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%-70% in their normalization due to microscopic effects as compared to the results of three-body models.
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.
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…
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.
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.
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…
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.
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, whi…
The nuclear structure dependence of direct reactions that remove a pair of like or unlike nucleons from a fast $^{12}$C projectile beam are considered. Specifically, we study the differences in the two-nucleon correlations present and the predicted removal cross sections when using $p$-shell shell-model and multi-$\hbarω$ no-core shell-model (NCSM) descriptions of the two-nucleon overlaps for the transitions to the mass $A$=10 projectile residues. The NCSM calculations use modern chiral two-nucleon and three-nucleon (NN+3N) interactions. The $np$-removal cross sections to low-lying $T$=0, $^{1…
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 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…
In this work, we introduce a new method to reduce the microscopic mean-field theory to a classical macroscopic dynamics during the initial stage of fusion reactions. We show that TDHF (Time-dependent Hartree-Fock) could be a useful tool to gain information on fusion barriers as well as on one-body dissipation effects. We apply the mean-field theory to the case of head-on reaction between $^{16}$O and $^{16,22,24,28}$O in order to quantify the effect of neutron skin on fusion. We show that the determination of fusion barrier requires, in addition to a precise knowledge of the relative distance …
We study the effects of the phonon-phonon coupling on the low-energy electric dipole response within a microscopic model based on an effective Skyrme interaction. The finite rank separable approach for the quasiparticle random phase approximation is used. Choosing as an example the isotopic chain of Calcium, we show the ability of the method to describe the low-energy $E1$ strength distribution. With one and the same set of parameters we describe available experimental data for $^{48}$Ca and predict the electric dipole strength function for $^{50}$Ca.
The microscopic structure of an isolated vortex line in superfluid neutron star matter is studied by solving the Bogoliubov-de Gennes equations. Our calculation, which is the starting point for a microscopic calculation of pinning forces in neutron stars, shows that the size of the vortex core varies differently with density, and is in general smaller than assumed in some earlier calculations of vortex pinning in neutron star crusts. The implications of this result are discussed
The competition between the isovector (T=1) and isoscalar (T=0) proton-neutron ($p-n$) correlations in $N=Z$ nuclei is investigated by calculating their correlation energies with a realistic effective interaction which reproduces observed nuclear properties very well, in a strict shell model treatment. It is shown in the realistic shell model that the double-differences of binding energies $(B(A+pn:T) + B(A) - B(A+p) - B(A+n))$ ($B(A)$ being the binding energy) are good indicators of the T=1 and T=0 $p-n$ correlations. Each of them, however, originates in plural kinds of correlations with T=1 …
Quadrupole and octupole deformation energy surfaces, low-energy excitation spectra, and electric transition rates in eight neutron-rich isotopic chains -- Ra, Th, U, Pu, Cm, Cf, Fm, and No -- are systematically analyzed using a quadrupole-octupole collective Hamiltonian model, with parameters determined by constrained reflection-asymmetric and axially-symmetric relativistic mean-field calculations based on the PC-PK1 energy density functional. The theoretical results of low-lying negative-parity bands, odd-even staggering, average octupole deformations $\langleβ_3\rangle$, and $B(E3; 3^-_1\to …
We model neutron star cooling with several microscopic nuclear equations of state based on different nucleon-nucleon interactions and three-body forces, and compatible with the recent GW170817 neutron star merger event. They all feature strong direct Urca processes. We find that all models are able to describe well the current set of cooling data for isolated neutron stars, provided that large and extended proton 1S0 gaps and no neutron 3PF2 gaps are active in the stellar matter. We then analyze the neutron star mass distributions predicted by the different models and single out the preferred …
The microscopic description of neutron scattering by $^{16}$O below 30 MeV is carried out by means of the continuum particle-vibration coupling (cPVC) method with the Skyrme nucleon-nucleon ($NN$) effective interaction. In the cPVC method, a proper boundary condition on a nucleon in continuum states is imposed, which enables one to evaluate the transition matrix in a straightforward manner. Experimental data of the total and total-elastic cross sections are reproduced quite well by the cPVC method. An important feature of the result is the fragmentation of the single-particle resonance into ma…
Modelling fission with microscopic input: excitation-energy-dependent fission paths for neutron-induced reactions
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔天文与天体物理研究所，布鲁塞尔自由大学）；Brussels Laboratory of the Universe - BLU-ULB（宇宙布鲁塞尔实验室）
Mean field calculations, based on the D1S, D1N and D1M parametrizations of the Gogny energy density functional, have been carried out to obtain the potential energy surfaces relevant to fission in several Ra isotopes with the neutron number 144 $\le$ N $\le$ 176. Inner and outer barrier heights as well as first and second isomer excitation energies are given. The existence of a well developed third minimum along the fission paths of Ra nuclei, is analyzed in terms of the energetics of the "fragments" defining such elongated configuration. The masses and charges of the fission fragments are stu…
The heavy-ion fusion reactions induced by neutron-rich nuclei are investigated with the improved quantum molecular dynamics (ImQMD) model. With a subtle consideration of the neutron skin thickness of nuclei and the symmetry potential, the stability of nuclei and the fusion excitation functions of heavy-ion fusion reactions $^{16}$O+$^{76}$Ge, $^{16}$O+$^{154}$Sm, $^{40}$Ca+$^{96}$Zr and $^{132}$Sn+$^{40}$Ca are systematically studied. The fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD model. The corresponding slope para…
We calculate the neutrino mean free path and the Equation of State of pure neutron matter at finite temperature within a selfconsistent scheme based on the Brueckner--Hartree--Fock approximation. We employ the nucleon-nucleon part of the recent realistic baryon-baryon interaction (model NSC97e) constructed by the Nijmegen group. The temperatures considered range from 10 to 80 MeV. We report on the calculation of the mean field, the residual interaction and the neutrino mean free path including short and long range correlations given by the Brueckner--Hartree--Fock plus Random Phase Approximati…
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…
We model the cooling of hybrid neutron stars combining a microscopic nuclear equation of state in the Brueckner-Hartree-Fock approach with different quark models. We then analyze the neutron star cooling curves predicted by the different models and single out the preferred ones. We find that the possibility of neutron p-wave pairing can be excluded in our scenario.
Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry based models. Ground-state, gamma and beta-bands, and their B(E2) transition strengths in 160-168Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q.Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered whose free parameters, fixed for all members of the chain are used to fine tune the momen…
Microscopic optical potentials for nucleon-nucleus (NA) scattering obtained from the full folding of the effective g matrices, solutions of the Bruckner-Bethe-Goldstone equation, with the densities of the target, are applied to the case of neutron-nucleus scattering. Given that the optical potentials are specified in all two-body angular momentum, spin and isospin channels available to the NA scattering, the only difference in this model description of proton and neutron scattering observables for a given nucleus is in the inclusion of the Coulomb interaction. A priori microscopic optical mode…
The interplay between quadrupole and octupole degrees of freedom is discussed in a series of neutron-rich actinides and superheavy nuclei with $92 \le$ Z $\le 110$ and $186 \le$ N $\le 202$. In addition to the static Hartree-Fock-Bogoliubov approach, dynamical beyond-mean-field correlations are taken into account via both parity restoration and symmetry-conserving Generator Coordinate Method calculations based on the Gogny-D1M energy density functional. Physical properties such as correlation energies, negative-parity excitation energies as well as reduced transition probabilities $B(E1)$ and …
We calculate neutron star's moment of inertia and deformabilities using various microscopic equations of state for nuclear and hybrid star configurations. Correlations between the various observables are examined and we confirm several universal relations. We focus in particular on the constraints for the neutron star radii imposed by a determination of the average tidal deformability of the binary neutron star system GW170817. We find compatible radii between 12 and 13 kilometers and identify the suitable equations of state.
We calculate the mean free path of protons and neutrons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. Those are obtained from calculations of the G-matrix including relativistic "Dirac" effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions may be helpful in conjunction with studies of rare isotopes.
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…
The quadrupole collectivity in Nd, Sm, Gd, Dy, Er, Yb, Hf and W nuclei with neutron numbers 122 $\le$ N $\le$ 156 is studied, both at the mean field level and beyond, using the Gogny energy density functional. Besides the robustness of the N=126 neutron shell closure, it is shown that the onset of static deformations in those isotopic chains with increasing neutron number leads to an enhanced stability and further extends the corresponding two-neutron driplines far beyond what could be expected from spherical calculations. Independence of the mean field predictions with respect to the particul…
A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the Self-Consistent Green's Function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD-BONN and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner--Hartree--Fock approximation, the variational approach and the virial expansion.
Starting from the microscopic low-momentum nucleon-nucleon interaction V{low k}, we present the first systematic shell model study of magnetic moments and magnetic dipole transition strengths of the basic low-energy one-quadrupole phonon excitations in nearly-spherical nuclei. Studying in particular the even-even N=52 isotones from 92Zr to 100Cd, we find the predicted evolution of the predominantly proton-neutron non-symmetric state reveals a restoration of collective proton-neutron mixed-symmetry structure near mid-shell. This provides the first explanation for the existence of pronounced col…
Selected aspects of the description of neutron-induced fission in 240Pu in the framework of the nuclear energy density functional theory at finite temperature are presented. In particular, we discuss aspects pertaining to the choice of thermodynamic state variables, the evolution of fission barriers as function of the incident neutron energy, and the temperatures of the fission fragments.
The differential cross section and the analyzing power are calculated for elastic scattering of $^6$He from a proton target using a microscopic folding optical potential, in which the $^6$He nucleus is described in terms of a $^4$He-core with two additional neutrons in the valence p-shell. In contrast to previous work of that nature, all contributions from the interaction of the valence neutrons with the target protons are taken into account.
We derive expressions for core + N + N overlap integrals starting from microscopic wave functions obtained in the ab initio no-core shell model. These overlap integrals correspond to three-body channel form factors and can be used to investigate the clustering of many-body systems into a core plus two nucleons. We consider the case when the composite system and the core are described in Slater determinant, harmonic oscillator bases, and we show how to remove spurious center of mass components exactly in order to derive translationally-invariant overlap integrals. We study in particular the Bor…
Background: Production of neutron-rich nuclei is of vital importance to both understanding nuclear structure far from stability and to informing astrophysical models of the rapid neutron capture process (r-process). Multinucleon transfer (MNT) in heavy-ion collisions offers a possibility to produce neutron-rich nuclei far from stability. Purpose: The $^{176}\mathrm{Yb}+{}^{176}\mathrm{Yb}$ reaction has been suggested as a potential candidate to explore the neutron-rich region surrounding the principal fragments. The current study has been conducted with the goal of providing guidance for futur…
Fission-fragment properties have been calculated for thermal neutron-induced fission on a $^{239}\textrm{Pu}$ target, using constrained Hartree-Fock-Bogoliubov calculations with a finite-range effective interaction. A quantitative criterion based on the interaction energy between the nascent fragments is introduced to define the scission configurations. The validity of this criterion is benchmarked against experimental measurements of the kinetic energies and of multiplicities of neutrons emitted by the fragments.
Recent observations of neutron-star properties, in particular the recent detection of gravitational waves emitted from binary neutron stars, GW 170817, open the way to put strong constraints on nuclear interactions. In this paper, we review the state of the art in calculating the equation of state of strongly interacting matter from first principle calculations starting from microscopic interactions among nucleons. We then review selected properties of neutron stars that can be directly compared with present and future observations.
We perform a systematic analysis of the density dependence of the nuclear symmetry energy within the microscopic Brueckner--Hartree--Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three body force of Urbana type. Our results are compared thoroughly to those arising from several Skyrme and relativistic effective models. The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion col…
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…
Within a microscopic approach the structure of Neutron Stars is usually studied by modelling the homogeneous nuclear matter of the core by a suitable Equation of State, based on a many-body theory, and the crust by a functional based on a more phenomenological approach. We present the first calculation of Neutron Star overall structure by adopting for the core an Equation of State derived from the Brueckner-Hartree-Fock theory and for the crust, including the pasta phase, an Energy Density Functional based on the same Equation of State, and which is able to describe accurately the binding ener…
In spite of the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star cannot flow freely, and is entrained by the nuclear lattice similarly to laboratory superfluid atomic gases in optical lattices. The role of entrainment on the neutron superfluid dynamics is reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in neutron-star crusts is presented. This model relies on a fully four-dimensionally covariant action principle. The equivalence of this formulation with the more traditional approach is demonstrated. In addition, the differ…
We calculate static properties of non-rotating neutron stars (NS's) using a microscopic equation of state (EOS) for asymmetric nuclear matter. The EOS is computed in the framework of the Brueckner--Bethe--Goldstone many--body theory. We introduce three-body forces in order to reproduce the correct saturation point of nuclear matter. A microscopic well behaved EOS is derived. We obtain a maximum mass configuration with $M_{max} = 1.8 M_\odot$, a radius $R = 9.7$ km and a central density $n_c = 1.34~fm^{-3}$. We find the proton fraction exceeds the critical value $x^{Urca}$, for the onset of dir…
It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured…
The properties of the deformed halo of 31Ne were discussed using the antisymmetrized molecular dynamics plus resonating group method (AMD+RGM). The AMD+RGM calculations describe a large neutron radius for the ground state and reveal that the ground state is dominated by core-excited components. The resonant states were also investigated by applying the analytical continuation of the coupling constant. It was found that the first excited state (the 5/2- state) is also dominated by core-excited components and has a small decay width, whereas the second excited state (the 7/2- state) is dominated…
The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of many neutrons interacting via realistic microscopic interactions and confined in external fields. We perform calculations for different external fields and across several shells to place important constraints on inhomogeneous neutron matter, and hence the large isospin limit of the nuclear energy density functionals that are used to predict properties of he…
