arXiv subjects

H. Hergert

Publications and source records attributed to H. Hergert.

At least 37 records · Page 2Linked to original sources

arXiv2021

ADG: Automated generation and evaluation of many-body diagrams III. Bogoliubov in-medium similarity renormalization group formalism

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green's function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0.0) of the ADG code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

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arXiv2021

Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian

We report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-beta ($0νββ$) decays in light nuclei with mass number ranging from $A=6$ to $A=22$. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two-plus-three-nucleon interaction from chiral effective field theory is employed, and both isospin-conserving ($ΔT=0$) and isospin-changing ($ΔT=2$) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of $ΔT=0$ transitions are in good agreement among all calculations, at the level of 10%. For $ΔT=2$, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps towards improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross-checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the $0νββ$ decays in heavier candidate nuclei, where quasi-exact benchmarks are not available.

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arXiv2020

A Guided Tour of Ab Initio Nuclear Many-Body Theory

Over the last decade, new developments in Similarity Renormalization Group techniques and nuclear many-body methods have dramatically increased the capabilities of ab initio nuclear structure and reaction theory. Ground and excited-state properties can be computed up to the tin region, and from the proton to the presumptive neutron drip lines, providing unprecedented opportunities to confront two- plus three-nucleon interactions from chiral Effective Field Theory with experimental data. In this contribution, I will give a broad survey of the current status of nuclear many-body approaches, and I will use selected results to discuss both achievements and open issues that need to be addressed in the coming decade.

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arXiv2020

Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of $^{48}$Ca

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of $^{48}$Ca to $^{48}$Ti, and find it to have the value $0.61$, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as $^{76}$Ge, $^{130}$Te, and $^{136}$Xe.

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arXiv2020

Benchmark neutrinoless double-beta decay matrix elements in a light nucleus

We compute nuclear matrix elements of neutrinoless double-beta decay mediated by light Majorana-neutrino exchange in the A = 6 system. The goal is to benchmark two many-body approaches, the No-Core Shell Model and the Multi-Reference In-Medium Similarity Renormalization Group. We use the SRG-evolved chiral N3LO-EM500 potential for the nuclear interaction, and make the approximation that isospin is conserved. We compare the results of the two approaches as a function of the cutoff on the many-body basis space. Although differences are seen in the predicted nuclear radii, the ground-state energies and neutrinoless double-beta decay matrix elements produced by the two approaches show significant agreement. We discuss the implications for calculations in heavier nuclei.

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arXiv2018

Generator-coordinate reference states for spectra and $0νββ$ decay in the in-medium similarity renormalization group

We use a reference state based on symmetry-restored states from deformed mean-field or generator-coordinate-method (GCM) calculations in conjunction with the in-medium similarity-renormalization group (IMSRG) to compute spectra and matrix elements for neutrinoless double-beta ($0νββ$) decay. Because the decay involves ground states from two nuclei, we use evolved operators from the IMSRG in one nucleus in a subsequent GCM calculation in the other. We benchmark the resulting IMSRG+GCM method against complete shell-model diagonalization for both the energies of low-lying states in $^{48}$Ca and $^{48}$Ti and the $0νββ$ matrix element for the decay of $^{48}$Ca, all in a single valence shell. Our approach produces better spectra than either the IMSRG with a spherical-mean-field reference or GCM calculations with unevolved operators. For the $0νββ$ matrix element the improvement is slight, but we expect more significant effects in full ab-initio calculations.

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arXiv2018

Dawning of the N=32 shell closure seen through precision mass measurements of neutron-rich titanium isotopes

A precision mass investigation of the neutron-rich titanium isotopes $^{51-55}$Ti was performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the $N=32$ shell closure and the overall uncertainties of the $^{52-55}$Ti mass values were significantly reduced. Our results confirm the existence of a weak shell effect at $N=32$, establishing the abrupt onset of this shell closure. Our data were compared with state-of-the-art \textit{ab-initio} shell model calculations which, despite very successfully describing where the $N=32$ shell gap is strong, overpredict its strength and extent in titanium and heavier isotones. These measurements also represent the first scientific results of TITAN using the newly commissioned Multiple-Reflection Time-of-Flight Mass Spectrometer (MR-TOF-MS), substantiated by independent measurements from TITAN's Penning trap mass spectrometer.

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arXiv2017

Ab initio electromagnetic observables with the in-medium similarity renormalization group

We present the formalism for consistently transforming transition operators within the in-medium similarity renormalization group framework. We implement the operator transformation in both the equations-of-motion and valence-space variants, and present first results for electromagnetic transitions and moments in medium-mass nuclei using consistently-evolved operators, including the induced two-body parts. These results are compared to experimental values, and--where possible--the results of no-core shell model calculations using the same input chiral interaction. We find good agreement between the equations-of-motion and valence space approaches. Magnetic dipole observables are generally in reasonable agreement with experiment, while the more collective electric quadrupole and octupole observables are significantly underpredicted, often by over an order of magnitude, indicating missing physics at the present level of truncation.

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arXiv2017

Effective proton-neutron interaction near the drip line from unbound states in $^{25,26}$F

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The $^{26}$F nucleus, composed of a deeply bound $\pi0d\_{5/2}$ proton and an unbound $\nu0d\_{3/2}$ neutron on top of an $^{24}$O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^π = 1^{+}\_1 - 4^{+}\_1$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^π = 1^{+}\_1, 2^{+}\_1,4^{+}\_1$ bound states have been determined, and only a clear identification of the $J^π =3^{+}\_1$ is missing.Purpose: We wish to complete the study of the $J^π = 1^{+}\_1 - 4^{+}\_1$ multiplet in $^{26}$F, by studying the energy and width of the $J^π =3^{+}\_1$ unbound state. The method was firstly validated by the study of unbound states in $^{25}$F, for which resonances were already observed in a previous experiment.Method: Radioactive beams of $^{26}$Ne and $^{27}$Ne, produced at about $440A$\,MeV by the FRagment Separator at the GSI facility, were used to populate unbound states in $^{25}$F and $^{26}$F via one-proton knockout reactions on a CH$\_2$ target, located at the object focal point of the R$^3$B/LAND setup. The detection of emitted $γ$-rays and neutrons, added to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the determination of the energy of three unbound states in $^{25}$F and two in $^{26}$F. Results: Based on its width and decay properties, the first unbound state in $^{25}$F is proposed to be a $J^π = 1/2^-$ arising from a $p\_{1/2}$ proton-hole state. In $^{26}$F, the first resonance at 323(33)~keV is proposed to be the $J^π =3^{+}\_1$ member of the $J^π = 1^{+}\_1 - 4^{+}\_1$ multiplet. Energies of observed states in $^{25,26}$F have been compared to calculations using the independent-particle shell model, a phenomenological shell-model, and the ab initio valence-space in-medium similarity renormalization group method.Conclusions: The deduced effective proton-neutron interaction is weakened by about 30-40\% in comparison to the models, pointing to the need of implementing the role of the continuum in theoretical descriptions, or to a wrong determination of the atomic mass of $^{26}$F.

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arXiv2016

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Green's Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

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arXiv2016

In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei

We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IM-SRG) framework for ab initio calculations of nuclei. The IM-SRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: The first is the Multireference IM-SRG (MR-IM-SRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IM-SRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IM-SRG and IM-SRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower $sd$ shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.

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arXiv2016

Radii and binding energies in oxygen isotopes: a puzzle for nuclear forces

We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art {\it ab initio} calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, {\it ab initio} calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes, but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.

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arXiv2016

A nucleus-dependent valence-space approach to nuclear structure

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture 3N forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1\% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper $p$ and $sd$ shells. Finally, we address the $1^+$/$3^+$ ground-state inversion problem in $^{22}\text{Na}$ and $^{46}\text{V}$. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei.

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arXiv2016

Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians

We present ab initio predictions for ground and excited states of doubly open-shell fluorine and neon isotopes based on chiral two- and three-nucleon interactions. We use the in-medium similarity renormalization group, in both flow-equation and Magnus formulations, to derive mass-dependent sd valence-space Hamiltonians. The experimental ground-state energies are reproduced through neutron number N=14, beyond which a new targeted normal-ordering procedure improves agreement with data and large-scale multi-reference calculations. For spectroscopy, we focus on neutron-rich 23-26F and 24-26Ne isotopes near N=14,16 magic numbers. In all cases we find an agreement with experiment competitive with established phenomenology. Moreover, yrast states are well described in 20Ne and 24Mg, providing an ab initio description of deformation in the medium-mass region.

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arXiv2015

The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei

We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell- model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

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arXiv2015

Non-observable nature of the nuclear shell structure. Meaning, illustrations and consequences

The concept of single-nucleon shells constitutes a basic pillar of our understanding of nuclear structure. Effective single-particle energies (ESPEs) introduced by French and Baranger represent the most appropriate tool to relate many-body observables to a single-nucleon shell structure. As briefly discussed in [T. Duguet, G. Hagen, Phys. Rev. C {\bf 85}, 034330 (2012)], the dependence of ESPEs on one-nucleon transfer probability matrices makes them purely theoretical quantities that "run" with the non-observable resolution scale $λ$ employed in the calculation. Given that ESPEs provide a way to interpret the many-body problem in terms of simpler theoretical ingredients, the goal is to specify the terms, i.e. the exact sense and conditions, in which this interpretation can be conducted meaningfully. State-of-the-art multi-reference in-medium similarity renormalization group and self-consistent Gorkov Green's function many-body calculations are employed to corroborate the formal analysis. This is done by comparing the behavior of several observables and of non-observable ESPEs (and spectroscopic factors) under (quasi) unitary similarity renormalization group transformations of the Hamiltonian parameterized by the resolution scale $λ$. The non-observable nature of the nuclear shell structure, i.e. the fact that it constitutes an intrinsically theoretical object with no counterpart in the empirical world, must be recognized and assimilated. Eventually, practitioners can refer to nuclear shells and spectroscopic factors in their analyses of nuclear phenomena if, and only if, they use consistent structure and reaction theoretical schemes based on a fixed resolution scale they have agreed on prior to performing their analysis and comparisons.

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arXiv2015

Isoscalar and neutron modes in the E1 spectra of Ni isotopes and the relevance of shell effects and the continuum

We study theoretically the electric dipole transitions of even Ni isotopes at low energies, using the self-consistent quasi-particle random-phase approximation (RPA) with the D1S Gogny interaction and a continuum-RPA model with the SLy4 Skyrme force. We analyze isoscalar states, isovector states, and the dipole polarizability. We define a reference value for the polarizability, to remove a trivial dependence on the mass number. We compare our results with data and other calculations, with a focus on collective states, shell effects, and threshold transitions. Our results support the presence of a strong isoscalar transition, with little or moderate E1 strength, as a universal feature of ordinary nuclei. In moderately neutron-rich Ni isotopes, namely 68Ni and neighboring isotopes, this transition is found bimodal due to couplings with surface neutrons. An adequate treatment of the continuum states appears essential for describing suprathreshold E1 strength, especially beyond 68Ni. Very exotic isotopes (N>50) are found highly polarizable, with practically all their E1 strength in the continuum. The dipole polarizability and the neutron skin thickness are influenced by shell structure in different ways, so they can appear anticorrelated. A comparison with existing results for lighter (Ca) and heavier (Sn) nuclei suggests that the so-called pygmy dipole strength is influenced strongly by shell effects and that, partly for that reason, its isospin structure depends on the mass region.

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arXiv2015

Nuclear structure studies of $^{24}$F

The structure of the $^{24}$F nucleus has been studied at GANIL using the $β$ decay of $^{24}$O and the in-beam $γ$-ray spectroscopy from the fragmentation of projectile nuclei. Combining these complementary experimental techniques, the level scheme of $^{24}$F has been constructed up to 3.6 Mev by means of particle-$γ$ and particle-$γγ$ coincidence relations. Experimental results are compared to shell-model calculations using the standard USDA and USDB interactions as well as ab-initio valence-space Hamiltonians calculated from the in-medium similarity renormalization group based on chiral two- and three-nucleon forces. Both methods reproduce the measured level spacings well, and this close agreement allows unidentified spins and parities to be consistently assigned.

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