We show that microscopic calculations based on chiral effective field theory interactions constrain the properties of neutron-rich matter below nuclear densities to a much higher degree than is reflected in commonly used equations of state. Combined with observed neutron star masses, our results lead to a radius R = 9.7 - 13.9 km for a 1.4 M_{solar} star, where the theoretical range is due, in about equal amounts, to uncertainties in many-body forces and to the extrapolation to high densities.
A new method is proposed to deduce the neutron radii of neutron-rich nuclei. This method requires measuring the reaction cross sections of both the neutron-rich nucleus and its stable isotope at the same energy on a proton target. Using this method and the available experimental data of $^{12,22}$C + $p$ and $^{9,14}$Be + $p$ at 40$A$ MeV, the neutron radii of $^{22}$C and $^{14}$Be have been deduced for the first time.
We discuss new limits on masses and radii of compact stars and we conclude that they can be interpreted as an indication of the existence of two classes of stars: "normal" compact stars and "ultra-compact" stars. We estimate the critical mass at which the first configuration collapses into the second.
It has been recently suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [B.A. Brown Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a su…
Multi-neutron systems are crucial to understanding the physics of neutron-rich nuclei and neutron stars. Neutron drops, neutrons confined in an external field, are investigated systematically in both non-relativistic and relativistic density functional theories and with ab initio calculations. We demonstrate a strong linear correlation, which is universal in the realm of mean-field models, between the rms radii of neutron drops and the neutron skin thickness of Pb-208 and Ca-48; i.e., the difference between the neutron and proton rms radii of a nucleus. Due to its high quality, this correlatio…
Logarithmic divergences in pion and proton charge radii associated with chiral loops are investigated to assess systematic uncertainties in current lattice determinations of charge radii. The chiral corrections offer a possible solution to the long standing problem of why present lattice calculations yield proton and pion radii which are similar in size.
A simple formula is derived that describes how the Coulomb interaction affects the proton radius in nuclei. It determines the difference between neutron and proton radii in nuclei with N approx Z. It also provides an estimate for the difference between the radii of the Z core neutrons and the protons in nuclei with a large neutron excess. The results obtained from the derived formula are compared with radii calculated in a Skyrme Hartree-Fock calculation.
We calculate the electric charge radii of the SU(3) pseudoscalar mesons and the SU(3) octet baryons in quenched and partially quenched chiral perturbation theory. We work in the isospin limit, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. The results are necessary for the extrapolation of future lattice calculations of meson and baryon charge radii. We also derive expressions for the nucleon and pion charge radii in SU(2) flavor away from the isospin limit.
Bulk nuclear observables such as charge radii and binding energies are well described by both nonrelativistic and covariant mean-field models. However, predictions of neutron radii, which are not tightly constrained by reliable data, vary significantly. The nature of this variation is investigated using correlations between basic properties of the models and the neutron skin thickness in lead. The results suggest that conventional covariant models are too limited. The study is guided by principles and insights of effective field theory (EFT), such as power counting, and the relation of mean-fi…
Within the complex-energy configuration interaction framework, we study correlations of valence neutrons to explain the behavior of charge radii in the neutron halo nuclei $^{6,8}$He. We find that the experimentally observed decrease of the charge radius between $^6$He and $^8$He is caused by a subtle interplay between three effects: dineutron correlations, a spin-orbit contribution to the charge radius, and a core swelling effect. We demonstrate that two-neutron angular correlations in the $2^+_1$ resonance of $^6$He differ markedly from the ground-state correlations in $^{6,8}$He.
We investigate the correlation between nuclear neutron radii and the radius of neutron stars. We use a well-established hadronic SU(3) model based on chiral symmetry that naturally includes non-linear vector meson and scalar meson - vector meson couplings. The relative strengths of the couplings modify the nuclear isospin-dependent interactions. We study the dependence of nuclear and neutron star radii on the coupling strengths. The relevance of the results for parity-violating electron-nucleus scattering and the URCA process in neutron stars is discussed.
We present predictions for proton skins based on isospin-asymmetric equations of state derived microscopically from high-precision chiral few-nucleon interactions. Moreover, we investigate the relation between the neutron skin of a nucleus and the difference between the proton radii of the corresponding mirror nuclei.
We compute the octet baryon charge radii to O(1/Heavy^3) in heavy baryon chiral perturbation theory. We examine the effect of including the decuplet of spin-3/2 baryons explicitly. We find that it does no t improve the level of agreement between the HBchiPT and experimental values for the Sigma^- charge radius.
Neutron matter presents a unique system for chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present the first complete N3LO calculation of the neutron matter energy. This includes the subleading three-nucleon (3N) forces for the first time and all leading four-nucleon (4N) forces. We find relatively large contributions from N3LO 3N forces. Our results provide constraints for neutron-rich matter in astrophysics with controlled theoretical uncertainties.
The binding energies, shapes and sizes of even-even beta-stable nuclei with A >= 40 and a few chains of isotopes with Z=50, 56, 82, 94 protons and isotones with N=50, 82, 126 neutrons are analyzed. The average isospin dependence of the radii of protons and neutrons evaluated within the relativistic mean field theory is studied. A simple, phenomenological formula for neutron radii is proposed.
The charge radii and magnetic moments of all the light and strange baryons are investigated within the framework of a constituent quark model based on Goldstone-boson-exchange dynamics. Following the point-form approach to relativistic quantum mechanics, the calculations are performed in a manifestly covariant manner. Relativistic (boost) effects have a sizeable influence on the results. The direct predictions of the constituent quark model are found to fall remarkably close to the available experimental data.
Neutron star radii are primarily determined by the pressure of isospin asymmetric matter which is proportional to the slope of the nuclear symmetry energy. Available terrestrial laboratory data on the isospin diffusion in heavy-ion reactions at intermediate energies constrain the slope of the symmetry energy. Using this constraint, we show that the radius (radiation radius) of a 1.4 solar mass neutron star is between 11.5 (14.4) and 13.6 (16.3) km.
Recent neutron star observations suggest that the masses and radii of neutron stars may be smaller than previously considered, which would disfavor a purely nucleonic equation of state. In our model, we use a the flavor SU(3) sigma model that includes delta resonances and hyperons in the equation of state. We find that if the coupling of the delta resonances to the vector mesons is slightly smaller than that of the nucleons, we can reproduce both the measured mass-radius relationship and the extrapolated equation of state.
A thick neutron skin emerges from the first determination of root mean square radii of the proton distributions for $^{17-22}$N from charge changing cross section measurements around 900$A$ MeV at GSI. Neutron halo effects are signaled for $^{22}$N from an increase in the proton and matter radii. The radii suggest an unconventional shell gap at $N$ = 14 arising from the attractive proton-neutron tensor interaction, in good agreement with shell model calculations. $Ab$ $initio$, in-medium similarity re-normalization group, calculations with a state-of-the-art chiral nucleon-nucleon and three-nu…
At present, neutron star radii from both observations and model predictions remain very uncertain. Whereas different models can predict a wide range of neutron star radii, it is not possible for most models to predict radii that are smaller than about 10 km, thus if such small radii are established in the future they will be very difficult to reconcile with model estimates. By invoking a new term in the equation of state that enhances the energy density, but leaves the pressure unchanged we simulate the current uncertainty in the neutron star radii. This new term can be possibly due to the exc…
The neutron-matter equation of state constrains the properties of many physical systems over a wide density range and can be studied systematically using chiral effective field theory (EFT). In chiral EFT, all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present details and additional results of the first complete N3LO calculation of the neutron-matter energy, which includes the subleading three-nucleon as well as the leading four-nucleon forces, and provides theoretical uncertainties. In addition, we discuss the impact of our results for as…
We study the Borromean nuclei formed by a core nucleus and two neutrons in a nonrelativistic effective field theory formalism considering both neutron-neutron and neutron-core interactions. We provide formulae of the charge and matter radii, and successfully reproduce the universal relation proposed by Hongo and Son based on the approximation of an infinite neutron-neutron scattering length and neglecting the neutron-core scattering. Once the realistic finite neutron-neutron and neutron-core scattering lengths are used, the charge and matter radii are influenced by the neutron-core channel in …
We calculate the chiral condensate in neutron matter at zero temperature based on nuclear forces derived within chiral effective field theory. Two-, three- and four-nucleon interactions are included consistently to next-to-next-to-next-to-leading order (N3LO) of the chiral expansion. We find that the interaction contributions lead to a modest increase of the condensate, thus impeding the restoration of chiral symmetry in dense matter and making a chiral phase transition in neutron-rich matter unlikely for densities that are not significantly higher than nuclear saturation density.
With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLO$_{\rm sat}$, yield accurate binding energies and radii of nuclei up to $^{40}$Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low…
{ {\bf Background:} Knowing the difference between the neutron and proton densities of nuclei is a significant topic because of its importance for understanding neutron star structures and cooling mechanisms. The coherent-nuclear photoproduction of pions, $({\g,π^0})$, combined with elastic electron scattering, has been suggested to be a very accurate probe of density differences. {\bf Purpose:} Study the ${(\g,π^0})$ reaction mechanism so as to better access the uncertainties involved in extracting the neutron density. {\bf Methods:} Include the effects of final-state pion-nucleus charge-exch…
The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference betwe…
Background: Measurements of neutron radii provide important constraints on the isovector sector of nuclear density functionals and offer vital guidance in areas as diverse as atomic parity violation, heavy-ion collisions, and neutron-star structure. Purpose: To assess the impact of spin-orbit currents on the electromagnetic- and weak-charge radii of a variety of nuclei. Special emphasis is placed on the experimentally accessible electroweak skin, defined as the difference between weak-charge and electromagnetic-charge radii. Methods: Two accurately calibrated relativistic mean field models are…
A review of current neutron star masses and radius measurements is given and the resulting constraints on modern equation of states for nuclear matter. Phase transitions in particular to quark matter is discussed and the novel color superconducting mixed phases.
The nuclear root-mean-square charge radius of $^{54}$Ni was determined with collinear laser spectroscopy to be $R(^{54}$Ni) = 3.737\,(3)~fm. In conjunction with the known radius of the mirror nucleus $^{54}$Fe, the difference of the charge radii was extracted as $ΔR_{\rm ch}$ = 0.049\,(4)~fm. Based on the correlation between $ΔR_{\rm ch}$ and the slope of the symmetry energy at nuclear saturation density ($L$), we deduced $20 \le L \le 70$\,MeV. The present result is consistent with the $L$ from the binary neutron star merger GW170817, favoring a soft neutron matter EOS, and barely consistent …
Radii of charge and neutron distributions are fundamental nuclear properties. They depend on both nuclear interaction parameters related to the equation of state of infinite nuclear matter and on quantal shell effects, which are strongly impacted by the presence of nuclear surface. In this work, by studying the dependence of charge and neutron radii, and neutron skin, on nuclear matter parameters, we assess different mechanisms that drive nuclear sizes. We apply nuclear density functional theory using a family of Skyrme functionals obtained by means of different optimization protocols targetin…
The analysis of self-consistency and proton-neutron interaction effects in the buildup of differential charge radii has been carried out in covariant density functional theoretical calculations without pairing interaction. Two configurations of the $^{218}$Pb nucleus, generated by the occupation of the neutron $1i_{11/2}$ and $2g_{9/2}$ subshells, are compared with the ground state configuration in $^{208}$Pb. The interaction of added neutron(s) and the protons forming the $Z=82$ proton core is responsible for a major contribution to the buildup of differential charge radii. It depends on the …
The existence of neutron stars with $2M_\odot$ requires the strong stiffness of the equation of state (EoS) of neutron-star matter. We introduce a multi-pomeron exchange potential (MPP) working universally among 3- and 4-baryons to stiffen the EoS. Its strength is restricted by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The EoSs are derived using the Brueckner-Hartree-Fock (BHF) and the cluster variational method (CVM) with the nuclear interactions ESC and AV18. The mass-radius relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV) equation, where…
We studied the charge radius ($r_{c}$), neutron radius ($r_n$), and neutron skin-thickness ($Δr=r_n-r_p$) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) with effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement are noted. We additionally assessed the two-neutron separation energy ($S_{2n}$) to mark the drip line nuclei of the considered isotopic s…
The pion mass dependence of hyperon electromagnetic properties is determined using two-flavor heavy baryon chiral perturbation theory. Specifically we compute chiral corrections to the charge radii, magnetic moments, and magnetic radii of the spin one-half hyperons, as well as the charge radii, magnetic moments, magnetic radii, electric quadrupole moments, and quadrupole radii of the spin three-half hyperons. Results for the nucleon and delta are also included. Efficacy of the two-flavor theory is investigated by analyzing the role played by virtual kaons. For the electromagnetic properties of…
We study the properties of neutron star using the chiral quark-meson coupling model, in which the quark-quark hyperfine interaction due to the exchanges of gluon and pion based on chiral symmetry is considered. We also examine the effects of hyperons and $Δ$-isobars in a neutron star. Extending the SU(6) spin-flavor symmetry to more general SU(3) flavor symmetry in the vector-meson couplings to baryons, the maximum mass of neutron star can reach the recently observed, massive pulsar mass, $1.97 \pm 0.04 M_{\odot}$. In this calculation, $Λ$ and $Ξ$ are generated in a neutron star, while $Σ$ and…
Electromagnetic mean squared radii of Lambda(1405) are evaluated in chiral unitary approach. In this approach we regard Lambda(1405) as dynamically generated resonances in the octet meson and octet baryon scattering, and also as KbarN bound state. Especially for the Lambda(1405) as KbarN bound state we obtain negative electric mean squared radius. With the small binding energy of Lambda(1405) in the chiral unitary approach, our results imply that Lambda(1405) has structure that K^- is widely spread around p.
The root mean square radii of the proton density distribution in $^{16-24}$O derived from measurements of charge changing cross sections with a carbon target at $\sim$900$A$ MeV together with the matter radii portray thick neutron skin for $^{22 - 24}$O despite $^{22,24}$O being doubly magic. Imprints of the shell closures at $N$ = 14 and 16 are reflected in local minima of their proton radii that provide evidence for the tensor interaction causing them. The radii agree with it ab initio calculations employing the chiral NNLO$_{\mathrm{sat}}$ interaction, though skin thickness predictions are …
Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond puls…
A new relation between the neutron skin of a heavy nucleus and the radius of a neutron star is proposed: the larger the neutron skin of the nucleus the larger the radius of the star. Relativistic models that reproduce a variety of ground-state observables can not determine uniquely the neutron skin of a heavy nucleus. Thus, a large range of neutron skins is generated by supplementing the models with nonlinear couplings between isoscalar and isovector mesons. We illustrate how the correlation between the neutron skin and the radius of the star can be used to place important constraints on the e…
The symmetry energy in nuclei is studied using a monopole-monopole two boby interaction which has an isospin dependent term. A Hartree theory is developed for this interaction which has an oscillator shell model basis with corresponding shell structure. The role of shell structure on the symmetry energy is then studied. We also find that the strength of the Heisenberg interaction is very important for understanding the difference between proton and neutron radii and features associated with halo nuclei. PACS numbers: 21.10.Sf, 21.65Cd, 21.65Ef
The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star's size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observat…
The ground-state properties of neutron-rich exotic Na and Mg isotopes with even numbers of neutrons, N, are studied up to driplines. The shell-model calculations with an ab initio effective nucleon-nucleon interaction reported in [Tsunoda, Otsuka, Takayanagi et al., Nature 587, 66 (2020)] are extended to observables such as magnetic dipole and electric quadrupole moments, and charge and matter radii. Good agreements with experimental data are found, and predictions are shown up to driplines. A prescription to extract the deformation parameters for the eigenstates of Monte Carlo Shell Model is …
Proton radii of $^{12-19}$C densities derived from first accurate charge changing cross section measurements at 900$A$ MeV with a carbon target are reported. A thick neutron surface evolves from $\sim$ 0.5 fm in $^{15}$C to $\sim$ 1 fm in $^{19}$C. The halo radius in $^{19}$C is found to be 6.4$\pm$0.7 fm as large as $^{11}$Li. Ab initio calculations based on chiral nucleon-nucleon and three-nucleon forces reproduce well the radii.
We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing 2$M_\odot$ neutron stars. Unified EoSs for the inner-crust-core region have been built for all the phenomenological models, both relativistic and non-relativistic. Our inve…
We calculate the properties of neutron matter and highlight the physics of chiral three-nucleon forces. For neutrons, only the long-range 2 pi-exchange interactions of the leading chiral three-nucleon forces contribute, and we derive density-dependent two-body interactions by summing the third particle over occupied states in the Fermi sea. Our results for the energy suggest that neutron matter is perturbative at nuclear densities. We study in detail the theoretical uncertainties of the neutron matter energy, provide constraints for the symmetry energy and its density dependence, and explore t…
We propose to use antiprotons to investigate the sizes of stable and neutron-rich exotic nuclei by measurements of the $\pbar A$ absorption cross section along isotopic chains in inverse kinematics. The expected effects are studied theoretically in a microscopic model. The $\pbar U$ optical potentials are obtained by folding free space $\pbar N$ scattering amplitudes with HFB ground state densities and solving the scattering equations by direct integration. The mass dependence of absorption cross sections is found to follow closely the nuclear root-mean-square radii. The total absorption cross…
It is a consequence of QCD's spontaneously broken chiral symmetry that the response of the neutron to long wavelength probes will be driven by excitation of its pion cloud. In this article I discuss manifestations of this in electromagnetic form factors and Compton scattering. Particular attention is given to the interplay between this physics and shorter-distance components of the neutron's electromagnetic structure.
Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain "magic" numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly-magic features are known in 40,48Ca, and recently suggested in two radioactive isotopes, 52,54Ca. Although many properties of experimentally known Ca isotopes have been successfully described by nuclear theory, it is still a challenge to predict their charge radii evolution. Here we present the first measurements of the charge radii of 49,51,52Ca, obtained from laser spectrosc…
We discuss the possibility to extract the neutron-neutron scattering length a_{nn} from experimental spectra on the reaction gamma d --> pi^+ nn. The transition operator is calculated to high accuracy from chiral perturbation theory. We argue that for properly chosen kinematics, the theoretical uncertainty of the method can be as low as 0.1 fm.
The self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique in the coordinate space is developed to investigate odd-$A$ nuclei by incorporating the blocking effect. In a calculation performed with the SLy4 parameter for the neutron-rich Mg isotopes with $A=36-42$ around the neutron shell closure N=28, the odd-even staggering in the neutron rms radius, i.e., a larger value in $^{39}$Mg than those in $^{38}$Mg and $^{40}$Mg, is found. The large neutron radius in $^{39}$Mg is due to the blocking effect on the pair correlation energy, for which th…
The electric mean squared radii <r^2>_E of Lambda(1405) are calculated in the chiral unitary model. We describe the Lambda(1405) as a dynamically generated resonance fully in the octet meson and octet baryon scattering. We also consider ``Lambda(1405)'' as a bound state of KbarN. For the later ``Lambda(1405),'' we obtain negative and larger absolute value of electric mean squared radius than that of ordinary baryons, which implies that Lambda(1405) have structure of widely spread K^- around p.
Applications of the chiral expansion to generalize the Gerasimov-Drell-Hearn sum rule for finite $Q^2$ are discussed. The observation of several authors that the corrections to the leading order contributions are large and limit the applicability to a very small range in $Q^2$, are valid when considering the sum rule for protons and neutrons, separately. When using the proton-neutron difference, the chiral expansion may be valid to considerably higher momentum transfers where hadronic degrees of freedom at large distances may connect up with quark and gluon degrees of freedom. This could mark …
Neutron matter presents a unique system in chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We discuss perturbative and first Quantum Monte Carlo (QMC) calculations of neutron matter with chiral EFT interactions and their astrophysical impact for the equation of state and neutron stars.
An isovector-scalar meson is incorporated self-consistently into the quark-meson coupling description of nuclear matter and its most prominent effects on the structure of neutron stars are investigated. The recent measurement of GW170817 is used to constrain the strength of the isovector-scalar channel. With the imminent measurements of the neutron star radii in the NICER mission it is particularly notable that the inclusion of the isovector-scalar force has a significant impact. Indeed, the effect of this interaction on the neutron star radii and masses is larger than the uncertainties introd…
A set of theoretical mass-radius relations for rigidly rotating neutron stars with exotic cores, obtained in various theories of dense matter, is reviewed. Two basic observational constraints are used: the largest measured rotation frequency (716 Hz) and the maximum measured mass ($2\;M_\odot$). Present status of measuring the radii of neutron stars is described. The theory of rigidly rotating stars in general relativity is reviewed and limitations of the slow rotation approximation are pointed out. Mass-radius relations for rotating neutron stars with hyperon and quark cores are illustrated u…
The electromagnetic mean squared radii, <r^2>_E and <r^2>_M, of Lambda(1405) are calculated in the chiral unitary model. We describe the excited baryons as dynamically generated resonances in the octet meson and octet baryon scattering. We evaluate values of <r^2>_E and <r^2>_M for the Lambda(1405) on the resonance pole and obtain their complex values. We also consider Lambda(1405) obtained by neglecting decay channels. For the latter case, we obtain negative and larger absolute electric mean squared radius than that of typical ground state baryons. This implies that Lambda(1405) has structure…
