Ab initio lattice study of neutron–alpha scattering with chiral forces at N3LO

We explore the lattice spacing dependence in Nuclear Lattice Effective Field Theory for few-body systems up to next-to-next-to leading order in chiral effective field theory including all isospin breaking and electromagnetic effects, the complete two-pion-exchange potential and the three-nucleon forces. We calculate phase shifts in the neutron-proton system and proton-proton systems as well as the scattering length in the neutron-neutron system. We then perform a full next-to-next-to-leading order calculation with two-nucleon and three-nucleon forces for the triton and helium-4 and analyse their binding energy correlation. We show how the Tjon band is reached by decreasing the lattice spacing and confirm the continuum observation that a four-body force is not necessary to describe light nuclei.

The triton lifetime from nuclear lattice effective field theory

We review the calculation of the Hoyle state of 12C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of 12C and 16O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei 16O, 20Ne, 24Mg, and 28Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of 16O.

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.

Understanding the strong interactions within baryonic systems beyond the up and down quark sector is pivotal for a comprehensive description of nuclear forces. This study explores the interactions involving hyperons, particularly the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} particle, within the framework of nuclear lattice effective field theory (NLEFT). By incorporating Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hyperons into the NLEFT framework, we extend our investigation into the S=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S = -1$$\\end{document} sector, allowing us to probe the third dimension of the nuclear chart. We calculate the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} separation energies (BΛ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\varLambda }$$\\end{document}) of hypernuclei up to the medium-mass region, providing valuable insights into hyperon–nucleon (YN) and hyperon–nucleon–nucleon (YNN) interactions. Our calculations employ high-fidelity chiral interactions at N3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ ^3$$\\end{document}LO for nucleons and extend it to Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hyperons with leading-order S-wave YN interactions as well as YNN forces constrained only by the A=4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=4,5$$\\end{document} systems. Our results contribute to a deeper understanding of the SU(3) symmetry breaking and establish a foundation for future improvements in hypernuclear calculations.

We employ the nuclear lattice effective field theory (NLEFT), an efficient tool for nuclear calculations, to solve the asymmetric multihadron systems. We take the DD*K three-body system as an illustration to demonstrate the capability of the method. Here the two-body chiral interactions between D, D*, and K are regulated with a soft lattice regulator and calibrated with the binding energies of the Tcc+, Ds0*(2317), and Ds1(2460) molecular states. We then calculate the three-body binding energy using the NLEFT and analyze the systematic uncertainties due to the finite volume effects, the sliding cutoff, and the leading-order three-body forces. Even when the three-body interaction is repulsive (even as large as the infinite repulsive interaction), the three-body system has a bound state unambiguously with binding energy no larger than the Ds1(2460)D threshold. To check the renormalization group invariance of our framework, we extract the first excited state. We find that when the ground state is fixed, the first excited states with various cutoffs coincide with each other when the cubic size goes larger. In addition, the standard angular momentum and parity projection technique is implemented for the quantum numbers of the ground and excited states. We find that both of them are S-wave states with quantum number JP=1−. Because the three-body state contains two charm quarks, it is easier to be detected in the Large Hadron Collider. Published by the American Physical Society 2025

In this contribution, we show some recent progress in the study of neutron-proton scattering with Nuclear Lattice Effective Field Theory (NLEFT). We present preliminary studies of both, the uncertainties in the np phase shifts extracted with NLEFT, and the lattice spacing dependence in the transfer matrix formalism. Such investigations have not been performed before in the literature, and will be relevant for Monte Carlo simulations of nuclear structure with NLEFT.

We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.

Extrapolations in Euclidean time form a central part of nuclear lattice effective field theory (NLEFT) calculations using the projection Monte Carlo method, as the sign problem in many cases prevents simulations at large Euclidean time. We review the next-to-next-to-leading order NLEFT results for the alpha nuclei up to 28Si, with emphasis on the Euclidean time extrapolations, their expected accuracy and potential pitfalls. We also discuss possible avenues for improving the reliability of Euclidean time extrapolations in NLEFT.

The equation of state (EOS) of neutron matter plays a decisive role in understanding the neutron star properties and the gravitational waves from neutron star mergers. At sufficient densities, the appearance of hyperons generally softens the EOS, leading to a reduction in the maximum mass of neutron stars well below the observed values of about 2 M ⊙. Even though repulsive three-body forces are known to solve this so-called “hyperon puzzle,” so far performing ab initio calculations with a substantial number of hyperons for neutron star properties has remained elusive. Starting from the newly developed auxiliary field quantum Monte Carlo algorithm to simulate hyperneutron matter without any sign oscillations, we derive three distinct EOSs by employing the state-of-the-art nuclear lattice effective field theory. We include NΛ, ΛΛ two-body forces, NNΛ, and NΛΛ three-body forces. Consequently, we determine essential astrophysical quantities such as the neutron star mass, radius, tidal deformability, and universal I–Love–Q relation. The maximum mass, radius, and tidal deformability of a 1.4 M ⊙ neutron star are predicted to be 2.17(1)(1) M ⊙, R 1.4M⊙ = 13.10(1)(7) km, and Λ 1.4 M ⊙ = 597 ( 5 ) ( 18 ) , respectively, based on our most realistic EOS. These predictions are in good agreement with the latest astrophysical constraints derived from observations of massive neutron stars, gravitational waves, and joint mass–radius measurements. In addition, for the first time in ab initio calculations, we investigate both nonrotating and rotating neutron star configurations. The results indicate that the impact of rotational dynamics on the maximum mass is small, regardless of whether hyperons are present in the EOS or not.

Nuclear Lattice Effective Field Theory is a new many-body approach that is firmly rooted in the symmetries of QCD. In particular, it allows for ab initio calculations of nuclear structure and reactions. In this talk, I focus on the emergence of α-clustering in nuclei based on this approach. I also discuss various recent achievements, the deficiencies of the chiral forces used at present and the prospects to improve upon these and the calculations of nuclear properties and dynamics.

We present an abinitio study of the charge and matter radii of oxygen isotopes from ^{16}O to ^{20}O using nuclear lattice effective field theory (NLEFT) with high-fidelity N^{3}LO chiral interactions. To efficiently address the MonteCarlo sign problem encountered in nuclear radius calculations, we introduce the partial pinhole algorithm, significantly reducing statistical uncertainties and extending the reach to more neutron-rich and proton-rich isotopes. Our computed charge radii for ^{16}O, ^{17}O, and ^{18}O closely match experimental data, and we predict a charge radius of 2.810(32)fm for ^{20}O. The calculated matter radii show excellent agreement with values extracted from low-energy proton and electron elastic scattering data, but are inconsistent with those derived from interaction cross sections and charge-changing cross section measurements. These discrepancies highlight model-dependent ambiguities in the experimental extraction methods of matter radii and underscore the value of precise theoretical benchmarks from NLEFT calculations.

This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.

We present a systematic ab initio study of clustering in hot dilute nuclear matter using nuclear lattice effective field theory with an SU(4)-symmetric interaction. We introduce a method called light-cluster distillation to determine the abundances of dimers, trimers, and alpha clusters as a function of density and temperature. Our lattice results are compared with an ideal gas model composed of free nucleons and clusters. Excellent agreement is found at very low density, while deviations from ideal gas abundances appear at increasing density due to cluster-nucleon and cluster-cluster interactions. In addition to determining the composition of hot dilute nuclear matter as a function of density and temperature, the lattice calculations also serve as benchmarks for virial expansion calculations, statistical models, and transport models of fragmentation and clustering in nucleus-nucleus collisions.

We present a systematic abinitio study of the low-lying states in beryllium isotopes from ^{7}Be to ^{12}Be using nuclear lattice effective field theory with the N^{3}LO interaction. Our calculations achieve good agreement with experimental data for energies, radii, and electromagnetic properties. We introduce a novel, model-independent method to quantify nuclear shapes, uncovering a distinct pattern in the interplay between positive and negative parity states across the isotopic chain. By combining MonteCarlo sampling of the many-body density operator with a novel nucleon-grouping algorithm, the prominent two-center cluster structures, the emergence of one-neutron halo, complex nuclear molecular dynamics such as π orbital and σ orbital, emerge naturally.