We present lattice calculations for the ground state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.
We use chiral perturbation theory to compute the effective nucleon propagator in an expansion about low density in the chiral limit. We neglect four-nucleon interactions and focus on pion exchange. Evaluating the nucleon self-energy on its mass shell to leading order, we show that the effective nucleon mass increases by a small amount. We discuss the relevance of our results to the structure of compact stars.
This is the second of two papers which investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature.
We report results of fully non-perturbative calculations, based on Auxiliary Field Quantum Monte Carlo (AFQMC) approach, for the dilute neutron matter at the density $ρ=0.003\fm^{-3}$. Fundamental quantities which characterize the superfluid state: the single particle energy gap $Δ(T)$, and the critical temperature $\Tc$ have been determined. The large value of $Δ(0)/\Tc\approx 3.2$ indicates that the system is not a BCS-type superfluid at low temperatures.
The internal structure of neutron stars and the physical properties of nuclei depend on the equation of state (EOS) of neutron matter. Dilute neutron matter is a quantum system of spin-1/2 Fermi particles interacting via s-wave scattering. Although a nuclear system and an ultracold atomic system have length scales and energy scales that differ by several orders of magnitude, both systems follow a common universal EOS considering their non-dimensional universal interaction parameters. In this study, we determine the EOS of neutron matter in the dilute region, where the influence of the s-wave s…
We report results of fully non-perturbative, Path Integral Monte Carlo (PIMC) calculations for dilute neutron matter. The neutron-neutron interaction in the s channel is parameterized by the scattering length and the effective range. We calculate the energy and the chemical potential as a function of temperature at the density $\dens=0.003\fm^{-3}$. The critical temperature $\Tc$ for the superfluid-normal phase transition is estimated from the finite size scaling of the condensate fraction. At low temperatures we extract the spectral weight function $A(p,ω)$ from the imaginary time propagator …
We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this paper we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the…
We discuss neutron matter calculations based on chiral effective field theory interactions and their predictions for the symmetry energy, the neutron skin of 208 Pb, and for the radius of neutron stars.
We review efforts to describe the approach to chiral symmetry restoration in neutron matter from the low-energy realization of QCD, chiral effective field theory.
We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground state energy as an expansion about the unitarity limit with corrections du…
We present predictions of the binding energy per nucleon and the neutron skin thickness in highly neutron-rich isotopes of Oxygen, Magnesium, and Aluminum. The calculations are carried out at and below the neutron drip line as predicted by our model. The nuclear properties are obtained via an energy functional whose input is the equation of state of isospin-asymmetric infinite matter. The latter is based on a microscopic derivation of the energy per particle in neutron matter applying chiral few-nucleon forces together with a phenomenological model for the equation of state of symmetric nuclea…
We calculate neutron star masses and radii from equations of state based on recent high-quality chiral nucleon-nucleon potentials up to fifth order of the chiral expansion and the leading chiral three- nucleon force. Our focus is on the radius of a 1.4 M_{Sun} neutron star, for which we report predictions that are consistent with the most recent constraints. We also show the full M(R) relations up to their respective maximum masses. Beyond the densities for which microscopic predictions are derived from chiral forces, the equations of state are obtained via polytropic continuations. However, t…
We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. We find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints.
A recent chiral perturbation theory calculation of the in-medium quark condensate $<\bar q q>$ is extended to the isospin-asymmetric case of pure neutron matter. In contrast to the behavior in isospin-symmetric nuclear matter we find only small deviations from the linear density approximation. This feature originates primarily from the reduced weight factors (e.g. 1/6 for the dominant contributions) of the $2π$-exchange mechanisms in pure neutron matter. Our result suggests therefore that the tendencies for chiral symmetry restoration are actually favored in systems with large neutron excess (…
We study the properties of rotating neutron stars within a generalized chiral SU(3)-flavor model. The influence of the rotation on the inner structure and the hyperon matter content of the star is discussed. We calculate the Kepler frequency and moments of inertia of the neutron star sequences. An estimate for the braking index of the associated pulsars is given.
Low-density neutron matter is characterized by fascinating emergent quantum phenomena, such as the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and stochastic reconfiguration techniques. Our approach is competitive with the auxiliary-field diffusion Monte Carlo method at a fraction of the computational cost. Using a leading-order pionless effective field theory Hamiltonian, we compute the energy per particle of infinite neutron …
We calculate the energy per particle in infinite neutron matter perturbatively using chiral N3LO two-body potentials plus N2LO three-body forces. The cutoff dependence of the predictions is investigated by employing chiral interactions with different regulators. We find that the inclusion of three-nucleon forces, which are consistent with the applied two-nucleon interaction, leads to a strongly reduced regulator dependence of the results.
We discuss the spatial structure of the Cooper pair in dilute neutron matter and neutron-rich nuclei by means of the BCS theory and the Skyrme-Hartree-Fock-Bogioliubov model, respectively. The neutron pairing in dilute neutron matter is close to the region of the BCS-BEC crossover in a wide density range, giving rise to spatially compact Cooper pair whose size is smaller than the average interaparticle distance. This behavior extends to moderate low density ($\sim 10^{-1}$ of the saturation density) where the Cooper pair size becomes smallerst ($\sim 5$ fm). The Cooper pair in finite nuclei al…
Temperature effects on the neutron matter equation of state are investigated in the framework of chiral effective field theory. Latest, state-of-the-art chiral two-nucleon forces are applied from third to fifth order in the chiral expansion together with chiral three-nucleon forces, allowing for a determination of the truncation error of the theoretical predictions. The thermodynamic quantities considered include the chemical potential, the internal energy, the entropy, and the free energy. In general, good order-by-order convergence of all predictions is observed. As to be expected, temperatu…
Singlet $S$-wave superfluidity of dilute neutron matter is studied within the correlated BCS method, which takes into account both pairing and short-range correlations. First, the equation of state (EOS) of normal neutron matter is calculated within the Correlated Basis Function (CBF) method in lowest cluster order using the ${}^1{S_0}$ and ${}^3P$ components of the Argonne $V_{18}$ potential, assuming trial Jastrow-type correlation functions. The ${}^1{S_0}$ superfluid gap is then calculated with the corresponding component of the Argonne $V_{18}$ potential and the optimally determined correl…
We report neutron star predictions based on our most recent equations of state. These are derived from chiral effective field theory, which allows for a systematic development of nuclear forces, order by order. We utilize high-quality two-nucleon interactions and include all three-nucleon forces up to fourth order in the chiral expansion. Our ab initio predictions are restricted to the domain of applicability of chiral effective field theory. However, stellar matter in the interior of neutron stars can be up to several times denser than normal nuclear matter at saturation, and its composition …
We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models …
We present recent results on lattice simulations using chiral effective field theory. In particular we discuss lattice simulations for dilute neutron matter at next-to-leading order and three-body forces in light nuclei at next-to-next-to-leading order.
Spin-polarized neutron matter is studied using chiral two- and three-body forces. We focus, in particular, on predictions of the energy per particle in ferromagnetic neutron matter at different orders of chiral effective field theory and for different choices of the resolution scale. We discuss the convergence pattern of the predictions and their cutoff dependence. We explore to which extent fully polarized neutron matter behaves (nearly) like a free Fermi gas. We also consider the more general case of partial polarization in neutron matter as well as the presence of a small proton fraction. I…
The nucleation process of quark matter in both cold and hot dense hadronic matter is investigated using a chiral approach to describe the quark phase. We use the Nambu-Jona-Lasinio and the Chromo Dielectric models to describe the deconfined phase and the non-linear Walecka model for the hadronic one. The effect of hyperons on the transition phase between hadronic and quark matter is studied. The consequences of the nucleation process for neutron star physics are outlined.
We have studied neutron-rich carbon isotopes in terms of the shell model employing a realistic effective hamiltonian derived from the chiral N3LOW nucleon-nucleon potential. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory. The calculated results are in very good agreement with the available experimental data, providing a sound description of this isotopic chain toward the neutron dripline. The correct location of the dripline is reproduced.
In the present work the conjunction of chiral SU(3) model with QCD sum rules is employed to explore the possibility of $ρ$ meson condensation in neutron stars. The quark and gluon condensates in terms of which the in-medium masses of $ρ$ mesons can be expressed are calculated using the chiral SU(3) model in the charge neutral matter which is relevant for neutron stars. It is observed that condition of $ρ$ meson condensation is satisfied for the density of about 7$ρ_{0}$, where $ρ_{0}$ is the nuclear saturation density. In the end, a brief qualitative discussion of the magnetic field is also in…
We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neut…
We develop a chiral SU(3) symmetric relativistic mean field (RMF) model with a logarithmic potential of scalar condensates. Experimental and empirical data of symmetric nuclear matter saturation properties, bulk properties of normal nuclei, and separation energies of single- and double-$Λ$ hypernuclei are well explained. The nuclear matter equation of state (EOS) is found to be softened by $σζ$ mixing which comes from determinant interaction. The neutron star matter EOS is further softened by $Λ$ hyperons.
Three-nucleon forces are an essential ingredient for an accurate description of nuclear few- and many-body systems. However, implementing them directly in many-body calculations is technically very challenging. Thus, there is a need for an efficient approximation method. By closing one nucleon line to a loop, it is possible to derive effective in-medium nucleon-nucleon interactions that represent the underlying three-nucleon forces, as constructed in Chiral Effective Field Theory. Since three-neutron forces are equally as important for the computation of the equation of state for pure neutron …
We investigate the equations of state for pure neutron matter and strange hadronic matter in $β$-equilibrium, including $Λ$, $Σ$ and $Ξ$ hyperons. The masses and radii of pure neutron stars and strange hadronic stars are obtained. For a pure neutron star, the maximum mass is about $1.8 M_{\mathrm{sun}}$, while for a strange hadronic star, the maximum mass is around $1.45 M_{\mathrm{sun}}$. The typical radii of pure neutron stars and strange hadronic stars are about 11.0-12.3 km and 10.7-11.7 km, respectively.
Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N$^2$LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included i…
We report ab initio calculations for neutron drops in a 10 MeV external harmonic-oscillator trap using chiral nucleon-nucleon plus three-nucleon interactions. We present total binding energies, internal energies, radii and odd-even energy differences for neutron numbers N = 2 - 18 using the no-core shell model with and without importance truncation. Furthermore, we present total binding energies for N = 8, 16, 20, 28, 40, 50 obtained in a coupled-cluster approach. Comparisons with Green's Function Monte Carlo results, where available, using Argonne v8' with three-nucleon interactions reveal im…
The long-range terms of the subleading chiral three-nucleon force [published in Phys.\,Rev.\,C77, 064004 (2008)] are specified to the case of three neutrons. From these $3n$-interactions an effective density-dependent neutron-neutron potential $V_\text{med}$ in pure neutron matter is derived. Following the division of the pertinent 3n-diagrams into two-pion exchange, two-pion-one-pion exchange and ring topology, all self-closings and concatenations of two neutron-lines to an in-medium loop are evaluated. The momentum and $k_n$-dependent potentials associated with the spin-operators $1,\, \vecσ…
We present the first results for the neutron matter equation of state (EOS) using nucleon-nucleon and three-nucleon chiral effective field theory interactions that are consistently evolved in the framework of the Similarity Renormalization Group (SRG). The dependence of the EOS on the SRG resolution scale is greatly reduced when induced three-nucleon forces (3NF) are included and the residual variation, which in part is from missing induced four-body interactions, is comparable to estimated many-body perturbation theory truncation errors. The relative growth with decreasing resolution of the 3…
We discuss the {\it SU}(2) chiral sigma model in the context of nuclear matter using a mean field approach at high density. In this model we include a dynamically generated isoscalar vector field and higher-order terms in the scalar field. With the inclusion of these, we reproduce the empirical values of the nuclear matter saturation density, binding energy, and nuclear incompressibility. The value of the incompressibility is chosen according to recently obtained heavy-ion collision data. We then apply the same dynamical model to neutron-rich matter in beta equilibrium, related to neutron star…
Considering the nucleon as a system of confined valence quarks surrounded by pions we derive a Galster-like parameterization of the neutron electric form factor $G_E^n$. Furthermore, we show that the proposed parameterization can be linked to properties of the pion cloud. By this, the high quality data for the pion form factor can be used in predictions of $G_E^n$ in the low $Q^2$ region, where the direct double polarization measurements are not available.
The equations of state for neutron matter, strange and non-strange hadronic matter in a chiral SU(3) quark mean field model are applied in the study of slowly rotating neutron stars and hadronic stars. The radius, mass, moment of inertia, and other physical quantities are carefully examined. The effect of nucleon crust for the strange hadronic star is exhibited. Our results show the rotation can increase the maximum mass of compact stars significantly. For big enough mass of pulsar which can not be explained as strange hadronic star, the theoretical approaches to increase the maximum mass are …
This contribution will survey recent progress toward an understanding of diverse pairing phenomena in dilute nuclear matter at small and moderate isospin asymmetry, with results of potential relevance to supernova envelopes and proto-neutron stars. Application of {\it ab initio} many-body techniques has revealed a rich array of temperature-density phase diagrams, indexed by isospin asymmetry, which feature both conventional and unconventional superfluid phases. At low density there exist a homogeneous translationally invariant BCS phase, a homogeneous LOFF phase violating translational invaria…
We derive from the subleading contributions to the chiral three-nucleon interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84, 054001 (2011)] their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter in an analytical way. For the variety of short-range and long-range terms that constitute the subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the results for 2-ring diagrams can be given in terms of elementary function…
We study several structure properties of finite nuclei using relativistic mean-field Lagrangians constructed according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities. The models are consistent with current experimental constraints for the equations of state of symmetric matter at both normal and supra-normal densities and of asymmetric matter at sub-saturation densities. It is shown that these models can successfully describe the binding energies and charge radii of finite nuclei. Compared to calculations with usual relativistic mean-field models, these model…
The differential isospin-fractionation (IsoF) during the liquid-gas phase transition in dilute asymmetric nuclear matter is studied as a function of nucleon momentum. Within a self-consistent thermal model it is shown that the neutron/proton ratio of the gas phase becomes {\it smaller} than that of the liquid phase for energetic nucleons, although the gas phase is overall more neutron-rich. Clear indications of the differential IsoF consistent with the thermal model predictions are demonstrated within a transport model for heavy-ion reactions. Future comparisons with experimental data will all…
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Errat…
The axial vector coupling constants of the $β$ decay processes of neutron and hyperon are calculated in SU(3) chiral colour dielectric model (CCDM). Using these axial coupling constants of neutron and hyperon, in CCDM we calculate the integrals of the spin dependent structure functions for proton and neutron. Our result is similar to the results obtained by MIT bag and Cloudy bag models.
In recent years, the combination of advanced quantum Monte Carlo (QMC) methods and local interactions derived from chiral effective field theory (EFT) has been shown to provide a versatile and systematic approach to nuclear systems. Calculations at next-to-next-to-leading order in chiral EFT have lead to fascinating results for nuclei and nucleonic matter. On the one hand, ground-state properties of nuclei are well reproduced up to $A\leq16$, even though these potentials have been fit to nucleon-nucleon scattering and few-body observables only. On the other hand, a reasonable description of ne…
We study the effect of the nucleon-nucleon-lambda (NN$Λ$) three-body force on neutron stars. In particular, we consider the NN$Λ$ force recently derived by the Jülich--Bonn--Munich group within the framework of chiral effective field theory at next-to-next-to-leading order. This force, together with realistic nucleon-nucleon, nucleon-nucleon-nucleon and nucleon-hyperon interactions, is used to calculate the equation of state and the structure of neutron stars within the many-body non-relativistic Brueckner-Hartree-Fock approach. Our results show that the inclusion of the NN$Λ$ force leads to a…
We have optimized the parameters of extended relativistic mean-field model using a selected set of global observables which includes binding energies and charge radii for nuclei along several isotopic and isotonic chains and the iso-scalar giant monopole resonance energies for the $^{90}$Zr and $^{208}$Pb nuclei. The model parameters are further constrained by the available informations on the energy per neutron for the dilute neutron matter and bounds on the equations of state of the symmetric and asymmetric nuclear matter at supra-nuclear densities. Two new parameter sets BSP and IUFSU* are …
In this work we present a framework that allows to solve the Faddeev equations for three-nucleon scattering using the wave-packet continuum-discretization method. We perform systematic benchmarks using results in the literature and study in detail the convergence of this method with respect to the number of wave packets. We compute several different elastic neutron-deuteron scattering cross-section observables for a variety of energies using chiral nucleon-nucleon interactions. For the interaction $\text{N2LO}_{\text{opt}}$ we find good agreement with data for nucleon scattering-energies $E_\t…
Neutron drip line in calcium isotopes from a chiral interaction
Peking University（北京大学）；Texas A&M University（德克萨斯农工大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Chalmers University of Technology（查尔姆斯理工大学）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Johannes Gutenberg-Universität（约翰内斯·古腾堡大学）；University of Tsukuba（筑波大学）
We present a microscopic calculation of the complete quasiparticle interaction, including central as well as noncentral components, in neutron matter from high-precision two- and three-body forces derived within the framework of chiral effective field theory. The contributions from two-nucleon forces are computed in many-body perturbation theory to first and second order (without any simplifying approximations). In addition we include the leading-order one-loop diagrams from the N2LO chiral three-nucleon force, which contribute to all Fermi liquid parameters except those associated with the ce…
We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-ord…
