Systematic comparisons across theoretical predictions for the properties of dense matter, nuclear physics data, and astrophysical observations (also called meta-analyses) are performed. Existing predictions for symmetric nuclear and neutron matter properties are considered, and they are shown in this paper as an illustration of the present knowledge. Asymmetric matter is constructed assuming the isospin asymmetry quadratic approximation. It is employed to predict the pressure at twice saturation energy-density based only on nuclear-physics constraints, and we find it compatible with the one from the gravitational-wave community. To make our meta-analysis transparent, updated in the future, and to publicly share our results, the Python toolkit nucleardatapy is described and released here. Hence, this paper accompanies nucleardatapy, which simplifies access to nuclear-physics data, including theoretical calculations, experimental measurements, and astrophysical observations. This Python toolkit is designed to easily provide data for: i) predictions for uniform matter (from microscopic or phenomenological approaches); ii) correlation among nuclear properties induced by experimental and theoretical constraints; iii) measurements for finite nuclei (nuclear chart, charge radii, neutron skins or nuclear incompressibilities, etc.) and hypernuclei (single particle energies); and iv) astrophysical observations. This toolkit provides data in a unified format for easy comparison and provides new meta-analysis tools. It will be continuously developed, and we expect contributions from the community in our endeavor.

Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this Letter, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for A=3 nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's function Monte Carlo (GFMC). It achieves a ground-state energy within 0.45% of the GFMC result for ^{3}H using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a 3.7% deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.

Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to generate uncertainty bands for physical observables in nuclear physics, such as the total cross section and nucleon-nucleon phase shifts. We demonstrate the method's flexibility by considering three scenarios: (i) a pointwise model, where expansion coefficients in chiral effective field theory are treated as random variables; (ii) a Gaussian-Process model for the coefficients; and (iii) phase shifts at various energies and partial waves calculated using local interactions from chiral effective field theory. In each case, conformal-prediction intervals are constructed and validated empirically. Our results show that conformal prediction provides reliable and adaptive uncertainty bands even in the presence of non-Gaussian behavior, such as skewness and heavy tails. These findings highlight conformal prediction as a robust and practical framework for quantifying theoretical uncertainties.

The Canadian subatomic physics community establishes its scientific, and thus funding, priorities through periodic Long-Range Plans (LRP). The community is now putting together a new LRP, which will be in effect from 2027 through 2034, with its scope extending through 2041. As part of this process, the Canadian Institute of Nuclear Physics (CINP) has put together a strategic report, following an extensive consultation process. The report describes the broad and ambitious research program undertaken by the Canadian nuclear physics research community, both onshore and abroad, touching on key questions regarding the origin, evolution, and structure of visible matter in the universe. This document provides a grid of different Canadian nuclear physics projects undertaken now and in the future, and their associated timelines. It concludes with specific recommendations for maximizing Canadian scientific output in nuclear physics.

This article discusses incorrect statements appearing in textbooks on quantum field theory (QFT); some of these mistakes also appear in the research literature. The focus is not on errors made by an individual author, but on conceptual muddledness that is widespread in introductory textbooks. We start from a bare-bones summary of QFT, meant to establish the notation. We then turn to our six paradigmatic themes, in each case quoting a specific example of the textbook mistake, a summary of material that is known to experts but is frequently mishandled in introductory works, pointers to authoritative references where the relevant concept is handled properly, as well as a concise correction that rectifies any issues. The goal of this work is to warn readers of the existence of several pitfalls and thereby stop these errors from further propagating in the literature on QFT.

We present theoretical and experimental evidence for a new phase of matter in neutron-rich systems that we call multimodal superfluidity. Using ab initio lattice calculations, we show that the condensate consists of coexisting s-wave pairs, p-wave pairs in entangled double pair combinations, and quartets composed of bound states of two s-wave pairs. We identify multimodal superfluidity as a general feature of single-flavor spin-1/2 fermionic systems with attractive s-wave and p-wave interactions, provided the system is stable against collapse into a dense droplet. Beyond neutrons at sub-saturation densities, we demonstrate that this phase appears in generalized attractive extended Hubbard models in one, two, and three dimensions. We elucidate the mechanism for this coexistence using self-consistent few-body Cooper models and compare with Bardeen-Cooper-Schrieffer theory. We also derive the form of the effective action and show that spin, rotational, and parity symmetries remain unbroken. Finally, we analyze experimental data to show that p-wave pair gaps and quartet gaps are present in atomic nuclei, and we discuss the consequences of this new phase for the structure and dynamics of neutron star crusts.

We report on the first quantum Monte Carlo calculations of helium isotopes with fully propagated theoretical uncertainties from the interaction to the many-body observables. To achieve this, we build emulators for solutions to the Faddeev equations for the binding energy and Gamow-Teller matrix element of ^3H, as well as for auxiliary-field diffusion Monte Carlo calculations of the ^4He charge radius, employing local two- and three-body interactions up to next-to-next-to-leading order in chiral effective field theory. We use these emulators to determine the posterior distributions for all low-energy couplings that appear in the interaction up to this order using Bayesian inference while accounting for theoretical uncertainties. We then build emulators for auxiliary-field diffusion Monte Carlo for helium isotopes and propagate the full posterior distributions to these systems. Our approach serves as a framework for ab initio studies of atomic nuclei with consistently treated and correlated theoretical uncertainties.

We study uncertainties in the equation of state of neutron stars using conformal prediction as a distribution-free and model-agnostic method that provides coverage guarantees. In particular, we apply the Conformalized Quantile Regression (CQR) method to posterior samples calculated from Bayesian inference, creating reliable uncertainty bands without assuming a specific form of the underlying distribution. We first construct CQR bands as a postprocessing step to the posterior samples of neutron star mas-radius relations provided by the NMMA collaboration and to Quantum Monte Carlo calculations of pure neutron matter. In all cases, empirical coverage studies confirm the robustness of the method.

We have used the auxiliary-field quantum Monte Carlo (AFQMC) many-body approach on the lattice to study the equation of state for a fermionic impurity interacting with a background sea of spin-polarized fermions. The impurity, or polaron, is an interesting system in both cold atomic and nuclear physics. Our approach is general, and we are able to straightforwardly study the polaron across these regimes. We first study the Fermi polaron at unitarity and for a wide range of scattering lengths, comparing against previous theoretical and experimental studies. We then explore the neutron polaron which has been shown to be a useful constraint for nuclear physics. We have also employed the recently developed parametric matrix model to emulate AFQMC solutions to the two-body problem on the lattice, to accelerate the tuning of our lattice Hamiltonian parameters directly to two-body energies in a periodic box, following L & uuml;scher's formula. Our lattice quantum Monte Carlo results for the polaron in both a cold atomic and nuclear physics context can serve as stringent benchmarks for future theoretical and experimental research.

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.

The gap equations lie at the core of the Bardeen-Cooper-Schrieffer (BCS) theory, a standard tool in the description of superfluidity. As a set of non-linear integral equations, the gap equations' inherent difficulties oftentimes hinder even the crudest descriptions of superfluid states. Hard-core potentials, high-density superfluids, and coupled-channel pairing are all reasons that have historically required one to provide special treatment to the gap equations to get a solution. In this paper we present a new method for solving the gap equations that holds the promise of being an efficient universal solver that requires the minimum amount of a priori knowledge of the targeted solutions. With theoretical evidence of exotic nuclear superfluidity posing new questions to our understanding of this fundamental property of nuclear systems, the presented method can be a valuable tool when exploring new pairing states, finite-temperature properties, or the development of sophisticated descriptions of nuclear superfludity.

Any experimental evidence of nucleons paired in spin-triplet states will confirm the existence of an exotic phase of nuclear systems. This type of nuclear superfluidity has been hypothesized in heavy nuclei, where the antagonizing spin-orbit effects are damped, and there it oftentimes coexists with traditional spin-singlet pairing, leading to the possibility of mixed-spin pairing. Realistic nuclear deformation, not considered in such studies, could make-or-break these proposals, since its effect on triplet pairing, and the competition (and coexistence) of the two superfluid phases, was expected to be crucial. We report on a thorough study on the effect of deformation on triplet, singlet, and mixed-spin pairing in the relevant region of the nuclear chart. We find that, at low isospin asymmetries, spin-triplet pairing is enhanced by deformation, while below the proton-drip line, the novel superfluid phase survives alongside the usual spin-singlet pairing. These results suggest that spin-triplet superfluidity exists in realistic nuclei and can be probed in the lab.

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. This article is part of the theme issue ‘The liminal position of Nuclear Physics: from hadrons to neutron stars’.

We present Quantum Monte Carlo calculations of the properties of a two-component mass imbalanced Fermi gas, corresponding to the ^6Li-^40K 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.

Open AccessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Petri Marina and Gezerlis Alexandros 2024The liminal position of Nuclear Physics: from hadrons to neutron starsPhil. Trans. R. Soc. A.38220230128http://doi.org/10.1098/rsta.2023.0128SectionOpen AccessIntroductionThe liminal position of Nuclear Physics: from hadrons to neutron stars Marina Petri Marina Petri https://orcid.org/0000-0002-3740-6106 School of Physics, Engineering and Technology, University of York, York YO10 5DD, UK [email protected] Contribution: Writing – original draft, Writing – review and editing Google Scholar Find this author on PubMed Search for more papers by this author and Alexandros Gezerlis Alexandros Gezerlis https://orcid.org/0000-0003-2232-2484 Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada [email protected] Contribution: Writing – original draft, Writing – review and editing Google Scholar Find this author on PubMed Search for more papers by this author Marina Petri Marina Petri https://orcid.org/0000-0002-3740-6106 School of Physics, Engineering and Technology, University of York, York YO10 5DD, UK [email protected] Contribution: Writing – original draft, Writing – review and editing Google Scholar Find this author on PubMed and Alexandros Gezerlis Alexandros Gezerlis https://orcid.org/0000-0003-2232-2484 Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada [email protected] Contribution: Writing – original draft, Writing – review and editing Google Scholar Find this author on PubMed Published:24 June 2024https://doi.org/10.1098/rsta.2023.0128The atomic nucleus was discovered more than a century ago, yet an array of foundational questions remains unanswered regarding both the force that keeps its constituents together and how one builds up heavier systems. In recent decades, other exciting frontiers have been reached, e.g. exploring new or invisible particles (neutrinos, dark matter). Nuclear physics plays a central role in our understanding of both the atomic nucleus and seemingly unrelated things, e.g. our understanding of the interaction of neutrinos with matter, or how stars are born and die. With this theme issue, we are bringing together contributions from prominent researchers in the field in order to showcase the vibrancy of nuclear physics, covering a broad selection of current frontier topics. Central to this theme issue is the interplay between experiment and theory as the driving force of breakthroughs in the field. With advances in both nuclear theory and experimental capabilities, it is more important than ever to build the foundations of a truly collaborative community. It is only when experiments are informed by theory, and theory guided by experiments, that real breakthroughs can be achieved. This theme issue will showcase these synergies, inspiring and triggering further such collaborations.This special issue brings together the wider nuclear physics community, from traditional nuclear structure, reactions and dynamics, to hadron physics, nuclear astrophysics and neutrino physics. Some of the contributions venture further afield and touch upon the relevance of machine-learning techniques to nuclear physics, while others discuss strongly correlated matter that (while sharing many commonalities with neutron matter) is experimentally accessible using ultracold atoms (not nucleons). This reinforces the liminal position of nuclear physics across many research frontiers. We also hope that this issue will prompt new theory-experiment synergies and that it will plant the seeds for cross-collaborations amongst different fields.All contributions to this theme issue involve a mixture of theoretical and experimental work: exactly because nuclear physics stands at the interface between different scales, research in the field needs to make use of all available tools, both traditional/established and novel/exploratory. To make matters concrete, in what follows we will briefly discuss the contributions that now lie between one set of covers, starting with the mainly theoretical ones. In addition to briefly highlighting what is novel in the works contained herein, we also attempt to find a guiding thread through all of the original works that form the present theme issue.The work by Soma and Duguet nicely illustrates the aforementioned juxtaposition of traditional and novel approaches. The article hones in on the tool known as effective single-particle energies, which originally arose in the context of single-particle studies of shell structure in atomic nuclei. The authors clearly delineate the non-observable character of effective single-particle energies but do not limit themselves to criticism: they make contact with both modern ab initio quantum many-body studies of nuclei and experimental work. Specifically, they employ the successful Gorkov–Green's function approach to tackle a system recently studied experimentally at iThemba LABS. Through a combination of pedagogical exposition and original results, the scheme-dependence of effective single-particle energies is brought into sharp relief. While results focus on a specific neutron spin-orbit splitting along N = 20 isotones, the lessons gleaned from such studies are much more general.The next theoretical work (as well as the two following ones) falls into the large category of Monte Carlo approaches, employing random numbers to study a problem in microphysics. Specifically, Drissi et al. employ a continuum quantum Monte Carlo approach: variational Monte Carlo, in which a sophisticated guess for the ground-state wave function of a quantum many-body system is optimized in order to estimate physical properties as accurately as possible. A promising such guess that has been heavily used recently is that of neural-network quantum states; the authors go over neural wave functions with an added emphasis on the optimization algorithm. They discuss the Kronecker Factored Approximate Curvature optimizer in detail and transcend its shortcomings via novel extensions. The authors also take the opportunity to reformulate their approach using the language of game theory; via the concept of decision geometry, they propose a new optimizer that behaves better than standard ones (or the authors' own earlier approaches). While the physical system tackled involves a central interaction, such approaches hold the promise of improving future nuclear calculations of related quantities.The work by Morrell et al. also studies spin-1/2 fermions (i.e. does not specifically address nucleons), which could function as a foundation for later nuclear studies. The main tool employed here is also quantum Monte Carlo; unlike the earlier work that used a continuum approach, Morrell et al. place their strongly interacting particles on a spatial lattice in addition to discretizing the (imaginary) time evolution. Crucially, the authors of this work are able to use very few temporal steps/a very coarse grid in the time direction via a quantum cumulant expansion, i.e. using automated algebra rather than the more typical numerical approach. The system studied is not just a toy problem: cold fermions at unitarity have been extensively probed in lab work over the last two decades using dilute atomic systems. Thus, the authors provide specific comparisons with results from an MIT experiment, not only for the pressure, but also for the compressibility and heat capacity. Unlike much of nuclear-structure physics, this work is carried out at finite temperatures; such approaches to the thermodynamics of strongly coupled systems can guide future work on nuclear astrophysics.The work by Curry et al. similarly employs a lattice Monte Carlo formalism, this time at 0 temperature. The specific technique used is auxiliary-field quantum Monte Carlo, which has in the past been quite successful in condensed-matter and cold-atom studies; its main characteristic feature is the choice of working in a Slater-determinant space. The authors start by benchmarking against one- and two-dimensional results for the Hubbard model, a mainstay of solid-state physics. They then discuss experimentally relevant results for cold fermions at unitarity (also touched upon in the previous paragraph), paying close attention to the question of how to extrapolate away the lattice/discretization effects. The authors then turn to nuclear systems, carefully tuning the two-body lattice interaction such that it reproduces the neutron–neutron scattering length and effective range. They round things off by studying the energy of a few to many strongly interacting neutrons for a variety of lattice sizes. Given the power of the many-body technique and the promise of these neutron-matter results, one can expect extensions to bound states/atomic nuclei using similar approaches in the near future.Moving to a more synergistic contribution on both experiment and theory, Roth and Petri review the developments of the ab initio frontier, where chiral effective field theories of the strong interaction are being exploited to derive nuclear interactions and form the foundation of modern ab initio methods. Such an approach is bringing us closer to the understanding of nuclei from first principles, rooted in the theory of the strong interaction, quantum chromodynamics (QCD). Key to advancing the frontiers of ab initio theory is pioneering experiments on atomic nuclei that confront ab initio predictions and provide unparalleled benchmarks for the development and refinement of the theoretical approaches. This contribution puts forward selected experimental efforts along the carbon and oxygen chains that aim at validating these calculations, with a focus on electromagnetic observables, which present a particular challenge for ab initio theory. What will decisively drive future developments and breakthroughs in our understanding of the atomic nucleus from first principles is the strong synergy between experiment and theory and this contribution celebrates this.The work of Uesaka and Itagaki discusses the manifestation of non-uniformity in nuclei in the form of nuclear clustering. This review presents an interesting collection of examples of nuclear clustering throughout the nuclear chart and considers the underlying driving mechanism for this phenomenon, in terms of the tensor and spin-orbit forces as well as modern nucleon–nucleon interactions. Clustering plays a critical role in the origin of elements with further implications for nuclear fission and the potential to produce superheavy elements. Experimental breakthroughs in probing clustering in medium and heavy nuclei are explored and new experimental approaches, through knockout reactions, are presented.Continuing the theme of synergistic theoretical and experimental work, and extending the impact of nuclear physics to the cosmos, Wiedeking and Goriely discuss the impact of photon strength functions (PSF) and nuclear level densities (NLD) on shaping the outcomes of various nucleosynthetic processes. The authors give an overview of both experimental and theoretical methods to determine PSF and NLD, how they impact the important quantities that enter the astrophysical simulations, i.e. the reaction rates, and subsequently, how this affects the obtained abundances. Indeed, large uncertainties for (p,γ), (n,γ) and (α,γ) reaction rates across many regions of the nuclear chart are uncovered from diverse NLD and PSF model combinations, leading to potentially significant abundance variations of the nucleosynthesis processes. This contribution reflects on the critical role that nuclear physics plays in the cosmos and highlights how advances in theory and experimentation are enhancing our grasp of the origin of elements.Nuclear physics input is critical not only to our understanding of the origin of the elements but to other exotic objects in the cosmos, most notably neutron stars. Neutron stars, dense remnants of supernova explosions, contain matter that reaches extreme densities and pressure. Currently, their true nature remains an open question. The presence of hyperons, particles containing strange quarks, affects the equation of state, influencing the neutron star's size and internal structure. Understanding the behaviour of hadrons and hyperons within neutron stars sheds light on the fundamental physics governing these enigmatic celestial objects. The excitation spectra of hyperons provide critical constraints to models of big-bang nucleosynthesis with the majority of visible matter in the Universe progressing through excited hyperon states. Novel experimental efforts that allow us to bridge the knowledge gap on the interaction between hyperons and nucleons and underpin the rich hyperon excitation spectra are underway at the new K-long facility. Zachariou et al. discuss the K-Long facility at the Thomas Jefferson Laboratory and its potential to investigate the hyperon–nucleon interaction and hyperon spectroscopy. Such experimental constraints are critical for understanding and testing QCD in the strange sector and for underpinning our understanding of dense nuclear matter.Scientific technological advances have allowed us to discover new phenomena, e.g. neutrino oscillations. Although this type of experiment lies well within the domain of high-energy physics, nuclear physics has a fundamental role to play, e.g. in measurements of single and double beta-decay spectra that illuminate the scale and nature of the neutrino mass, and in neutrino–nucleus scattering that underpins oscillation experiments. It is these experimental advances that have brought down barriers between long-standing traditional fields of physics. The contribution by Parno et al. celebrates the intersection between long-standing traditional fields of physics by discussing experimental neutrino physics in a nuclear landscape. The authors present two nuclear laboratories for exploring neutrino physics, through nuclear beta decays, to shed light on the absolute neutrino-mass scale and answer the question of whether neutrinos are Majorana particles. Parno et al. further discuss the nuclear physics of high-energy neutrino interactions, essential for interpreting long-baseline neutrino-oscillation experiments, the use of low-energy neutrino scattering to illuminate nuclear properties and supernova nucleosynthesis, neutrino probes of fission reactors, searches for sterile neutrinos and applications in quantum sensing.This issue concludes with one of the most exciting facilities for nuclear physics research that is coming online in the near future, the Facility for Antiproton and Ion Research (FAIR), and discusses Nuclear Structure opportunities with GeV radioactive beams across a range of fields and scales: from low-energy physics via the investigation of multi-neutron systems and halos, to high-density nuclear matter and the equation of state, following heavy-ion collisions, fission, study of short-range correlations in nuclei, as well as hypernuclei. The R3B setup features prominently as a versatile experiment to perform kinematically complete measurements with high-energy radioactive ion beams, and various physics cases pursued within its experimental capabilities are presented. Even more interestingly, the authors put forward future opportunities at FAIR of studying exotic nuclei scattering off light ions and electrons in storage rings, as well as the concept of multi-GeV experiments with radioactive beams.As our brief summaries show, the works presented here involve many length scales, subfields and methodologies. It is worth reiterating that bringing together both theoretical and experimental works in the same venue (while not commonly done) is a good way to highlight past progress and jumpstart future discoveries. We have certainly enjoyed working with the authors, referees and the editorial office in putting this theme issue together. We hope the reader will, too. Data accessibility This article has no additional data. Declaration of AI use We have not used AI-assisted technologies in creating this article. Authors' contributions M.P.: writing–original draft, writing—review and editing; A.G.: writing—original draft, writing—review and editing. Both authors gave final approval for publication and agreed to be held accountable for the work performed therein. Conflict of interest declaration This theme issue was put together by the Guest Editor team under supervision from the journal's Editorial staff, following the Royal Society's ethical codes and best-practice guidelines. The Guest Editor team invited contributions and handled the review process. Individual Guest Editors were not involved in assessing papers where they had a personal, professional or financial conflict of interest with the authors or the research described. Independent reviewers assessed all papers. Invitation to contribute did not guarantee inclusion. Funding No funding has been received for this article. Footnotes One contribution of 11 to a theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'. © 2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetails This Issue23 July 2024Volume 382Issue 2275Theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars' compiled and edited by Professor Marina Petri and Professor Alexandros Gezerlis Article InformationDOI:https://doi.org/10.1098/rsta.2023.0128Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Manuscript received13/05/2024Manuscript accepted13/05/2024Published online24/06/2024 License:© 2024 The Authors.Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Citations and impact Keywordsnuclear physicshadron physicsneutrino physicsnuclear structurenuclear reactionsnuclear astrophysics Subjectsastrophysicsatomic and molecular physicsnuclear physics

We report on the first results for the second-order perturbation theory correction to the ground-state energy of a nuclear many-body system in a continuum quantum Monte Carlo calculation. Second-order (and higher) perturbative corrections are notoriously difficult to compute in most ab initio many-body methods, where the focus is usually on obtaining the ground-state energy. By mapping our calculation of the second-order energy correction to an evolution in imaginary time using the diffusion Monte Carlo method, we are able to calculate these nuclear corrections for the first time. After benchmarking our method in the few-body sector, we explore the effect of charge-independence-breaking terms in the nuclear Hamiltonian. We then employ that approach to investigate the many-body, perturbative, order-by-order convergence that is fundamental in modern theories of the nucleon-nucleon interaction derived from chiral effective field theory. We find cutoff-dependent perturbativeness between potentials at higher chiral order and also that the difference between leading order and next-to-leading order potentials is nonperturbative; both of these results have important implications for future nuclear many-body calculations. Our approach is quite general and promises to be of wide applicability.

This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of scientific or engineering data; these mistakes are also quite prevalent in the research literature. Crucially, we do not address errors made by an individual author, focusing instead on mistakes that are widespread in the introductory literature. After some background on frequentist and Bayesian linear regression, we turn to our six paradigmatic cases, providing in each instance a specific example of the textbook mistake, pointers to the specialist literature where the topic is handled properly, along with a correction that summarizes the salient points. The mistakes (and corrections) are broadly relevant to any technical setting where statistical techniques are used to draw practical conclusions, ranging from topics introduced in an elementary course on experimental measurements all the way to more involved approaches to regression.

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.

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.