscopy provides tight constraints on the hyperon-nucleon interactions and we discuss the impact of induced hyperon-nucleon-nucleon interactions.

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arXiv2014

Collective excitations in deformed sd-shell nuclei from realistic interactions

Background: Collective excitations of nuclei and their theoretical descriptions provide an insight into the structure of nuclei. Replacing traditional phenomenological interactions with unitarily transformed realistic nucleon-nucleon interactions increases the predictive power of the theoretical calculations for exotic or deformed nuclei. Purpose: Extend the application of realistic interactions to deformed nuclei and compare the performance of different interactions, including phenomenological interactions, for collective excitations in the sd-shell. Method: Ground-state energies and charge radii of 20-Ne, 28-Si and 32-S are calculated with the Hartree-Fock method. Transition strengths and transition densities are obtained in the Random Phase Approximation with explicit angular-momentum projection. Results: Strength distributions for monopole, dipole and quadrupole excitations are analyzed and compared to experimental data. Transition densities give insight into the structure of collective excitations in deformed nuclei. Conclusions: Unitarily transformed realistic interactions are able to describe the collective response in deformed sd-shell nuclei in good agreement with experimental data and as good or better than purely phenomenological interactions. Explicit angular momentum projection can have a significant impact on the response.

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arXiv2014

Progress on Light-Ion Fusion Reactions with Three-Nucleon Forces

The description of structural and dynamical properties of nuclei starting from the fundamental interaction between nucleons has been a long-standing goal in nuclear physics. The ab initio No-Core Shell Model combined with the Resonating-Group Method (NCSM/RGM) is capable of addressing both structural and reaction properties of light-nuclei. While promising results have already been achieved starting from a two-body Hamiltonian, a truly realistic prediction of nuclear observables requires the treatment of the three-nucleon interaction. Using similarity-renormalization-group evolved two- and three-nucleon interactions, we will present recent applications to n-4He scattering process when accounting for the chiral two- plus three-nucleon interaction versus the chiral two-nucleon interaction. We compare our results to phase shifts obtained from R-matrix analysis of data up to 16 MeV neutron energy, below the d-3H threshold.

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arXiv2013

Ab Initio Path to Heavy Nuclei

We present the first ab initio calculations of nuclear ground states up into the domain of heavy nuclei, spanning the range from 16-O to 132-Sn based on two- plus three-nucleon interactions derived within chiral effective field theory. We employ the similarity renormalization group for preparing the Hamiltonian and use coupled-cluster theory to solve the many-body problem for nuclei with closed sub-shells. Through an analysis of theoretical uncertainties resulting from various truncations in this framework, we identify and eliminate the technical hurdles that previously inhibited the step beyond medium-mass nuclei, allowing for reliable validations of nuclear Hamiltonians in the heavy regime. Following this path we show that chiral Hamiltonians qualitatively reproduce the systematics of nuclear ground-state energies up to the neutron-rich Sn isotopes.

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arXiv2013

Extension of coupled-cluster theory with a non-iterative treatment of connected triply excited clusters to three-body Hamiltonians

We generalize the coupled-cluster (CC) approach with singles, doubles, and the non-iterative treatment of triples termed $Λ$CCSD(T) to Hamiltonians containing three-body interactions. The resulting method and the underlying CC approach with singles and doubles only (CCSD) are applied to the medium-mass closed-shell nuclei O16, O24, and Ca40. By comparing the results of CCSD and $Λ$CCSD(T) calculations with explicit treatment of three-nucleon interactions to those obtained using an approximate treatment in which they are included effectively via the zero-, one-, and two-body components of the Hamiltonian in normal-ordered form, we quantify the contributions of the residual three-body interactions neglected in the approximate treatment. We find these residual normal-ordered three-body contributions negligible for the $Λ$CCSD(T) method, although they can become significant in the lower-level CCSD approach, particularly when the nucleon-nucleon interactions are soft.

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arXiv2013

Evolved Chiral NN+3N Hamiltonians for Ab Initio Nuclear Structure Calculations

We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p-shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p-shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-3N contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper p-shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.

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arXiv2013

Ab initio many-body calculations of nucleon-4He scattering with three-nucleon forces

We extend the ab initio no-core shell model/resonating-group method to include three-nucleon (3N) interactions for the description of nucleon-nucleus collisions. We outline the formalism, give algebraic expressions for the 3N-force integration kernels, and discuss computational aspects of two alternative implementations. The extended theoretical framework is then applied to nucleon-4He scattering using similarity-renormalization-group (SRG) evolved nucleon-nucleon plus three-nucleon potentials derived from chiral effective field theory. We analyze the convergence properties of the calculated phase shifts and explore their dependence upon the SRG evolution parameter. We include up to six excited states of the 4He target and find significant effects from the inclusion of the chiral 3N force, e.g., it enhances the spin-orbit splitting between the 3/2- and 1/2- resonances and leads to an improved agreement with the phase shifts obtained from an accurate R-matrix analysis of the five-nucleon experimental data. We find remarkably good agreement with measured differential cross sections at various energies, while analyzing powers manifest larger deviations from experiment for certain energies and angles.

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arXiv2013

Systematics of 2+ states in C isotopes from the ab initio no-core shell model

We study low-lying states of even carbon isotopes in the range A = 10 - 20 within the large- scale no-core shell model (NCSM). Using several accurate nucleon-nucleon (NN) as well as NN plus three-nucleon (NNN) interactions, we calculate excitation energies of the lowest 2+ state, the electromagnetic B(E2; 2+1 -> 0+1) transition rates, the 2+1 quadrupole moments as well as se- lected electromagnetic transitions among other states. Recent experimental campaigns to measure 2+-state lifetimes indicate an interesting evolution of nuclear structure that pose a challenge to reproduce theoretically from first principles. Our calculations do not include any effective charges or other fitting parameters. However, calculated results extrapolated to infinite model spaces are also presented. The model-dependence of those results is discussed. Overall, we find a good agree- ment with the experimentally observed trends, although our extrapolated B(E2; 2+1 -> 0+1) value for 16C is lower compared to the most recent measurements. Relative transition strengths from higher excited states are investigated and the influence of NNN forces is discussed. In particular for 16C we find a remarkable sensitivity of the transition rates from higher excited states to the details of the nuclear interactions.

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arXiv2012

Spectra of Open-Shell Nuclei with Padé-Resummed Degenerate Perturbation Theory

We apply degenerate many-body perturbation theory at high orders for the ab-initio description of ground states and excitation spectra of open-shell nuclei using soft realistic nucleon-nucleon interactions. We derive a recursive formulation of standard degenerate many-body perturbation theory that enables us to evaluate order-by-order perturbative energy and state corrections up to the 30th order. We study 6,7-Li as test cases using a similarity renormalization group (SRG) evolved nucleon-nucleon interaction from chiral effective field theory. The simple perturbation series exhibits a strong, often oscillatory divergence, as was observed previously for ground states of closed-shell nuclei. Even for very soft interactions resulting from SRG evolutions up to large flow parameter, i.e. low momentum scales, the perturbation series still diverges. However, a resummation of the perturbation series via Padé approximants yields very stable and converged ground and excited-state energies in very good agreement with exact no-core shell-model calculations for the same model space.

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arXiv2012

Ab Initio Calculations of Medium-Mass Nuclei with Explicit Chiral 3N Interactions

We present the first ab initio coupled-cluster calculations of medium-mass nuclei with explicit chiral three-nucleon (3N) interactions. Using a spherical formulation of coupled cluster with singles and doubles excitations including explicit 3N contributions, we study ground states of 16,24-O, 40,48-Ca and 56-Ni. We employ chiral NN plus 3N interactions softened through a similarity renormalization group (SRG) transformation at the three-body level. We investigate the impact of all truncations and quantify the resulting uncertainties---this includes the contributions from triples excitations, the truncation of the set of three-body matrix elements, and the omission of SRG-induced four-body interactions. Furthermore, we assess the quality of a normal-ordering approximation of the 3N interaction beyond light nuclei. Our study points towards the predictive power of chiral Hamiltonians in the medium-mass regime.

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arXiv2012

No-Core Shell Model Analysis of Light Nuclei

The fundamental description of both structural properties and reactions of light nuclei in terms of constituent protons and neutrons interacting through nucleon-nucleon and three-nucleon forces is a long-sought goal of nuclear theory. I will briefly present a promising technique, built upon the {\em ab initio} no-core shell model, which emerged recently as a candidate to reach such a goal: the no-core shell model/resonating-group method. This approach, capable of describing simultaneously both bound and scattering states in light nuclei, complements a microscopic cluster technique with the use of two-nucleon realistic interactions, and a microscopic and consistent description of the nucleon clusters. I will discuss applications to light nuclei binary scattering processes and fusion reactions that power stars and Earth based fusion facilities, such as the deuterium-$^3$He fusion, and outline the progress toward the inclusion of the three-nucleon force into the formalism and the treatment of three-body clusters.

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arXiv2012

No-Core MCSM calculation for $^{10}$Be and $^{12}$Be low-lying spectra

The low-lying excited states of $^{10}$Be and $^{12}$Be are investigated within a no-core Monte Carlo Shell Model (MCSM) framework employing a realistic potential obtained via the Unitary Correlation Operator Method. The excitation energies of the 2$^+_1$ and 2$^+_2$ states and the B(E2;$\,2^+_{1,2}\rightarrow$ 0$^+_{g.s.}$) for $^{10}$Be in the MCSM with a standard treatment of spurious center-of-mass motion show good agreement with experimental data. Some properties of low-lying states of $^{10}$Be are studied in terms of quadrupole moments, E2 transitions and single-particle occupation numbers. The E2 transition probability of $^{10}$C, the mirror nucleus of $^{10}$Be, is also presented with a good agreement to experiment. The triaxial deformation of $^{10}$Be and $^{10}$C is discussed in terms of the B(E2) values. The removal of the spurious center-of-mass motion affects differently on various states: for instance, negligible effects on the 2$^+_1$ and 2$^+_2$ levels of $^{10}$Be, while significant and favorable shift for the 1$^-_1$ level. It is suggested that the description of $^{12}$Be needs a larger model space as well as some other higher excited states of $^{10}$Be, as an indicator that these are dominated by intruder configurations.

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arXiv2011

Ab Initio Calculations of Medium-Mass Nuclei with Normal-Ordered Chiral NN+3N Interactions

We study the use of truncated normal-ordered three-nucleon interactions in ab initio nuclear structure calculations starting from chiral two- plus three-nucleon Hamiltonians evolved consistently with the similarity renormalization group (SRG). We present three key steps: (i) a rigorous benchmark of the normal-ordering approximation in the importance-truncated no-core shell model (IT-NCSM) for 4-He, 16-O, and 40-Ca; (ii) a direct comparison of the IT-NCSM results with coupled-cluster calculations at the singles and doubles level (CCSD) for 16-O; and (iii) first applications of SRG-evolved chiral NN+3N Hamiltonians in CCSD for the medium-mass nuclei 16,24-O and 40,48-Ca. We show that the normal-ordered two-body approximation works very well beyond the lightest isotopes and opens a path for ab initio studies of medium-mass and heavy nuclei with chiral two- plus three-nucleon interactions. At the same time we highlight the predictive power of chiral Hamiltonians.

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