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At least 55 records · Page 3
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DOE OSTI2023

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast and accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (N N) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (n p) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Furthermore, our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Magnetic moments of A = 3 nuclei obtained from chiral effective field theory operators

Chiral effective field theory (χEFT) provides a framework for obtaining internucleon interactions in a systematically improvable fashion from first principles, while also providing for the derivation of consistent electroweak current operators. In this study, we apply consistently derived interactions and currents towards calculating the magnetic dipole moments of the A = 3 systems 3 H and 3 He. We focus here on LENPIC interactions obtained using semilocal coordinate-space (SCS) regularization. Starting from the momentum-space representation of the LENPIC χEFT vector current, we derive the SCS-regularized magnetic dipole operator up through next-to-next-to-leading order (N 2 LO). We then carry out no-core shell-model calculations for 3 H and 3 He systems using the SCS LENPIC interaction at N 2 LO in χEFT and evaluate the magnetic dipole moments obtained using the consistently derived one-nucleon and two-nucleon electromagnetic currents. As anticipated by prior results with χEFT currents, the current corrections through N 2 LO provide improved, but not yet complete, agreement with experiment for the 3 H and 3 He magnetic dipole moments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Maximally local two-nucleon interactions at N 3 LO in Δ -less chiral effective field theory

We present new maximally local two-nucleon interactions derived in Δ -less chiral effective field theory up to next-to-next-to-next-to-leading order ( N 3 LO ), which include all contact and pion-exchange contributions to the nuclear Hamiltonian up to this order. Our interactions are fit to nucleon-nucleon phase shifts using a Bayesian statistical approach, and explore a wide cutoff range from 0.6 – 0.9 fm ( ≈ 660 – 440 MeV ). These interactions can be straightforwardly employed in quantum Monte Carlo methods, such as the auxiliary field diffusion Monte Carlo method. Together with local three-nucleon forces, calculations with these new interactions will provide improved benchmarks for the structure of atomic nuclei and serve as crucial input to analyses of astrophysical phenomena of neutron stars, such as binary neutron-star mergers. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Microscopic optical potentials for medium-mass isotopes derived at the first order of Watson multiple-scattering theory

We perform a first-principles calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with self-consistent Green's function theory with a nucleon-nucleon t matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off calcium and nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65–200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the calcium and nickel isotopic chains. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Emulating ab initio computations of infinite nucleonic matter

We construct efficient emulators for the computation of the infinite nuclear matter equation of state. These emulators are based on the subspace-projected coupled-cluster method for which we here develop a new algorithm called small-batch voting to eliminate spurious states that might appear when emulating quantum many-body methods based on a non-Hermitian Hamiltonian. The efficiency and accuracy of these emulators facilitate a rigorous statistical analysis within which we explore nuclear matter predictions for > 10 6 different parametrizations of a chiral interaction model with explicit Δ -isobars at next-to-next-to leading order. Constrained by nucleon-nucleon scattering phase shifts and bound-state observables of light nuclei up to He 4 , we use history matching to identify nonimplausible domains for the low-energy coupling constants of the chiral interaction. Within these domains we perform a Bayesian analysis using sampling and importance resampling with different likelihood calibrations and study correlations between interaction parameters, calibration observables in light nuclei, and nuclear matter saturation properties. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Nuclear-matter saturation and symmetry energy within Δ -full chiral effective field theory

Nuclear saturation and the symmetry energy are key properties of low-energy nuclear physics that depend on fine details of the nuclear interaction. The equation of state around saturation is also an important anchor for extrapolations to higher densities and studies of neutron stars. Here we develop a unified statistical framework that uses realistic nuclear forces to link the theoretical modeling of finite nuclei and infinite nuclear matter. We construct fast and accurate emulators for nuclear-matter observables and employ an iterative history-matching approach to explore and reduce the enormous parameter domain of Δ -full chiral interactions. We perform rigorous uncertainty quantification and find that model calibration including O 16 observables gives saturation predictions that are more precise than those that only use few-body data. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

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.

Ab initio calculations↗
DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗
DOE OSTI2024

In-medium similarity renormalization group with flowing 3-body operators, and approximations thereof

Here, we explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, identical fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even- A carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as N 7 provides an excellent approximation of the full three-body treatment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Perturbative treatment of nonlocal chiral interactions in auxiliary-field diffusion Monte Carlo calculations

Nuclear many-body systems, ranging from nuclei to neutron stars, are some of the most interesting physical phenomena in our universe, and quantum Monte Carlo (QMC) approaches are among the most accurate many-body methods currently available to study them. In recent decades, interactions derived from chiral effective field theory (EFT) have been widely adopted in the study of nuclear many-body systems. One drawback of the QMC approach is the requirement that the nuclear interactions need to be local, whereas chiral EFT interactions usually contain nonlocalities. In this work, we leverage the capability of computing second-order perturbative corrections to the ground-state energy in order to develop a self-consistent approach to including nonlocal operators in QMC calculations. In conclusion, we investigate both the deuteron and the neutron-matter equation of state in order to show the robustness of our technique and pave the way for future QMC calculations at higher orders in the EFT, where nonlocal operators cannot be avoided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Symmetric Nuclear Matter from the Strong Interaction

We study the equation of state of symmetric nuclear matter at zero temperature over a wide range of densities using two complementary theoretical approaches. At low densities, up to twice nuclear saturation density, we compute the energy per particle based on modern nucleon-nucleon and three-nucleon interactions derived within chiral effective field theory. For higher densities, we derive for the first time constraints in a Fierz-complete setting directly based on quantum chromodynamics using functional renormalization group techniques. Here, we find remarkable consistency of the results obtained from both approaches as they come together in density and the natural emergence of a maximum in the speed of sound 𝑐𝑆 at supranuclear densities. The presence of this maximum appears tightly connected to the formation of a diquark gap. Notably, this maximum is observed to exceed the asymptotic value 𝑐$^{2}_{𝑆}$ =1/3 while its exact position in terms of the density cannot yet be determined conclusively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties

Here, we introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (𝜒⁢EFT ). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as 𝜒⁢EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the 𝜒⁢EFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

The amplitude for the neutrinoless double β (0νββ) decay of the two-neutron system nn → ppe – e – constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale 0νββ searches. Assuming that the 0νββ process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. Here, we develop a method to estimate the numerical value of its coefficient (in analogy to the Cottingham formula for electromagnetic contributions to hadron masses) and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in dimensional regularization, is given in terms of the renormalized amplitude Aν(|p|, |p'|) , matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for 0νββ decay.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Ab Initio Computation of the Longitudinal Response Function in 40 Ca

In this work, we present a consistent ab initio computation of the longitudinal response function RL in 40 Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for R L in 4 He and the Coulomb sum rule in 40 Ca against experimental data and other calculations. For R L in 40 Ca we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards ab initio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Ab Initio Prediction of the 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i Big Bang Radiative Capture

We report the rate at which helium ( 4 He ) and deuterium (d) fuse together to produce lithium-6 ( 6 Li) and a γ ray, 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i, is a critical puzzle piece in resolving the discrepancy between big bang predictions and astronomical observations for the primordial abundance of 6 Li . The accurate determination of this radiative capture rate requires the quantitative and predictive description of the fusion probability across the big bang energy window (30 keV ≲ E ≲ 400 keV), where measurements are hindered by low counting rates. We present first-principle (or, ab initio) predictions of the 4 $\mathrm{H}$e($d, γ$) 6 $\mathrm{L}$i astrophysical S factor using validated nucleon-nucleon and three-nucleon interactions derived within the framework of chiral effective field theory. By employing the ab initio no-core shell model with continuum to describe 4 He-d scattering dynamics and bound 6 Li product on an equal footing, we accurately and consistently determine the contributions of the main electromagnetic transitions driving the radiative capture process. Our results reveal an enhancement of the capture probability below 100 keV owing to previously neglected magnetic dipole (M1) transitions and reduce by an average factor of 7 the uncertainty of the thermonuclear capture rate between 0.002 and 2 GK.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗