arXiv subjects

R. B. Wiringa

Publications and source records attributed to R. B. Wiringa.

At least 37 records · Page 2Linked to original sources

arXiv2020

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

The energy density is calculated in coordinate space for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of $^{8}$Be is also calculated using the Green's function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4$πr^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with \textit{ab initio} self-consistent Green's function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this paper indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of $^{208}$Pb is considered.

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arXiv2020

Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei

We report Quantum Monte Carlo calculations of weak transitions in $A\leq 10$ nuclei, based on the Norfolk two- and three-nucleon chiral interactions, and associated one- and two-body axial currents. We find that the contribution from two-body currents is at the $2$ - $3\%$ level, with the exception of matrix elements entering the rates of $^8$Li, $^8$B, and $^8$He beta decays. These matrix elements are suppressed in impulse approximation based on the (leading order) Gamow Teller transition operator alone; two-body currents provide a $20$ - $30\%$ correction, which is, however, insufficient to bring theory in agreement with experimental data. For the other transitions, the agreement with the data is satisfactory, and the results exhibit a negligible to mild model dependence when different combinations of Norfolk interactions are utilized to construct the nuclear wave functions. We report a complete study of two-body weak transition densities which reveals the expected universal behavior of two-body currents at short distances throughout the range of $A\,$=$\,3$ to $A\,$=$\,10$ systems considered here.

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arXiv2019

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

We report benchmark calculations of the energy per particle of pure neutron matter as a function of the baryon density using three independent many-body methods: Brueckner-Bethe-Goldstone, Fermi hypernetted chain/single-operator chain, and auxiliary-field diffusion Monte Carlo. Significant technical improvements are implemented in the latter two methods. The calculations are made for two distinct families of realistic coordinate-space nucleon-nucleon potentials fit to scattering data, including the standard Argonne $v_{18}$ interaction and two of its simplified versions, and four of the new Norfolk $Δ$-full chiral effective field theory potentials. The results up to twice nuclear matter saturation density show some divergence among the methods, but improved agreement compared to earlier work. We find that the potentials fit to higher-energy nucleon-nucleon scattering data exhibit a much smaller spread of energies.

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arXiv2019

A renormalized approach to neutrinoless double-beta decay

The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

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arXiv2019

Many-body effects in (p,pN) reactions within a unified approach

We study knockout reactions with proton probes within a theoretical framework where {\it ab initio} Quantum Monte Carlo wave functions are combined with the Faddeev/Alt-Grassberger-Sandhas few-body reaction formalism. New Quantum Monte Carlo wave functions are used to describe $^{12}$C, yielding, for the first time, results consistent with the experimental point rms radii, electron scattering data and (p,2p) total cross sections data. Our results for $\mathrm{A}\leq 12$ and $(N-Z) \leq 3$ nuclei show that the theoretical ratios between the (i) {\it ab initio} and Mean Field Approximation theoretical cross sections, $\mathcal{R}_σ$, (ii) corresponding ratios between the spectroscopic factors, $\mathcal{R}_Σ$, summed over states below particle emission, depend moderately on the nucleon separation energy S$_{\rm N}$. These ratios are determined by a delicate interplay between the radii of the parent and the residual nuclei and the nucleon separation energy, and were found to be always smaller for the knockout of the more correlated deficient species nucleon. In the case of the symmetric $^{12}$C nucleus, the theoretical ratios still appear to indicate that protons are more correlated than neutrons.

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arXiv2019

Comparison between Variational Monte Carlo and Shell Model Calculations of Neutrinoless Double Beta Decay Matrix Elements in Light Nuclei

Benchmark comparisons between many-body methods are performed to assess the ingredients necessary for an accurate calculation of neutrinoless double beta decay matrix elements. Shell model and variational Monte Carlo (VMC) calculations are carried out for $A=10$ and $12$ nuclei. Different variational wavefunctions are used to evaluate the uncertainties in the {\it ab initio} calculations, finding fairly small differences between the VMC double beta decay matrix elements. For shell model calculations, the role of model space truncation, radial wavefunction choices, and short-range correlation are investigated and all found to be important. Based on the detailed comparisons between the VMC and shell model approaches, we conclude that accurate descriptions of neutrinoless double beta decay matrix elements require a proper treatment of both long-range and short-range correlations.

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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.

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arXiv2018

Zemach moments and radii of 2,3H and 3,4He

We present benchmark calculations of Zemach moments and radii of 2,3H and 3,4He using various few-body methods. Zemach moments are required to interpret muonic atom data measured by the CREMA collaboration at the Paul Scherrer Institute. Conversely, radii extracted from spectroscopic measurements can be compared with ab initio computations, posing stringent constraints on the nuclear model. For a given few-body method, different numerical procedures can be applied to compute these quantities. A detailed analysis of the numerical uncertainties entering the total theoretical error is presented. Uncertainties from the few-body method and the calculational procedure are found to be smaller than the dependencies on the dynamical modeling and the single nucleon inputs, which are found to be <= 2%. When relativistic corrections and two-body currents are accounted for, the calculated moments and radii are in very good agreement with the available experimental data.

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arXiv2018

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $Δ$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with $Δ$ intermediate states are only retained at the OPE level, and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2--3 fm$^{-1}$. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.

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arXiv2018

Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

The Gamow-Teller (GT) matrix element contributing to tritium $β$ decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schrödinger equation with the chiral two- and three-nucleon interactions including $Δ$ intermediate states that have recently been constructed in configuration space. Predictions up to N3LO in the chiral expansion of the axial current (with $Δ$'s) overestimate the empirical value by 1--4 \%. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs $c_D$ and $c_E$ that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores $Δ$'s, of the contributions due to loop corrections in the axial current at N4LO. Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful.

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arXiv2017

Neutrinoless double beta decay matrix elements in light nuclei

We present the first ab initio calculations of neutrinoless double beta decay matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we have also studied the impact of two-body short range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.

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arXiv2017

Quantum Monte Carlo calculations of weak transitions in $A\,$=$\,$6--10 nuclei

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $β$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, i.e., the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.

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arXiv2017

Variational calculation of the ground state of closed-shell nuclei up to $A=40$

Variational calculations of ground-state properties of $^4$He, $^{16}$O, and $^{40}$Ca are carried out employing realistic phenomenological two- and three-nucleon potentials. The trial wave function includes two- and three-body correlations acting on a product of single-particle determinants. Expectation values are evaluated with a cluster expansion for the spin-isospin dependent correlations considering up to five-body cluster terms. The optimal wave function is obtained by minimizing the energy expectation value over a set of up to 20 parameters by means of a nonlinear optimization library. We present results for the binding energy, charge radius, one- and two-body densities, single-nucleon momentum distribution, charge form factor, and Coulomb sum rule. We find that the employed three-nucleon interaction becomes repulsive for $A\geq16$. In $^{16}$O the inclusion of such a force provides a better description of the properties of the nucleus. In $^{40}$Ca instead, the repulsive behavior of the three-body interaction fails to reproduce experimental data for the charge radius and the charge form factor. We find that the high-momentum region of the momentum distributions, determined by the short-range terms of nuclear correlations, exhibit a universal behavior independent of the particular nucleus. The comparison of the Coulomb sum rules for $^4$He, $^{16}$O, and $^{40}$Ca reported in this work will help elucidate in-medium modifications of the nucleon form factors.

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arXiv2017

Light-nuclei spectra from chiral dynamics

A major goal of nuclear theory is to explain the spectra and stability of nuclei in terms of effective many-body interactions amongst the nucleus' constituents-the nucleons, i.e., protons and neutrons. Such an approach, referred to below as the basic model of nuclear theory, is formulated in terms of point-like nucleons, which emerge as effective degrees of freedom, at sufficiently low energy, as a result of a decimation process, starting from the fundamental quarks and gluons, described by Quantum Chromodynamics (QCD). A systematic way to account for the constraints imposed by the symmetries of QCD, in particular chiral symmetry, is provided by chiral effective field theory, in the framework of a low-energy expansion. Here we show, in quantum Monte Carlo calculations accurate to $\leq\!2\%$ of the binding energy, that two- and three-body chiral interactions fitted {\sl only} to bound- and scattering-state observables in, respectively, the two- and three-nucleon sectors, lead to predictions for the energy levels and level ordering of nuclei in the mass range $A\,$=$\,$4-12 in very satisfactory agreement with experimental data. Our findings provide strong support for the fundamental assumptions of the basic model, and pave the way to its systematic application to the electroweak structure and response of these systems as well as to more complex nuclei.

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arXiv2015

Quantum Monte Carlo methods for nuclear physics

Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

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arXiv2015

Neutrino-nucleus interactions and the short-range structure of nuclei

Improvements in theoretical modeling of Short Range structures and phenomena, and comparisons with data, will require sustained collaboration between nuclear theorists and neutrino experimentalists. The extensive history of studying this area of nuclear physics in electron- and hadron-scattering experiments, coupled with the transformative capabilities of LArTPCs to identify neutrinos, will provide a ripe opportunity for new discoveries that will further our understanding of the nucleus.

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arXiv2014

Quantum Monte Carlo calculations of electromagnetic transitions in 8Be with meson-exchange currents derived from chiral effective field theory

We report quantum Monte Carlo calculations of electromagnetic transitions in 8Be. The realistic Argonne v18 two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen M1 and eight E2 transition matrix elements between these states are then evaluated. The E2 matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The M1 matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with empirical mixing coefficients to compare to experiment. Alternate mixings are also explored. In general, we find that transitions between states that have the same dominant spatial symmetry are in reasonable agreement with experiment, but those transitions between different spatial symmetries are often underpredicted.

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arXiv2013

Nucleon and nucleon-pair momentum distributions in A <= 12 nuclei

We report variational Monte Carlo calculations of single-nucleon momentum distributions for A <= 12 nuclei and nucleon-pair and nucleon-cluster momentum distributions for A <= 8. The wave functions have been generated for a Hamiltonian containing the Argonne v18 two-nucleon and Urbana X three-nucleon potentials. The single-nucleon and nucleon-pair momentum distributions exhibit universal features attributable to the one-pion-exchange tensor interaction. The single-nucleon distributions are broken down into proton and neutron components and spin-up and spin-down components where appropriate. The nucleon-pair momentum distributions are given separately for pp and pn pairs. The nucleon-cluster momentum distributions include dp in 3He, tp and dd in 4He, alpha-d in 6Li, alpha-t in 7Li, and alpha-alpha in 8Be. Detailed tables are provided on-line for download.

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