arXiv subjects

Robert Roth

Publications and source records attributed to Robert Roth.

At least 37 records · Page 2Linked to original sources

arXiv2022

Multi-reference many-body perturbation theory for nuclei II -- Ab initio study of neon isotopes via PGCM and IM-NCSM calculations

The neon isotopic chain displays a rich phenomenology, ranging from clustering in the ground-state of the self-conjugate doubly open-shell stable $^{20}$Ne isotope to the physics of the island of inversion around the neutron-rich $^{30}$Ne isotope. This second (i.e. Paper II) of the present series proposes an extensive ab initio study of neon isotopes based on two complementary many-body methods, i.e. the quasi-exact in-medium no-core shell model (IM-NCSM) and the projected generator coordinate method (PGCM) that is ideally suited to capturing strong static correlations associated with shape deformation and fluctuations. Calculations employ a state-of-the-art generation of chiral effective field theory Hamiltonians and evaluate the associated systematic uncertainties. In spite of missing so-called dynamical correlations, which can be added via the multi-reference perturbation theory proposed in the first paper (i.e. Paper I) of the present series, the PGCM is shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing the physics of the island of inversion constitutes a challenge that seems to require the inclusion of dynamical correlations. This is addressed in the third paper (i.e. Paper III) of the present series.

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arXiv2022

Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT

In spite of missing dynamical correlations, the projected generator coordinate method (PGCM) was recently shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing absolute binding energies and reaching high accuracy eventually requires the inclusion of dynamical correlations on top of the PGCM. In this context, the present work discusses the first realistic results of a novel multi-reference perturbation theory (PGCM-PT) that can do so within a symmetry-conserving scheme for both ground and low-lying excited states. First, proof-of-principle calculations in a small ($e_{\mathrm{max}}=4$) model space demonstrate that exact binding energies of closed- (\nucl{O}{16}) and open-shell (\nucl{O}{18}, \nucl{Ne}{20}) nuclei are reproduced within $0.5-1.5\%$ at second order, i.e. through PGCM-PT(2). Moreover, profiting from the pre-processing of the Hamiltonian via multi-reference in-medium similarity renormalization group transformations, PGCM-PT(2) can reach converged values within smaller model spaces than with an unevolved Hamiltonian. Doing so, dynamical correlations captured by PGCM-PT(2) are shown to bring essential corrections to low-lying excitation energies that become too dilated at leading order, i.e., at the strict PGCM level. The present work is laying the foundations for a better understanding of the optimal way to grasp static and dynamical correlations in a consistent fashion, with the aim of accurately describing ground and excited states of complex nuclei via ab initio many-body methods.

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arXiv2020

Many-body perturbation theories for finite nuclei

In recent years many-body perturbation theory encountered a renaissance in the field of ab initio nuclear structure theory. In various applications it was shown that perturbation theory, including novel flavors of it, constitutes a useful tool to describe atomic nuclei, either as a full-fledged many-body approach or as an auxiliary method to support more sophisticated non-perturbative many-body schemes. In this work the current status of many-body perturbation theory in the field of nuclear structure is discussed and novel results are provided that highlight its power as a efficient and yet accurate (pre-processing) approach to systematically investigate medium-mass nuclei. Eventually a new generation of chiral nuclear Hamiltonians is benchmarked using several state-of-the-art flavours of many-body perturbation theory.

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arXiv2019

Family of Chiral Two- plus Three-Nucleon Interactions for Accurate Nuclear Structure Studies

We present a family of nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to N3LO in the chiral expansion that provides an accurate ab initio description of ground-state energies and charge radii up to the medium-mass regime with quantified theory uncertainties. Starting from the NN interactions proposed by Entem, Machleidt and Nosyk, we construct 3N interactions with consistent chiral order, non-local regulator, and cutoff value and explore the dependence of nuclear observables over a range of mass numbers on the 3N low-energy constants. By fixing these constants using the 3-H and 16-O ground-state energies, we obtain interactions that robustly reproduce experimental energies and radii for large range from p-shell nuclei to the nickel isotopic chain and resolve many of the deficiencies of previous interactions. Based on the order-by-order convergence and the cutoff dependence of nuclear observables, we assess the uncertainties due the interaction, which yield a significant contribution to the total theory uncertainty.

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arXiv2019

Similarity renormalization group evolution of hypernuclear Hamiltonians

Unitary transformations of a Hamiltonian generally induce interaction terms beyond the particle rank present in the untransformed Hamiltonian that have to be captured and included in a many-body calculation. In systems with strangeness such as hypernuclei, the three-body terms induced by the hyperon-nucleon interaction are strong, so their inclusion is crucial. We present in detail a procedure for computing hyperon-nucleon-nucleon interaction terms that are induced during a similarity renormalization group (SRG) flow. The SRG is carried out in a basis spanned by antisymmetric harmonic-oscillator states with respect to three-body Jacobi coordinates. We discuss basis construction, antisymmetrization, numerical evaluation of the flow equations, and separation of the genuine three-body terms. We then use the hypernuclear no-core shell model with SRG-evolved Hamiltonians, addressing the sensitivity of hypernuclear states and hyperon separation energies to changes in the nucleonic Hamiltonian by example of $^7_Λ$Li, $^9_Λ$Be, $^{11}_Λ$B, $^{13}_Λ$C, and the hyper-helium chain. We also present a survey of the hyper-hydrogen chain, exploring the structure of hypernuclei with extreme neutron-proton asymmetries.

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arXiv2019

Seeds for Generalized Taxicab Numbers

The generalized taxicab number $T(n,m,t)$ is equal to the smallest number that is the sum of $n$ positive $m$th powers in $t$ ways. This definition is inspired by Ramanujan's observation that $1729 = 1^3+ 12^3 =9^3 + 10^3 $ is the smallest number that is the sum of two cubes in two ways and thus $1729= T(2,3,2)$. In this paper we prove that for any given positive integers $m$ and $t$, there exists a number $s$ such $T(s+k,m,t) =T(s,m,t) +k$ for every $k \geq 0$. The smallest such $s$ is termed the seed for the generalized taxicab number. Furthermore, we find explicit expressions for this seed number when the number of ways $t$ is 2 or 3 and present a conjecture for $t \geq 4$ ways.

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arXiv2019

Nuclear Charge Radii of $^{10,11}$B

The first determination of the nuclear charge radius by laser spectroscopy for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-resolution measurement of the isotope shift in the $2s^2 2p\, ^2\mathrm{P}_{1/2} \rightarrow 2s^2 3s\, ^2\mathrm{S}_{1/2}$ ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes $^{10,11}$B and the results are used to extract their difference in the mean-square charge radius $\langle r^2_\mathrm{c}\rangle^{11} - \langle r^2_\mathrm{c}\rangle^{10} = -0.49\,(12)\,\mathrm{fm}^2$. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used as a benchmark for new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches.

physics.atom-ph↗

arXiv2018

Natural orbitals for ab initio no-core shell model calculations

We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated one-body density matrix that is obtained in second-order many-body perturbation theory. Using a perturbatively improved density matrix as starting point informs the single-particle basis about the dominant correlation effects on the global structure of the many-body state, while keeping the computational cost for the basis optimization at a minimum. Already the comparison of the radial single-particle wavefunctions reveals the superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We compare the model-space convergence of energies, root-mean-square radii, and selected electromagnetic observables with all three basis sets for selected p-shell nuclei using chiral interactions with explicit three-nucleon terms. In all cases the natural-orbital basis provides the fastest and most robust convergence, making it the most efficient basis for no-core shell model calculations. As an application we present no-core shell model calculations for the ground-state energies of all oxygen isotopes and assess the accuracy of the normal-ordered two-body approximation of the three-nucleon interaction in the natural-orbital basis.

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arXiv2018

Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei

A novel Rayleigh-Schrödinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a reference state that solves the Hartree-Fock-Bogoliubov variational problem, the approach reduces to the well-tested Møller-Plesset, i.e., Hartree-Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative many-body approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory.

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arXiv2018

Hypernuclear No-Core Shell Model

We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$Λ$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis of HO states where antisymmetrization and computation of matrix elements is simple and to which an importance-truncation scheme can be applied. For the Jacobi-coordinate formulation, we give an iterative procedure for the construction of the antisymmetric basis for arbitrary particle number and present the formulae used to embed two- and three-baryon interactions into the many-body space. For the Slater-determinant formulation, we discuss the conversion of the YN interaction matrix elements from relative to single-particle coordinates, the importance-truncation scheme that tailors the model space to the description of the low-lying spectrum, and the role of the redundant center-of-mass degrees of freedom. We conclude with a validation of both formulations in the four-body system, giving converged ground-state energies for a chiral Hamiltonian, and present a short survey of the $A\le7$ hyper-helium isotopes.

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arXiv2018

Open-Shell Nuclei from No-Core Shell Model with Perturbative Improvement

We introduce a hybrid many-body approach that combines the flexibility of the No-Core Shell Model (NCSM) with the efficiency of Multi-Configurational Perturbation Theory (MCPT) to compute ground- and excited-state energies in arbitrary open-shell nuclei in large model spaces. The NCSM in small model spaces is used to define a multi-determinantal reference state that contains the most important multi-particle multi-hole correlations and a subsequent second-order MCPT correction is used to capture additional correlation effects from a large model space. We apply this new ab initio approach for the calculation of ground-state and excitation energies of even and odd-mass carbon, oxygen, and fluorine isotopes and compare to large-scale NCSM calculations that are computationally much more expensive.

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arXiv2018

Light Neutron-Rich Hypernuclei from the Importance-Truncated No-Core Shell Model

We explore the systematics of ground-state and excitation energies in singly-strange hypernuclei throughout the helium and lithium isotopic chains --- from $^5_Λ$He to $^{11}_Λ$He and from $^7_Λ$Li to $^{12}_Λ$Li --- in the ab initio no-core shell model with importance truncation. All calculations are based on two- and three-baryon interaction from chiral effective field theory and we employ a similarity renormalization group transformation consistently up to the three-baryon level to improve the model-space convergence. While the absolute energies of hypernuclear states show a systematic variation with the regulator cutoff of the hyperon-nucleon interaction, the resulting neutron separation energies are very stable and in good agreement with available data for both nucleonic parents and their daughter hypernuclei. We provide predictions for the neutron separation energies and the spectra of neutron-rich hypernuclei that have not yet been observed experimentally. Furthermore, we find that the neutron drip lines in the helium and lithium isotopic chains are not changed by the addition of a hyperon.

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arXiv2017

Electromagnetic Strength Distributions from the Ab Initio No-Core Shell Model

We present an ab initio approach for the description of collective excitations and transition strength distributions of arbitrary nuclei up into the sd-shell that based on the No-Core Shell Model in combination with the Lanczos strength-function method. Starting from two- and three-nucleon interactions from chiral effective field theory, we investigate the electric monopole, dipole, and quadrupole response of the even oxygen isotopes from 16-O to 24-O. The method describes the full energy range from low-lying excitations to the giant resonance region and beyond in a unified and consistent framework, including a complete description of fragmentation and fine-structure. This opens unique opportunities for understanding dynamic properties of nuclei from first principles and to further constrain nuclear interactions. We demonstrate the computational efficiency and the robust model-space convergence of our approach and compare to established approximate methods, such as the Random Phase Approximation, shedding new light on their deficiencies.

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arXiv2017

Open-Shell Nuclei and Excited States from Multi-Reference Normal-Ordered Hamiltonians

We discuss the approximate inclusion of three-nucleon interactions into ab initio nuclear structure calculations using a multi-reference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens a path to open-shell nuclei and excited states. Based on different multi-determinantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that this multi-reference normal-ordered two-body approximation is able to capture the effects of the 3N interaction with sufficient accuracy, both, for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies.

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arXiv2017

Ab Initio Description of Open-Shell Nuclei: Merging No-Core Shell Model and In-Medium Similarity Renormalization Group

We merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multi-reference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of ground and excited states of closed and open-shell nuclei. Building on the key advantages of the two methods---the decoupling of excitations at the many-body level in the IM-SRG and the access to arbitrary nuclei, eigenstates, and observables in the NCSM---their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. We present applications in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. The efficiency and rapid convergence of the new approach make it ideally suited for ab initio studies of the complete spectroscopy of nuclei up into the medium-mass regime.

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arXiv2016

Can Ab Initio Theory Explain the Phenomenon of Parity Inversion in ${}^{11}$Be?

The weakly bound exotic ${}^{11}$Be nucleus, famous for its ground-state parity inversion and distinct n+ ${}^{10}$Be halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ${}^{11}$Be spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the $3/2^-_1$ resonance energy. Finally, we predict low-lying $3/2^+$ and $9/2^+$ resonances that are not or not sufficiently measured in experiments.

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arXiv2016

Induced Hyperon-Nucleon-Nucleon Interactions and the Hyperon Puzzle

We present the first ab initio calculations for $p$-shell hypernuclei including hyperon-nucleon-nucleon (YNN) contributions induced by a Similarity Renormalization Group transformation of the initial hyperon-nucleon interaction. The transformation including the YNN terms conserves the spectrum of the Hamiltonian while drastically improving model-space convergence of the Importance-Truncated No-Core Shell Model, allowing a precise extraction of binding and excitation energies. Results using a hyperon-nucleon interaction at leading order in chiral effective field theory for lower- to mid-$p$-shell hypernuclei show a good reproduction of experimental excitation energies while hyperon binding energies are typically overestimated. The induced YNN contributions are strongly repulsive and we show that they are related to a decoupling of the $Σ$ hyperons from the hypernuclear system, i.e., a suppression of the $Λ$-$Σ$ conversion terms in the Hamiltonian. This is linked to the so-called hyperon puzzle in neutron-star physics and provides a basic mechanism for the explanation of strong $Λ$NN three-baryon forces.

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arXiv2016

Sensitivities and correlations of nuclear structure observables emerging from chiral interactions

Starting from a set of different two- and three-nucleon interactions from chiral effective field theory, we use the importance-truncated no-core shell model for ab initio calculations of excitation energies as well as electric quadrupole (E2) and magnetic dipole (M1) moments and transition strengths for selected p-shell nuclei. We explore the sensitivity of the excitation energies to the chiral interactions as a first step towards and systematic uncertainty propagation from chiral inputs to nuclear structure observables. The uncertainty band spanned by the different chiral interactions is typically in agreement with experimental excitation energies, but we also identify observables with notable discrepancies beyond the theoretical uncertainty that reveal insufficiencies in the chiral interactions. For electromagnetic observables we identify correlations among pairs of E2 or M1 observables based on the ab initio calculations for the different interactions. We find extremely robust correlations for E2 observables and illustrate how these correlations can be used to predict one observable based on an experimental datum for the second observable. In this way we circumvent convergence issues and arrive at far more accurate results than any direct ab initio calculation. A prime example for this approach is the quadrupole moment of the first 2^+ state in C-12, which is predicted with an drastically improved accuracy.

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