Search

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. 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., Comment: 13 pages, 8 figures, minor changes to correspond to published version

We present Quantum Monte Carlo calculations of the properties of a two-component mass imbalanced Fermi gas, corresponding to the $^6$Li-$^{40}$K mixture. We compute the equation of state of the unpolarized system as a function of the scattering length with particular attention paid to the unitary limit, where the effect of the effective range of the interaction is explored. We have also computed the pair distribution function and the momentum distribution over a range of interaction strengths to provide information about the structure of the system. Finally, we have computed the heavy/light quasiparticle spectrum. Our theoretical predictions, based on Quantum Monte Carlo calculations, can be tested by future experiments with ultracold fermionic gases., Comment: 8 pages, 7 figures, corresponds to the published version

The past years have witnessed tremendous progress in understanding the properties of neutron stars and of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations provided novel constraints on neutron-star structure, that is intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is very broad and the system spans many orders of magnitude in densities. Here, we review theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities, and discuss the related consequent properties of neutron stars. We describe how the equation of state can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments. We review neutron-star observations, with particular emphasis on information provided by gravitational-wave signals and electromagnetic observations. Finally, we discuss future challenges and opportunities in the field., Comment: 55 pages, 26 figures

The Short-Time approximation is a method introduced to evaluate electroweak nuclear response for systems with $A\geq12$, extending the reach of first-principle many-body Quantum Monte Carlo calculations. Using realistic two- and three-body nuclear interactions and consistent one- and two-body electromagnetic currents, we calculate longitudinal and transverse response densities and response functions of $^{12}\text{C}$. We compare the resulting cross sections with experimental data for electron-nucleus scattering, finding good agreement., Comment: 13 pages, 13 figures

The accuracy of $V_{ud}$ determinations from superallowed $\beta$ decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parameterized by a quantity $\delta_\text{NS}$, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of $\delta_\text{NS}$ and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way towards ab-initio calculations of $\delta_\text{NS}$ and thereby addresses the dominant uncertainty in $V_{ud}$., Comment: 7 pages, 1 figure; journal version

Radiative corrections are essential for an accurate determination of $V_{ud}$ from superallowed $\beta$ decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for $V_{ud}$. In this work, we provide a detailed account of the electroweak corrections to superallowed $\beta$ decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. We present a first numerical evaluation of the dominant corrections in light nuclei based on Quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parameterize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab-initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in $V_{ud}$, as illustrated in detail for the $^{14}$O $\to$ $^{14}$N transition., Comment: 44 pages, 9 figures; journal version

The validation, verification, and uncertainty quantification of computationally expensive theoretical models of quantum many-body systems require the construction of fast and accurate emulators. In this work, we develop emulators for auxiliary field diffusion Monte Carlo (AFDMC), a powerful many-body method for nuclear systems. We introduce a reduced-basis method (RBM) emulator for AFDMC and study it in the simple case of the deuteron. Furthermore, we compare our RBM emulator with the recently proposed parametric matrix model (PMM) that combines elements of RBMs with machine learning. We contrast these two approaches with a traditional Gaussian Process emulator. All three emulators constructed here are based on a very limited set of 5 training points, as expected for realistic AFDMC calculations, but validated against $\mathcal{O}(10^3)$ exact solutions. We find that the PMM, with emulator errors of only $\approx 0.1 \%$ and speed-up factors of $\approx 10^7$, outperforms the other two emulators when applied to AFDMC., Comment: Comments Welcome

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold-atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. We perform initial calculations for a range of nuclear systems from two- to few-body neutron systems., Comment: 14 pages, 6 figures, 2 tables

In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy $s$-wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also enables a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.

Ultra-cold Fermi gases display diverse quantum mechanical properties, including the transition from a fermionic superfluid BCS state to a bosonic superfluid BEC state, which can be probed experimentally with high precision. However, the theoretical description of these properties is challenging due to the onset of strong pairing correlations and the non-perturbative nature of the interaction among the constituent particles. This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture to efficiently encode pairing, and other quantum mechanical correlations. Our approach offers substantial improvements over comparable ans\"atze constructed within the Slater-Jastrow framework and outperforms state-of-the-art diffusion Monte Carlo methods, as indicated by our lower ground-state energies. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions. Moreover, we demonstrate that transfer learning stabilizes and accelerates the training of the neural-network wave function, enabling the exploration of the BCS-BEC crossover region near unitarity. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases., Comment: 12 pages, 6 figures

Three-nucleon forces are crucial for the accurate description of nuclear systems, including dense matter probed in neutron stars. We explore nuclear Hamiltonians that reproduce two-nucleon scattering data and properties of light nuclei, but differ in the three-nucleon interactions among neutrons. While no significantly improved constraints can be obtained from current astrophysical data, we show that observations of neutron star mergers by next-generation detectors like the proposed Einstein Telescope could provide strong evidence to distinguish between these Hamiltonians.

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

We study the effects of three-nucleon short-range correlations on nuclear coordinate-space densities. For this purpose, novel three-body densities are calculated for ground state nuclei using the auxiliary-field diffusion Monte Carlo method. The results are analyzed in terms of the Generalized Contact Formalism, extended to include three-body correlations, revealing the universal behavior of nucleon triplets at short distances. We identify the quantum numbers of such correlated triplets and extract scaling factors of triplet abundances that can be compared to upcoming inclusive electron scattering data.

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science, Comment: 70 pages, 3 figures, White Paper for the Long Range Plan for Nuclear Science

We calculate the $\beta$ spectrum in the decay of $^6$He using Quantum Monte Carlo methods with nuclear interactions derived from chiral Effective Field Theory and consistent weak vector and axial currents. We work at second order in the multipole expansion, retaining terms suppressed by $\mathcal O(q^2/m_\pi^2)$, where $q$ denotes low-energy scales such as the reaction's $\mathcal Q$-value or the electron energy, and $m_\pi$ the pion mass. We go beyond the impulse approximation by including the effects of two-body vector and axial currents. We estimate the theoretical error on the spectrum by using four potential models in the Norfolk family of local two- and three-nucleon interactions, which have different cut-off, fit two-nucleon data up to different energies and use different observables to determine the couplings in the three-body force. We find the theoretical uncertainty on the $\beta$ spectrum, normalized by the total rate, to be well below the permille level, and to receive contributions of comparable size from first and second order corrections in the multipole expansion. We consider corrections to the $\beta$ decay spectrum induced by beyond-the-Standard Model charged-current interactions in the Standard Model Effective Field Theory, with and without sterile neutrinos, and discuss the sensitivity of the next generation of experiments to these interactions.

We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two- and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parametrization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited., Comment: 13 pages, 5 figures

The spin susceptibility in pure neutron matter is computed from auxiliary field diffusion Monte Carlo calculations over a wide range of densities. The calculations are performed for different spin asymmetries, while using twist-averaged boundary conditions to reduce finite-size effects. The employed nuclear interactions include both the phenomenological Argonne AV8$^\prime$+UIX potential and local interactions that are derived from chiral effective field theory up to next-to-next-to-leading order., Comment: 15 pages, 10 figures

We perform a joint Bayesian inference of neutron-star mass and radius constraints based on GW170817, observations of quiescent low-mass X-ray binaries (QLMXBs), photospheric radius expansion X-ray bursts (PREs), and X-ray timing observations of J0030+0451. With this data set, the form of the prior distribution still has an impact on the posterior mass-radius (MR) curves and equation of state (EOS), but this impact is smaller than recently obtained when considering QLMXBs alone. We analyze the consistency of the electromagnetic data by including an "intrinsic scattering" contribution to the uncertainties, and find only a slight broadening of the posteriors. This suggests that the gravitational-wave and electromagnetic observations of neutron-star structure are providing a consistent picture of the neutron-star mass-radius curve and the EOS., Comment: 6 pages, 4 figures and supplemental material

Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schr\"odinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chiral effective field theory., Comment: 36 pages, 9 figures

Understanding quasielastic electron- and neutrino-scattering from nuclei has taken on new urgency with current and planned neutrino oscillation experiments, and with electron scattering experiments measuring specific final states, such as those involving nucleon pairs in ``back-to-back'' configurations. Accurate many-body methods are available for calculating the response of light ($A \leq 12$) nuclei to electromagnetic and weak probes, but they are computationally intensive and only applicable to the inclusive response. In the present work we introduce a novel approach, based on realistic models of nuclear interactions and currents, to evaluate the short-time (high-energy) inclusive and exclusive response of nuclei. The approach accounts reliably for crucial two-nucleon dynamics, including correlations and currents, and provides information on back-to-back nucleons observed in electron and neutrino scattering experiments. We demonstrate that in the quasielastic regime and at moderate momentum transfers both initial- and final-state correlations, and two-nucleon currents are important for a quantitatively successful description of the inclusive response and final state nucleons. Finally, the approach can be extended to include relativistic---kinematical and dynamical---effects, at least approximately in the two-nucleon sector, and to describe the response in the resonance-excitation region., Comment: 36 pages, 11 figures

Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report $T$=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line excitation energy for different interaction strengths, and we find agreement between cold gases and neutron matter for very low densities. We also calculate density profiles, which allow us to determine the density depletion at the vortex core, which depends strongly on the short-ranged interaction in cold atomic gases, but it is of $\approx$ 25% for neutron matter in the density regimes studied in this work. Our results can be used to constrain neutron matter properties by using measurements from cold Fermi gases experiments., Comment: 11 pages, 8 figures

We compute the matrix elements for elastic scattering of dark matter (DM) particles off light nuclei ($^2$H, $^3$H, $^3$He, $^4$He and $^6$Li) using quantum Monte Carlo methods. We focus on scalar-mediated DM-nucleus interactions and use scalar currents obtained to next-to-leading order in chiral effective theory. The nuclear ground states are obtained from a phenomenological nuclear Hamiltonian that includes the Argonne $v_{18}$ two-body interaction and the three-body Urbana IX interaction. Within this approach, we study the impact of one- and two-body currents and discuss the size of nuclear uncertainties, including for the first time two-body effects in $A=4$ and $A=6$ systems. Our results provide the nuclear structure input needed to assess the sensitivity of future experimental searches of (light) dark matter using light nuclei, such as $^3$He and $^4$He., Comment: 9 pages, 6 figures

The longitudinal and transverse density- and spin-density response functions in Pure Neutron Matter (PNM) are derived over a wide range of densities within the Time Dependent Local Spin Density Approximation (TDLSDA). The underlying density functional was derived from an Auxiliary Field Diffusion Monte Carlo (AFDMC) computation of the equation of state of unpolarized and fully spin polarized pure neutron matter. In order to assess the dependence of the results on the specific underlying nucleon-nucleon Hamiltonian, we used both the phenomenological Argonne AV8'+UIX force, and local chiral forces up to N2LO. The resulting response function has then been applied to the study of the neutrino mean free path in PNM.

The dense matter equation of state (EOS) determines neutron star (NS) structure but can be calculated reliably only up to one to two times the nuclear saturation density, using accurate many-body methods that employ nuclear interactions from chiral effective field theory constrained by scattering data. In this work, we use physically motivated ansatzes for the speed of sound $c_S$ at high density to extend microscopic calculations of neutron-rich matter to the highest densities encountered in stable NS cores. We show how existing and expected astrophysical constraints on NS masses and radii from X-ray observations can constrain the speed of sound in the NS core. We confirm earlier expectations that $c_S$ is likely to violate the conformal limit of $c_S^2\leq c^2/3 $, possibly reaching values closer to the speed of light $c$ at a few times the nuclear saturation density, independent of the nuclear Hamiltonian. If QCD obeys the conformal limit, we conclude that the rapid increase of $c_S$ required to accommodate a $2 $ M$_\odot$ NS suggests a form of strongly interacting matter where a description in terms of nucleons will be unwieldy, even between one and two times the nuclear saturation density. For typical NSs with masses in the range $1.2-1.4~$ M$_\odot$, we find radii between $10$ and $14$ km, and the smallest possible radius of a $1.4$ M$_{\odot}$ NS consistent with constraints from nuclear physics and observations is $8.4$ km. We also discuss how future observations could constrain the EOS and guide theoretical developments in nuclear physics., Comment: 24 pages, 14 figures, published version

The behavior of QCD at high baryon density and low temperature is crucial to understanding the properties of neutron stars and gravitational waves emitted during their mergers. In this paper we study small systems of baryons in periodic boundary conditions to probe the properties of QCD at high baryon density. By comparing calculations based on nucleon degrees of freedom to simple quark models we show that specific features of the nuclear spectrum, including shell structure and nucleon pairing, emerge if nucleons are the primary degrees of freedom. Very small systems should also be amenable to studies in lattice QCD, unlike larger systems where the fermion sign problem is much more severe. Through comparisons of lattice QCD and nuclear calculations it should be possible to gain, at at least a semi-quantitative level, more understanding of the cold dense equation of state as probed in neutron stars., Comment: 7 pages, 7 figures, 1 table

Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T=0 ab initio diffusion Monte Carlo calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas., Comment: 20 pages, 6 figures, 1 table; v2 corresponds to published version

We report $T=0$ diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. We investigate how vortex core structure properties behave over the BEC-BCS crossover. We calculate the vortex excitation energy, density profiles, and vortex core properties related to the current. We find a density suppression at the vortex core on the BCS side of the crossover, and a depleted core on the BEC limit. Size-effect dependencies in the disk geometry were carefully studied., Comment: 10 pages, 7 figures

The structure of neutron stars is determined by the equation of state of the matter inside the star, which relies on the knowledge of nuclear interactions. While radii of neutron stars mostly depend on the equation of state of neutron matter at nuclear densities, their maximum mass can be drastically affected by the appearance of hyperons at higher densities in the inner core of the star. We summarize recent quantum Monte Carlo results on the calculation of the equation of state of neutron matter at nuclear and higher densities. We report about the development of realistic hyperon-nucleon interactions based on the available experimental data for light- and medium-heavy hypernuclei and on the effect of $\Lambda$ hyperons to the neutron star structure., Comment: 12 pages, 7 figures, Proceedings of the 12th International Conference on Hypernuclear and Strange Particle Physics (HYP2015), Tohoku University, Sendai, Japan, September 7-12, 2015. arXiv admin note: text overlap with arXiv:1208.1736, arXiv:1308.6002

Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein Condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions., Comment: 10 pages, 9 figures; v2 corresponds to the published version

We report diffusion Monte Carlo results for the ground state of unpolarized spin-1/2 fermions in a cylindrical container and properties of the system with a vortex-line excitation. The density profile of the system with a vortex line presents a non-zero density at the core. We calculate the ground-state energy per particle, the superfluid pairing gap, and the excitation energy per particle. These simulations can be extended to calculate the properties of vortex excitations in other strongly interacting systems, such as superfluid neutron matter using realistic nuclear Hamiltonians., Comment: 7 pages, 5 figures

The prediction of neutron stars properties is strictly connected to the employed nuclear interactions. The appearance of hyperons in the inner core of the star is strongly dependent on the details of the underlying hypernuclear force. We summarize our recent quantum Monte Carlo results on the development of realistic two- and three-body hyperon-nucleon interactions based on the available experimental data for light- and medium-heavy hypernuclei., Comment: 4 pages, 1 figure, Proceedings of the 21st International Conference on Few-Body Problems in Physics, Chicago, Illinois, USA

In the last years auxiliary field diffusion Monte Carlo has been used to assess the properties of hypernuclear systems, from light- to medium-heavy hypernuclei and hyper-neutron matter. One of the main findings is the key role played by the three-body hyperon-nucleon-nucleon interaction in the determination of the hyperon separation energy of hypernuclei and as a possible solution to the hyperon puzzle. However, there are still aspects of the employed hypernuclear potential that remain to be carefully investigated. In this paper we show that the isospin dependence of the Lambda-NN force, which is crucial in determining the NS structure, is poorly constrained by the available experimental data.