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Converged ab initio calculations of heavy nuclei
We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of E 3max =28, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of 132 Sn converged to within a few MeV with respect to the E 3max truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum J rel > 9/2 to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of 132 Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.
High-Precision Spectroscopy of 20 O Benchmarking Ab Initio Calculations in Light Nuclei
The excited states of unstable 20 O were investigated via γ-ray spectroscopy following the 19 O(d, p) 20 O reaction at 8 A MeV. By exploiting the Doppler shift attenuation method, the lifetimes of the $2^+_2$ and $3^+_1$ states were firmly established. From the γ-ray branching and E2/M1 mixing ratios for transitions deexciting the $2^+_2$ and $3^+_1$ states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of γ-ray transition probabilities with the valence space in medium similarity renormalization group ab initio calculations was performed for the first time in a nucleus far from stability. It was shown that the ab initio approaches using chiral effective field theory forces are challenged by detailed high-precision spectroscopic properties of nuclei. Finally, the reduced transition probabilities were found to be a very constraining test of the performance of the ab initio models.
Ground-state properties of light 4 n self-conjugate nuclei in ab initio no-core Monte Carlo shell model calculations with nonlocal N N interactions
We report J π = 0 + ground-state energies and point-proton radii of 4 He, 8 Be, 12 C, 16 O, and 20 Ne nuclei calculated by the ab initio no-core Monte Carlo shell model with the JISP16 and Daejeon16 nonlocal NN interactions. Ground-state energies are obtained in the basis spaces up to seven oscillator shells (N shell =7) with several oscillator energies (ℏω) around the optimal oscillator energy for the convergence of ground-state energies. These energy eigenvalues are extrapolated to obtain estimates of converged ground-state energies in each basis space using energy variances of computed energy eigenvalues. We further extrapolate these energy-variance-extrapolated energies obtained in the finite basis spaces to infinite basis-space results with an empirical exponential form. This form features a dependence on the basis-space size but is independent of the value of ℏω used for the harmonic-oscillator basis functions. Point-proton radii for these states of atomic nuclei are also calculated following techniques employed for the energies. From these results, it is found that the Daejeon16 NN interaction provides good agreement with experimental data up to approximately 16 O, while the JISP16 NN interaction provides good agreement with experimental data up to approximately 12 C. Beyond these nuclei, the interactions produce overbinding accompanied by radii that are too small. These findings suggest and encourage further revisions of nonlocal NN interactions towards the investigation of nuclear structure in heavier-mass regions.
Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory
We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N 3 LO, fourth order) of the Δ-less version of the theory. The long-range parts of these potentials are fixed by the very accurate πN LECs as determined in the Roy-Steiner equations analysis. At the highest order (N 3 LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable χ 2 /datum of 1.45. A comparison of the N 3 LO potential with the phenomenological Argonne v 18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P D ≲ 4.0 % for our N 3 LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.
Ab initio calculations of monopole sum rules: From finite nuclei to infinite nuclear matter
We compute moments of the isoscalar monopole response of 𝑁 = 𝑍 closed-shell nuclei based on chiral nucleon-nucleon plus three-nucleon interactions. We employ the random-phase approximation (RPA) and two ab initio many-body approaches, the in-medium similarity renormalization group (IMSRG) and coupled-cluster theory (CC). In the IMSRG framework, the moments are obtained as ground-state expectation values, whereas in the CC approach, they are evaluated through excited-state calculations. We find good agreement between the IMSRG and CC results across all nuclei studied. RPA provides a reasonable approximation to the correlated methods if the interaction is soft. From the calculated moments, we extract average energies of the monopole response, compute finite-nucleus incompressibilities, and estimate the incompressibility of symmetric nuclear matter by a fit to a leptodermous expansion. Our extrapolated values are lower than those obtained in nuclear-matter calculations with the same interactions, but the values are consistent with phenomenological ranges.
Nuclear structure and elastic scattering observables obtained consistently with different N N interactions
Nucleon-nucleon ($NN$) interactions based on chiral effective theories are commonly used in ab initio calculations of light nuclei. Here we present a study based on three different $NN$ interactions (up to next-to-next-to-leading order) for which structure and elastic proton scattering observables are consistently calculated for $^4$He, $^{12}$C, and $^{16}$O. The interactions are compared at the two-body level in terms of Wolfenstein amplitudes, and their predictions for ground state energies, point-proton radii, and charge form factors, as well as proton elastic scattering observables in the leading-order spectator expansion in the energy range between 65 and 160 MeV projectile energy are presented. Finally, to gain further insight into differences visible in elastic scattering observables, we investigate the behavior of the calculated effective nucleon-nucleus interactions for the $^{12}$C nucleus based on the different $NN$ interactions.
Ab initio calculations of overlap integrals for μ → e conversion in nuclei
The rate for μ → e conversion in nuclei is set to provide the most stringent test of lepton-flavor symmetry and a window into physics beyond the Standard Model. However, to disentangle new lepton-flavor-violating interactions, in combination with information from μ → ey and μ → 3e, it is critical that uncertainties at each step of the analysis be controlled and fully quantified. In this regard, nuclear response functions related to the coupling to neutrons are notoriously problematic, since they are not directly constrained by experiment. We address these shortcomings by combining ab initio calculations with a recently improved determination of charge distributions from electron scattering by exploiting strong correlations among charge, point-proton, and point-neutron radii and densities. We present overlap integrals for 27 Al, 48 Ca, and 48 Ti including full covariance matrices, allowing, for the first time, for a comprehensive consideration of nuclear structure uncertainties in the interpretation of μ → e experiments.
Recent advances in chiral EFT based nuclear forces and their applications
During the past two decades, chiral effective field theory has evolved into a powerful tool to derive nuclear forces from first principles. Nearly all two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory, while, with few exceptions, three-nucleon forces, which play a subtle, but crucial role in microscopic nuclear structure calculations, have been derived up to fifth order. We review the current status of these forces as well as their applications in nuclear many-body systems. While the ab initio description of light nuclei is generally very successful, we point out and analyze problems encountered with medium-mass nuclei. We also survey the construction of equations of state for symmetric nuclear matter and neutron-rich matter based on chiral forces. A focal point is the symmetry energy and its impact on neutron skins and systems of astrophysical relevance. The physics of neutron-rich systems, from nuclei to compact stars, is essentially determined by the density dependence of the symmetry energy. Here, we review the status of predictions in comparison with latest empirical constraints, with particular attention to those extracted from parity-violating electron scattering.
Ab Initio Computation of Charge Densities for Sn and Xe Isotopes
We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLO sat chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for 100 Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.
Ab initio benchmarks of neutrinoless double- β decay in light nuclei with a chiral Hamiltonian
Here, we report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-β (0νββ) decays in light nuclei with mass numbers 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 toward 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 quasiexact benchmarks are not available.
Tunable-fidelity wave functions for the ab initio description of scattering and reactions
Here, the no-core shell model (NCSM) is an ab initio method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an ab initio treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass A ≲ 16 nuclei, except for variants where the basis is further down-selected via some truncation scheme. We consider a basis selection method for the NCSM that was first introduced in the context of the large-scale shell model and captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling ab initio reaction calculations in sd-shell nuclei. The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). As the energy threshold above which configurations are disregarded is increased, the size of the basis becomes an almost-continuous variable, allowing for tunable fidelity in the obtained wave functions. The resulting wave functions can then be used directly in ab initio reaction calculations. We present calculations for 7 Li and n + 12 C scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from 24 Mg. The method presented in this work appears promising for future studies of nuclei with mass A > 16, opening multiple future research directions impacting both nuclear astrophysics and nuclear technology applications.
A = 3 ( e , e ' ) x B ≥ 1 cross-section ratios and the isospin structure of short-range correlations
We study the relation between measured high-x B , high-Q 2 , helium-3 to tritium, (e,e') inclusive-scattering cross-section ratios and the relative abundance of high-momentum neutron-proton (np) and proton-proton (pp) short-range correlated (SRC) nucleon pairs in three-body (A=3) nuclei. In this study, analysis of this data using a simple pair-counting cross-section model suggested a much smaller np/pp ratio than previously measured in heavier nuclei, questioning our understanding of A=3 nuclei and, by extension, all other nuclei. Here we examine this finding using spectral-function-based cross-section calculations, with both an ab initio A=3 spectral function and effective Generalized Contact Formalism (GCF) spectral functions using different nucleon-nucleon interaction models. The ab initio calculation agrees with the data, showing good understanding of the structure of A=3 nuclei. An 8% uncertainty on the simple pair-counting model, as implied by the difference between it and the ab initio calculation, gives a factor of 5 uncertainty in the extracted np/pp ratio. Thus we see no evidence for the claimed "unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3."
Uncertainty quantification in electromagnetic observables of nuclei
We present strategies to quantify theoretical uncertainties in modern ab initio calculations of electromagnetic observables in light and medium-mass nuclei. We discuss how uncertainties build up from various sources, such as the approximations introduced by the few- or many-body solver and the truncation of the chiral effective field theory expansion. We review the recent progress encompassing a broad range of electromagnetic observables in stable and unstable nuclei.
Weak Transitions in Light Nuclei
Nuclei are used for high-precision tests of the Standard Model and for studies of physics beyond the Standard Model. Without a thorough understanding of nuclei, we will not be able to meaningfully interpret the growing body of experimental data nor will we be able to disentangle new physics signals from underlying nuclear effects. This calls for accurate calculations of nuclear structure and reactions. In this work, we focus on electroweak decays in nuclei with mass number A ≤ 10 and report on ab initio Quantum Monte Carlo calculations of reduced matrix elements entering beta decays and electron captures in nuclei with mass number A ≤ 10. The many-body wave functions are calculated using selected Norfolk two- and three-nucleon potential models and associated one- and two-body axial currents at tree-level obtained from a chiral effective field theory with pions, nucleons, and Δ. The agreement with the experimental data is satisfactory except for transitions in A = 8 nuclei. In this specific case, the theory significantly underpredicts the experimental data, which indicates the need of further improvements in the corresponding nuclear wave functions. In this study, emphasis is placed on the contributions of two-body axial currents that are carefully analyzed using two-body transition densities. This allow us to study the spatial distribution and short-range behavior of two-body dynamics. In particular, the transition densities when scaled to peak at 1.0 exhibit universal short-range behavior across the considered nuclei, while they differ in the long-range tails.
Many-body factorization and position–momentum equivalence of nuclear short-range correlations
While mean-field approximations, such as the nuclear shell model, provide a good description of many bulk nuclear properties, they fail to capture the important effects of nucleon–nucleon correlations such as the short-distance and high-momentum components of the nuclear many-body wave function1. Here, we study these components using the effective pair-based generalized contact formalism and ab initio quantum Monte Carlo calculations of nuclei from deuteron to 40 Ca. We observe a universal factorization of the many-body nuclear wave function at short distance into a strongly interacting pair and a weakly interacting residual system. The residual system distribution is consistent with that of an uncorrelated system, showing that short-distance correlation effects are predominantly embedded in two-body correlations. Spin- and isospin-dependent ‘nuclear contact terms’ are extracted in both coordinate and momentum space for different realistic nuclear potentials. The contact coefficient ratio between two different nuclei shows very little dependence on the nuclear interaction model. These findings thus allow extending the application of mean-field approximations to short-range correlated pair formation by showing that the relative abundance of short-range pairs in the nucleus is a long-range (that is, mean field) quantity that is insensitive to the short-distance nature of the nuclear force.
Machine learning approach to pattern recognition in nuclear dynamics from the ab initio symmetry-adapted no-core shell model
A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amid a vast data of large-scale calculations. The method utilizes a neural network that is trained on ab initio results from the symmetry-adapted no-core shell model (SA-NCSM) for light nuclei. We show that the SA-NCSM, which expands ab initio applications up to medium-mass nuclei by using dominant symmetries of nuclear dynamics, can reach heavier nuclei when coupled with the machine learning approach. In particular, we find that a neural network trained on probability amplitudes for s- and p-shell nuclear wave functions not only predicts dominant configurations for heavier nuclei but in addition, when tested for the 20 Ne ground state, accurately reproduces the probability distribution. The non-negligible configurations predicted by the network provide an important input to the SA-NCSM for reducing ultralarge model spaces to manageable sizes that can be, in turn, utilized in SA-NCSM calculations to obtain accurate observables. The neural network is capable of describing nuclear deformation and is used to track the shape evolution along the 20-42 Mg isotopic chain, suggesting a shape coexistence that is more pronounced toward the very neutron-rich isotopes. We provide first descriptions of the structure and deformation of 24 Si and 40 Mg of interest to x-ray burst nucleosynthesis, and even of the extremely heavy nuclei such as 166,168 Er and 236 U, that build on first-principles considerations.
Ab initio leading order effective potential for elastic proton scattering based on the symmetry-adapted no-core shell model
Calculating microscopic optical potentials for elastic scattering at intermediate energies from light nuclei in an ab initio fashion within the Watson expansion has been established within the last few years. Based on the Watson expansion of the multiple scattering series, we employ a nonlocal translationally invariant nuclear density derived within the symmetry-adapted no-core shell model (SA-NCSM) framework from a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction and the very same interaction for a consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for medium-heavy nuclei. The leading order effective (optical) folding potential is computed by integrating over a translationally invariant SA-NCSM one-body scalar density, spin-projected momentum distribution, and the Wolfenstein amplitudes 𝐴, 𝐶, and 𝑀. The resulting nonlocal potentials serve as input for a momentum space Lippmann-Schwinger equation. In the SA-NCSM, the model space is systematically up-selected using Sp(3,ℝ) symmetry considerations. For the light nucleus of 6 He, we establish a systematic selection scheme in the SA-NCSM for scattering observables. Then, we apply this scheme to calculations of scattering observables, such as differential cross sections, analyzing powers, and spin rotation functions for elastic proton scattering from 20 Ne and 40 Ca in the energy regime between 65 and 200 MeV, and compare to available data. Furthermore, our calculations show that the leading order effective nucleon-nucleus potential in the Watson expansion of multiple scattering theory obtained from an up-selected SA-NCSM model space describes 40 Ca elastic scattering observables reasonably well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the nucleon-nucleon amplitudes and the one-body scalar and spin nuclear densities.