We review a variety of theoretical and experimental investigations aimed at improving our knowledge of the nuclear matter equation of state. Of particular interest are nuclear matter extreme states in terms of density and/or isospin asymmetry. The equation of state of matter with unequal concentrations of protons and neutrons has numerous applications. These include heavy-ion collisions, the physics of rare, short-lived nuclei and, on a dramatically different scale, the physics of neutron stars. The "common denominator" among these (seemingly) very different systems is the symmetry energy, which plays a crucial role in both the formation of the neutron skin in neutron-rich nuclei and the radius of a neutron star (a system 18 orders of magnitude larger and 55 orders of magnitude heavier). The details of the density dependence of the symmetry energy are not yet sufficiently constrained. Throughout this article, our emphasis will be on the importance of adopting a microscopic approach to the many-body problem, which we believe to be the one with true predictive power.
We calculate several neutron star properties, for static and/or rotating stars, using equations of state based on different microscopic models. These include our Dirac-Brueckner-Hartree-Fock model and others derived from the non-relativistic Brueckner-Hartree-Fock approach implemented with microscopic three-body forces. The model dependence is discussed.
This paper presents an analysis of neutron skins based on fully microscopic equations of state, including chiral two- and three-nucleon forces consistently at N3LO. Other theoretical predictions and recent constraints are also addressed, such as those from the PREX II experiment and the latest parity-violating electron scattering measurement of the 27Al neutron skin.
The past two decades have witnessed tremendous progress in the microscopic description of atomic nuclei. The Topical Review `The Future of Nuclear Structure' aims at summarizing the current state-of-the-art microscopic calculations in Nuclear Theory and to give a useful reference for young researches who wish to learn more about this exciting discipline.
A fully antisymmetrized microscopic model is developed for light two-neutron halo nuclei using a hyper-spherical basis to describe halo regions. The many-body wavefunction is optimized variationally. The model is applied to 6He bound by semi realistic Minnesota nucleon-nucleon forces. The two-neutron separation energy and the radius of the halo are reproduced in agreement with experiment. Antisymmetrization effects between 4He and halo neutrons are found to be crucial for binding of 6He. We also properly extract two-neutron overlap functions and find that there is a significant increase of 30%…
Two-neutron densities obtained from microscopic wave functions of $^6$He and $^8$He are investigated to reveal di-neutron correlations. In particular, the comparison of the two-neutron density with the product of one-neutron densities is useful for a quantitative discussion of di-neutron correlations. The calculations show that the S=0 spatial two-neutron correlation increases at the surface of $^6$He$(0^+_1)$ and $^8$He$(0^+_2)$. The enhancement is remarkable in the $^6$He$(0^+_1)$ ground state but not as prominent in the $^8$He$(0^+_1)$ ground state. Configuration mixing of many Slater deter…
The microscopic coupled-channel calculation of inelastic proton scattering is performed for the study of neutron excitations in $2^+_1$ states of $^{18}$O, $^{10}$Be, $^{12}$Be, and $^{16}$C. Proton-nucleus potentials in the coupled-channel calculation are microscopically derived by folding the Melbourne $g$-matrix $NN$ interaction with matter and transition densities of target nuclei obtained by the structure model calculation of antisymmetrized molecular dynamics. The calculated result reasonably reproduces the elastic and inelastic proton scattering cross sections, and supports the dominant…
The neutron emission rates in thermal excited nuclei are conventionally described by statistical models with a phenomenological level density parameter that depends on excitation energies, deformations and mass regions. In the microscopic view of hot nuclei, the neutron emission rates can be determined by the external neutron gas densities without any free parameters. Therefore the microscopic description of thermal neutron emissions is desirable that can impact several understandings such as survival probabilities of superheavy compound nuclei and neutron emissivity in reactors. To describe t…
We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of sign-problems for seniority-conserving nuclear interactions. This technique allows a microscopic calculation of angular momentum and parity projected nuclear level densities. We present results for the $^{55}$Fe, $^{56}$Fe and $^{57}$Fe isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density.
The two--neutron separation energy of $^6$He has been reproduced for the first time in a realistic parameter--free microscopic multicluster model comprising the $α+n+n$ and $t+t$ clusterizations, with $α$ cluster breathing excitations included. The contribution of the $t+t$ channel is substantial. A very thick (0.85 fm) neutron halo has been found in full agreement with the results of the latest phenomenological analysis.
The screening potential in the $^1S_0$ and $^3S_1$ pairing channels in neutron and nuclear matter in different approximations is discussed. It is found that the vertex corrections to the potential are much stronger in nuclear matter than in neutron matter.
A microscopic nuclear equation of state compatible with all current astrophysical constraints constructed within the Brueckner-Hartree-Fock formalism is presented and extended in a consistent way to finite temperature. The effects of finite temperature on the properties of neutron stars are studied in detail and a universal relation regarding stellar stability is proposed.
A microscopic calculation of the equation of state for asymmetric nuclear matter is presented. We employ realistic nucleon-nucleon forces and operate within the Dirac-Brueckner-Hartree-Fock approach to nuclear matter. The focal point of this paper is a (momentum-space) G-matrix which properly accounts for the asymmetry between protons and neutrons. This will merge naturally into the development of an effective interaction suitable for applications to asymmetric nuclei, which will be the object of extensive study in the future.
We investigate the structure of the neutron-rich $Λ$-hypernucleus $_Λ^{10}$Li by using microscopic shell-model calculations considering a $Λ$-$Σ$ coupling effect. The calculated $Σ$-mixing probability in the $_Λ^{10}$Li ground state is found to be about 0.34 % which is coherently enhanced by the $Λ$-$Σ$ coupling configurations, leading to the energy shift 0.28 MeV which is about 3 times larger than that in $_Λ^{7}$Li. The importance of the $Σ$ configuration obtained by the $ΣN$ interaction and the potentiality of the neutron-rich environment are discussed.
The microscopic role of nuclear magnetism in rotating frame is investigated for the first time in the framework of the cranked relativistic mean field theory. It is shown that nuclear magnetism modifies the expectation values of single-particle spin, orbital and total angular momenta along the rotational axis effectively creating additional angular momentum. This effect leads to the increase of kinematic and dynamic moments of inertia at given rotational frequency and has an impact on effective alignments.
We report on shell-model calculations employing effective interactions derived from a new realistic nucleon-nucleon (NN) potential based on chiral effective field theory. We present results for 18O, 134Te, and 210Po. Our results are in excellent agreement with experiment indicating a remarkable predictive power of the chiral NN potential for low-energy microscopic nuclear structure.
We report on the spin.dependent neutron scattering length on 3He from a microscopic calculation of p-3H, n-3He, and d-2H scattering employing the Argonne v18 nucleon-nucleon potential with and without additional three-nucleon force. The results and that of a comprehensive R-matrix analysis are compared to a recent measurement. The overall agreement for the scattering lengths is quite good. The imaginary parts of the scattering lengths are very sensitive to the inclusion of three-nucleon forces, whereas the real parts are almost insensitive.
We discuss the results of calculations of the shear viscosity and thermal conductivity of pure neutron matter, carried out within the Landau-Abrikosov-Khalatnikov formalism. The probability of neutron-neutron collisions in the nuclear medium has been obtained from a realistic potential, using both the correlated basis function and the $G$-matrix approach. The results of our work indicate that medium modifications of nucleon-nucleon scattering are large, their inclusion leading to a dramatic enhancement of the transport coefficients. On the other hand, the results obtained from the two theoreti…
We studied in a microscopic multiphonon approach the proton-neutron symmetry and phonon structure of some low-lying states recently discovered in 92Zr. We confirm the breaking of F-spin symmetry, but argue that the breaking mechanism is more complex than the one suggested in the original shell model analysis of the data. We found other new intriguing features of the spectrum, like a pronounced multiphonon fragmentation of the states and a tentative evidence of a three-phonon mixed symmetry state.
We derive a T-violating P-conserving optical potential for neutron-nucleus scattering, starting from a uniquely determined two-body $ρ$-exchange interaction with the same symmetry. We then obtain limits on the T-violating $ρ$-nucleon coupling $\overline{g}_ρ$ from neutron-transmission experiments in $^{165}$Ho. The limits may soon compete with those from measurements of atomic electric-dipole moments.
The neutron halo structure of $^{6}$He and of $^{8}$He is studied in a microscopic three-body and five-body model, respectively. Various cluster arrangements are included to embody a variety of correlations between the clusters. The intercluster wave function is determined with the stochastic variational method. The $^{6}$He and $^{8}$He energies are reproduced with the same effective force very well. The radii and densities are compared with the results of empirical analyses. The calculated difference of the neutron and proton radii exceeds 0.8 fm, confirming the thick neutron skin. The two-n…
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.
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 properties of spin polarized neutron matter are studied both at zero and finite temperature within the framework of the Brueckner--Hartree--Fock formalism, using the Argonne v18 nucleon-nucleon interaction. The free energy, energy and entropy per particle are calculated for several values of the spin polarization, densities and temperatures together with the magnetic susceptibility of the system. The results show no indication of a ferromagnetic transition at any density and temperature.
Our understanding of nuclear fission, a fundamental nuclear decay, is still incomplete due to the complexity of the process. In this paper, we describe a study of spontaneous fission using the symmetry-unrestricted nuclear density functional theory. Our results show that the observed bimodal fission can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. We also predict a new phenomenon of trimodal spontaneous fission for some rutherfordium, seaborgium, and hassium isotopes.
We investigate how the neutron drip line is related to the density dependence of the symmetry energy, by using a macroscopic nuclear model that allows us to calculate nuclear masses in a way dependent on the equation of state of asymmetric nuclear matter. The neutron drip line obtained from these masses is shown to appreciably shift to a neutron-rich side in a nuclear chart as the density derivative of the symmetry energy increases. Such shift is clearly seen for light nuclei, a feature coming mainly from the surface property of neutron-rich nuclei.
An updated and improved version of the effective interaction based on the Argonne\textendash Urbana nuclear Hamiltonian\textemdash derived using the formalism of Correlated Basis Functions (CBF) and the cluster expansion technique\textemdash is employed to obtain a number of properties of cold nuclear matter at arbitrary neutron excess within the formalism of many-body perturbation theory. The numerical results\textemdash including the ground-state energy per nucleon, the symmetry energy, the pressure, the compressibility, and the single-particle spectrum\textemdash are discussed in the contex…
We explore the use of mean field models to approximate microscopic nuclear equations of state derived from chiral effective field theory across the densities and temperatures relevant for simu- lating astrophysical phenomena such as core-collapse supernovae and binary neutron star mergers. We consider both relativistic mean field theory with scalar and vector meson exchange as well as energy density functionals based on Skyrme phenomenology and compare to thermodynamic equa- tions of state derived from chiral two- and three-nucleon forces in many-body perturbation theory. Quantum Monte Carlo s…
Motivated by the newly observed $^{39}$Na in experiments, systematic calculations of global nuclear binding energies with seven Skyrme forces are performed. We demonstrate the strong correlation between the two-neutron separation energies ($S_{2n}$) of $^{39}$Na and the total number of bound nuclei of the whole nuclear landscape. Furthermore, with calculated nuclear masses, we perform astrophysical rapid-neutron capture process ($r$-process) simulations by using nuclear reaction code TALYS and nuclear reaction network code SkyNet. $r$-process abundances from ejecta of neutron star mergers and …
After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue th…
Extrapolations from nuclei to neutron stars hinge on the symmetry term in nuclear binding formulas. The term describes reduction in the binding associated with neutron-proton (np) imbalance. Regrettably, binding formulas in the literature commonly lack an intrinsic consistency with regard to the symmetry term. Our elementary considerations determine the universal macroscopic limit for the term and predict its weakening in light nuclei due to emergence of the nuclear asymmetry-skin. Experimental systematic of isobaric-analogue states allows for a determination of the volume and surface coeffici…
We discuss the one-body potentials for protons and neutrons obtained from Dirac-Brueckner-Hartree-Fock calculations of neutron-rich matter, in particular their dependence upon the degree of proton/neutron asymmetry. The closely related symmetry potential is compared with empirical information from the isovector component of the nuclear optical potential.
Ab initio gap equation for ^1S_0 pairing in a nuclear slab is solved for the Argonne v18 NN-potential. The gap function is compared in detail with the one found previously for the separable form of the Paris potential. The difference between the two gaps turned out to be about 10%. Dependence of the gap on the chemical potential mu is analyzed.
The symmetry energy for nuclear matter and its relation to the neutron skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.
Neutron stars are the most dense objects in the observable Universe and conventionally one uses nuclear theory to obtain the equation of state (EOS) of dense hadronic matter and the global properties of these stars. In this work, we review various aspects of nuclear matter within an effective Chiral model and interlink fundamental quantities both from nuclear saturation as well as vacuum properties and correlate it with the star properties.
The recent extensions of the covariant energy density functional theory with the quasiparticle-vibration coupling (QVC) are reviewed. Formulation of the Quasiparticle Random Phase Approximation (QRPA) in the relativistic framework is discussed. Self-consistent extensions of the relativistic QRPA imply the QVC which is implemented in two-body propagators in the nuclear medium. This provides fragmentation of the QRPA states describing the damping of the vibrational motion.
The pervasive role of the nuclear symmetry energy in establishing some nuclear static and dynamical properties, and in governing some attributes of neutron star properties is highlighted.
The theory of nuclear forces has made great progress since the turn of the millenium using the framework of chiral effective field theory (ChEFT). The advantage of this approach, which was originally proposed by Weinberg, is that it has a firm basis in quantum-chromodynamics and allows for quantitative calculations. Moreover, this theory generates two-nucleon forces (2NF) and many-body forces on an equal footing and provides an explanation for the empirically known fact that 2NF >> 3NF >> 4NF. I will present the recent advances in more detail and put them into historical context. In addition, …
We discuss a microscopic framework for phenomenological boson-fermion models of nuclear structure based on the U($n/m$) type of superalgebras. The generalized Dyson mapping of fermion collective superalgebras provides a basis to do so and to understand how collectivity selects the required preservation of boson plus fermion number as a good quantum number. We also consider the difference between dynamical and invariant supersymmetries based on possible supermultiplets of spectra of neighboring odd and even nuclei. We point out that different criteria exist for choosing the appropriate single p…
Collective inertial mass coefficients with respect to translational, relative, and rotational motions are microscopically calculated, along the collective reaction path self-consistently determined, based on the adiabatic self-consistent collective coordinate (ASCC) method. The impact of the time-odd component of the mean-field potential on the inertial masses are investigated. The results are compared with those calculated with the cranking formulae. The inertial masses based on the ASCC method reproduce the exact total nuclear mass for the translational motion as well as the exact reduced ma…
In neutron star crust, non-uniform structure of nuclear matter is expected, which is called the "pasta" structure. From the recent studies of giant flares in magnetars, these structures might be related to some observables and physical quantities of the neutron star crust. To investigate the above quantities, we numerically explore the pasta structures with a fully threedimensional geometry and study the properties of low-density nuclear matter, based on the relativistic mean-field model and the Thomas-Fermi approximation. We observe typical pasta structures for fixed proton number-fraction an…
The wobbling excitations of the triaxial superdeformed (TSD) bands in the Lu and Hf region are studied by the microscopic framework of the cranked mean-field and the random-phase approximation (RPA). In contrast to the previous works, where the Nilsson potential was used, the more realistic Woods-Saxon potential is employed as a nuclear mean-field. The wobbling-like RPA solutions have been found systematically in the nuclei studied and their characteristic properties are investigated in details. This confirms the wobbling phonon excitations in TSD nuclei from the microscopic calculations. The …
Nuclear level density (NLD) and radiative strength function (RSF) are described simultaneously within a microscopic approach, which takes into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for $^{170, 171, 172}$Yb isotopes shows the importance of exact thermal pairing in the description of NLD at low and intermediate excitation energies and invalidates the assumption based on the Brink-Axel hypothesis in the description of …
It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003)) that the widths of narrow proton resonances are related to neutron Asymptotic Normalization Coefficients (ANCs) of their bound mirror analogs because of charge symmetry of nucleon-nucleon interactions. This relation is approximated by a simple analytical formula which involves proton resonance energies, neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. In the present paper, we perform microscopic-cluster model calculations for the ratio of proton widt…
The relativistic mean-field framework, extended to include correlations related to restoration of broken symmetries and to fluctuations of the quadrupole deformation, is applied to a study of shape transitions in Nd isotopes. It is demonstrated that the microscopic self-consistent approach, based on global effective interactions, can describe not only general features of transitions between spherical and deformed nuclei, but also the singular properties of excitation spectra and transition rates at the critical point of quantum shape phase transition.
We evaluate the performance of modern nuclear energy density functionals for predicting inner and outer fission barrier heights and energies of fission isomers of even-even actinides. For isomer energies and outer barrier heights, we find that the self-consistent theory at the HFB level is capable of providing quantitative agreement with empirical data.
The understanding of the interaction of nucleons in nuclear and neutron-rich matter at non-zero temperature is important for a variety of applications ranging from heavy-ion collisions to nuclear astrophysics. In this paper we apply the Dirac-Brueckner-Hartree-Fock method along with the Bonn B nucleon-nucleon potential to predict single-particle properties in symmetric nuclear matter and pure neutron matter at finite temperature. It is found that temperature effects are generally small but can be significant at low density and momentum.
Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.
The microscopic approach of fission rates and neutron emission rates in compound nuclei have been applied to $^{258}$No and $^{286}$Cn. The microscopic framework is based on the finite-temperature Skyrme-Hartree-Fock+BCS calculations, in which the fission barriers and mass parameters are self-consistently temperature dependent. The fission rates from low to high temperatures can be obtained based on the imaginary free energy method. The neutron emission rates are obtained with neutron gases at surfaces. Finally the survival probabilities of superheavy nuclei can be calculated microscopically. …
Correlated Basis Function (CBF) perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a nuclear Hamiltonian strongly constrained by phenomenology. We report the results of a study of the superfluid gap in pure neutron matter, associated with the formation of Cooper pairs in the $^1S_0$ channel. The calculations have been carried out using an improved version of the CBF effective interaction, in which three-nucleon forces are taken into account using a microscopic model. Our results show that a non-vanishing superfluid ga…
Nuclear and neutron matters are investigated in the low density region, well below the nuclear saturation density. Microscopic calculations, based on the Bethe-Brueckner approach with a few realistic nucleon-nucleon potentials, are compared with the predictions of a set of phenomenological effective interactions, mostly employed in nuclear structure studies. An energy functional is constructed on the basis of the microscopic bulk EoS and applied to a selection of nuclei throughout the mass table. The results provide a microscopic basis for a link between nuclear surface behaviour and neutron E…
Microscopic signatures of nuclear ground-state shape phase transitions in Nd isotopes are studied using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. As a function of the physical control parameter -- the number of nucleons, energy gaps between the ground state and the excited vibrational states with zero angular momentum, isomer shifts, and monopole tran…
Nuclear capture of antiprotons from atomic states is studied. Partial widths for single nucleon capture events leading to cold residual nuclei are calculated. Recent CERN experiments that compare the neutron and proton captures are analysed. Nuclear density distributions at extreme nuclear surface are calculated and tested against the experimental results.
We carry out the microscopic calculations of the atomic EDM in deuterium, Xe and Hg atomic systems. Due to Schiff's theorem, we obtain the atomic EDM only from the finite nuclear size effects, but it is found that the atomic EDM is appreciably larger than expected. This is essentially due to the new mechanism in which the nuclear excitations are taken into account while atomic states stay in the ground state. The EDM of deuterium is found to be $d_D \simeq 0.017 d_n$ while the EDM of Xe and Hg become $d_{\rm Xe} \simeq 1.6 d_n$ and $d_{\rm Hg} \simeq -2.8 d_n$, respectively. It turns out that …
We investigate the properties of isospin-symmetric nuclear matter and neutron stars in a chiral model approach adopting the SU(2) parity doublet formulation. This ansatz explicitly incorporates chiral symmetry restoration with the limit of degenerate masses of the nucleons and their parity partners. Instead of searching for an optimized parameter set we explore the general parameter dependence of nuclear matter and star properties in the model. We are able to get a good description of ground state nuclear matter as well as large values of mass for neutron stars in agreement with observation.
