Based on the general analysis of the grand canonical partition function in the S-matrix framework, the calculated results on symmetry energy, free energy and entropy of dilute warm nuclear matter are presented. At a given temperature and density, the symmetry energy or symmetry free energy of the clusterized nuclear matter in the S-matrix formulation deviates, particularly at low temperature and relatively higher density, in a subtle way, from the linear dependence on the square of the isospin asymmetry parameter $X=(ρ_n-ρ_p)/(ρ_n+ρ_p)$, contrary to those obtained for homogeneous nucleonic matter. The symmetry coefficients, in the conventional definition, can then be even negative. The symmetry entropy similarly shows a very different behavior.
Observed well-developed $α$ cluster states in $^{16}$O, located above the four $α$ threshold, are investigated from the viewpoint of Bose-Einstein condensation of $α$ clusters by using a field-theoretical superfluid cluster model in which the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV $0_7^+$ and 18.8 MeV $0_8^+$ states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with th…
It is shown that a dilute property of an $α$ particle condensate can be seen in the Airy structure of nuclear rainbow and prerainbow scattering. The dilute property of the Hoyle state of $^{12}$C with a developed $α$ cluster structure is discussed by studying refractive $^3$He+$^{12}$C and $α$+$^{12}$C scattering.
The symmetry energy coefficients of dilute clusterized nuclear matter are evaluated in the $S$-matrix framework. Employing a few different definitions commonly used in the literature for uniform nuclear matter, it is seen that the different definitions lead to perceptibly different results for the symmetry coefficients for dilute nuclear matter. They are found to be higher compared to those obtained for uniform matter in the low density domain. The calculated results are in reasonable consonance with those extracted recently from experimental data.
It is shown within the strong-coupling BCS approach that, starting from the zero-density limit of superfluid nuclear matter, with increasing density deuterons first shrink before they start expanding.
Results on dissipative isoscalar modes of a hot and dilute nuclear droplet are presented. As compared to the adiabatic limit (part I), realistic dissipation yields a substantial reduction of the growth rates for all unstable modes, while the area of spinodal instability in the ($\varrho$,T)-plane remains unchanged. The qualitative features of multifragmentation through spinodal decomposition as obtained in the adiabatic limit are not significantly affected by dissipation.
We explore the thermodynamic properties of homogeneous cold (zero-temperature) nuclear matter including nucleons and $α$-particle condensation at low densities by using a generalized nonlinear relativistic mean-field (gNL-RMF) model. In the gNL-RMF model, the $α$-particle is included as explicit degree of freedom and treated as point-like particle with its interaction described by meson exchanges and the in-medium effects on the $α$ binding energy is described by density- and temperature-dependent energy shift with the parameters obtained by fitting the experimental Mott density. We find that …
The isothermal compression of a dilute nucleonic gas invoking cluster degrees of freedom is studied in an equilibrium statistical model; this clusterized system is found to be more stable than the pure nucleonic system. The equation of state (EoS) of this matter shows features qualitatively very similar to the one obtained from pure nucleonic gas. In the isothermal compression process, there is a sudden enhancement of clusterization at a transition density rendering features analogous to the gas-liquid phase transition in normal dilute nucleonic matter. Different observables like the caloric c…
The thermodynamic properties of heated nuclear matter are explored using an exactly solvable canonical ensemble model. This model reduces to the results of an ideal Fermi gas at low temperatures. At higher temperatures, the fragmentation of the nuclear matter into clusters of nucleons leads to features that resemble a Bose gas. Some parallels of this model with the phenomena of Bose condensation and with percolation phenomena are discussed. A simple expression for the hadronic equation of state is obtained from the model.
Non-uniform structures of nuclear matter are studied in a wide density-range. Using the density functional theory with a relativistic mean-field model, we examine non-uniform structures at sub-nuclear densities (nuclear ``pastas'') and at high densities, where kaon condensate is expected. We try to give a unified view about the change of the matter structure as density increases, carefully taking into account the Coulomb screening effects from the viewpoint of first-order phase transition.
Dynamics of dilute nuclear matter with light clusters and in-medium effects
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania（意大利国家核物理研究所（INFN）卡塔尼亚分部）；INFN, Laboratori Nazionali del Sud（意大利国家核物理研究所（INFN）南方实验室）；Dipartimento di Fisica e Astronomia（物理与天文学系）
We consider the thermodynamics of the matter made up of equal number of neutrons and protons and of scalar dibaryons. They interact via the exchange of scalar and vector mesons. The interaction is taken into account in the mean field approximation. The condensation of dibaryons in this matter and the phase transition of matter to quark matter are considered. Possible signatures of dibaryons in Heavy Ion Collisions are speculated on.
In this article we review the present status of alpha clustering in nuclear systems. First of all, an important aspect is condensation in nuclear matter. Second, the alpha container model, recently been proposed by Tohsaki-Horiuchi-Schuck-Roepke (THSR), will be outlined and the ensuing condensate aspect of the Hoyle state at 7.65 MeV in 12C will be investigated in some detail. After 15 years since the proposal of the alpha condensation concept a critical assessment of this idea will be given. Alpha gas states in other nuclei like 16O and 13C will be considered. The THSR wave function can also …
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.
Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structur…
The solutions to the zero-sound frequency equation and pion dispersion equation are considered for the different values of the parameters of the effective particle-hole interaction. The branches of solutions, responsible for the long-wave instability [Pomeranchuk] of the nuclear matter ω_P(k) are presented for the both equations. It is shown that in the pion dispersion equation the solutions ω_P(k) result in the instability not only for values of the spin-isospin constant g'\leq -1/2, violating stability criteria, but for all g' < g'_p (|g'_p|\ll 1 and g'_p < 0). At g' > g'_p the branches ω_P(…
Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The equation of state, the composition, Bose condensation of bound fermions, the disappearance of bound states at increasing density because of Pauli blocking are of relevance for different applications in astrophysics, heavy ion collisions, and nuclear structure.
We investigate the critical temperature of Bose-Einstein condensation of $K^-$ mesons in neutron star matter. This is studied within the framework of relativistic field theoretical models at finite temperature where nucleon-nucleon and (anti)kaon-nucleon interactions are mediated by the exchange of mesons. The melting of the antikaon condensate is studied for different values of antikaon optical potential depths. We find that the critical temperature of antikaon condensation increases with baryon number density. Further it is noted that the critical temperature is lowered as antikaon optical p…
We report on recent progress in understanding pairing phenomena in low-density nuclear matter at small and moderate isospin asymmetry. A rich phase diagram has been found comprising various superfluid phases that include a homogeneous and phase-separated BEC phase of deuterons at low density and a homogeneous BCS phase, an inhomogeneous LOFF phase, and a phase-separated BCS phase at higher densities. The transition from the BEC phases to the BCS phases is characterized in terms of the evolution, from strong to weak coupling, of the condensate wavefunction and the second moment of its density d…
The onset of quartetting, i.e. alpha-particle condensation, in symmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the alpha-particles. The critical temperature can reach values up to around 6 MeV. Also the disappearance of alpha-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0_2^+ of 12C, is identified as an "alpha-particle condensate" state. It is conjectured that such st…
The behavior of pseudoscalar mesons in nuclear medium is reviewed with an emphasis on the possibility of their Bose-Einstein condensation in dense matter. In particular pion condensation is reexamined in detail, stimulated by recent theoretical and observational developments.
Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations. An effective Lagrangian for the scalar excitation modes is derived after performing a boson…
A comparison of pairing properties in cuprates and nuclear matter is briefly discussed. Quartet (alpha-particle) condensation is a very important aspect of nuclear physics. The physics of the Hoyle state in 12 C will be outlined and its crucial role for the existence of life on earth explained.
Alpha clustering and alpha condensation in lighter nuclei is presently strongly and increasingly discussed in the literature both from the experimental side as from the theoretical one. A discussion of the present status of the theory as well as outlooks for future developements will be presented.
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular by the appearance of bound states. A recently developed quantum statist…
Due to the large value of the scattering length in nuclear systems, standard density--functional theories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in Effective Field Theories for systems with large scattering lengths, a new energy--density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron an…
The theory of quartet condensation is further developed. The onset of quartetting in homgeneous fermionic matter is studied with the help of an in-medium modified four fermion equation. It is found that at very low density quartetting wins over pairing. At zero temperature, in analogy to pairing, a set of equations for the quartet order parameter is given. Contrary to pairing, quartetting only exists for strong coupling and breaks down for weak coupling. Reasons for this finding are detailed. In an application to nuclear matter, the critical temperature for alpha particle condensation can reac…
The critical temperature for $α$-particle condensation in nuclear matter with Fermi surface imbalance between protons and neutrons is determined. The in-medium four-body Schrödinger equation, generalizing the Thouless criterion of the BCS transition, is applied using a Hartree-Fock wave function for the quartet projected onto zero total momentum in matter with different chemical potentials for protons and neutrons.
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 present a comprehensive analysis of hot and dilute isospin-asymmetric nuclear matter employing the temperature-dependent effective-relativistic mean-field theory (E-RMF). The E-RMF is applied to study the effect of $δ$ and $ω-ρ$ meson cross-coupling on the thermal properties of asymmetric nuclear matter using two recently developed IOPB-I and G3 parameter sets. These sets are known to reproduce the nuclear matter properties in agreement with various experimental and observational constraints. We consider the nuclear matter to be homogeneous and study the equation of state (EoS) for densitie…
When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional (EDF) calculations both with the relativistic and the Gogny approaches on the diluted $^{16}$O nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. Complementary approaches ar…
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…
We have investigated the compositions of hot and dense nuclear matter with the focus on the quantum-statistical effects for light clusters. Our main observation is that the formation of heavy nuclei in stellar matter leads to the reduction of the number densities of light clusters. As a result, the quantum statistical effects such as Bose-Einstein condensation of deuterons and $α$-particles are suppressed. The deviations in number densities of light clusters between Boltzmann and quantum statistics at sub-nuclear densities and temperatures 1-3 MeV are $\sim$0.2$\%$ at most. The condensation of…
We report variational calculations of symmetric nuclear matter and pure neutron matter, using the new Argonne v18 two-nucleon and Urbana IX three-nucleon interactions. At the equilibrium density of 0.16 fm^-3 the two-nucleon densities in symmetric nuclear matter are found to exhibit a short-range spin-isospin structure similar to that found in light nuclei. We also find that both symmetric nuclear matter and pure neutron matter undergo transitions to phases with pion condensation at densities of 0.32 fm^-3 and 0.2 fm^-3, respectively. Neither transtion occurs with the Urbana v14 two-nucleon in…
Bose-Einstein condensation of antikaons in cold and dense beta-equilibrated matter under the influence of strong magnetic fields is studied within a relativistic mean field model. For magnetic fields $> 5 \times 10^{18}$G, the phase spaces of charged particles are modified resulting in compositional changes in the system. The threshold density of $K^-$ condensation is shifted to higher density compared with the field free case. In the presence of strong fields, the equation of state becomes stiffer than that of the zero field case.
An effective chiral Lagrangian in heavy-fermion formalism whose parameters are constrained by kaon-nucleon and kaon-nuclear interactions next to the leading order in chiral expansion is used to describe kaon condensation in dense ``neutron star" matter. The critical density is found to be robust with respect to the parameters of the chiral Lagrangian and comes out to be $ρ_c\sim (3 - 4)ρ_0$. Once kaon condensation sets in, the system is no longer composed of neutron matter but of nuclear matter. Possible consequences on stellar collapse with the formation of compact ``nuclear stars" or light-m…
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 perio…
The critical density for kaon condensation in ``nuclear star" matter is computed up to two-loop order {\it in medium} (corresponding to next-to-next-to-leading order in chiral perturbation theory in free space) with a heavy-baryon effective chiral Lagrangian whose parameters are determined from $KN$ scattering and kaonic atom data. To the order considered, the kaon self-energy has highly non-linear density dependence in dense matter. We find that the four-Fermi interaction terms in the chiral Lagrangian play an important role in triggering condensation, predicting for ``natural" values of the …
Analyses of comprehensive sets of strong-interaction data consisting of level shifts, widths and yields in strange atoms of K mesons and Sigma hyperons are reviewed. The introduction of density dependent optical potentials, in both cases, improves significantly the fit to the data. A strongly attractive antikaon-nuclear potential of order 150-200 MeV in nuclear matter is suggested by fits to the kaonic-atom data, with interesting possible repercussions on kaon condensation and on the evolution of strangeness in high-density stars. The case for relatively narrow, deeply bound antikaon atomic st…
Joint Institute for Nuclear Research（俄罗斯联合核研究所）；National Center of Physics and Mathematics（国家物理数学中心）；Matej Bel University（马特伊·贝尔大学）；National Research Nuclear University (MEPhI)（国立研究核子大学（莫斯科工程物理学院））
We report on a comprehensive study of the phase structure of cold, dilute nuclear matter featuring a SD condensate at non-zero isospin asymmetry, within wide ranges of temperatures and densities. We find a rich phase diagram comprising three superfluid phases, namely a Larkin-Ovchinnikov-Fulde-Ferrell phase, the ordinary BCS phase, and a heterogeneous, phase-separated BCS phase, with associated crossovers from the latter two phases to a homogeneous or phase-separated Bose-Einstein condensate of deuterons. The phase diagram contains two tricritical points (one a Lifshitz point), which may degen…
We show that an antiferrosmectic-C phase has lower energy at high densities than the non-magnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers, and staggered layer by layer.
$α$ particle condensation is a novel state in nuclear systems. We briefly review the present status on the study of $α$ particle condensation and address the open problems in this research field: $α$ particle condensation in heavier systems other than the Hoyle state, linear chain and $α$ particle rings, Hoyle-analogue states with extra neutrons, $α$ particle condensation related to astrophysics, etc.
An upper limit to the critical density for the transition to the deconfined phase, at zero temperature, has been evaluated by analyzing the behavior of the gluon condensate in nuclear matter. Due to the non linear baryon density effects, the upper limit to the critical density, ρ_c turns out about nine times the saturation density, rho_0 for the value of the gluon condensate in vacuum <(α_s/π) G^2>=0.012 GeV^4. For neutron matter ρ_c \simeq 8.5 ρ_0. The dependence of the critical density on the value of the gluon condensate in vacuum is studied.
We study the isospin-singlet neutron-proton pairing in bulk nuclear matter as a function of density and isospin asymmetry within the BCS formalism. In the high-density, weak-coupling regime the neutron-proton paired state is strongly suppressed by a minor neutron excess. As the system is diluted, the BCS state with large, overlapping Cooper pairs evolves smoothly into a Bose-Einstein condensate of tightly bound neutron-proton pairs (deuterons). In the resulting low-density system a neutron excess is ineffective in quenching the pair correlations because of the large spatial separation of the d…
We examine the effects of color screening on the transition of a parton plasma into a hadron gas at RHIC energies. It is found that as expected, color screening posed itself as a significant barrier for hadronization. Parton-hadron conversion would therefore be delayed and prolonged when compared to that occuring in a vacuum. Due to the on-going expansion, the resulting hadron densities are lowered. Parton equilibration is also shown to be seriously disrupted in the process.
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for i…
We study the composition of nuclear matter at sub-saturation densities, non-zero temperatures, and isospin asymmetry, under the conditions characteristic of binary neutron star mergers, stellar collapse, and low-energy heavy-ion collisions. The composition includes light clusters with mass number $A\le 4$, a heavy nucleus ($\isotope[56]{Fe}$), the $Δ$-resonances, the isotriplet of pions, as well as the $Λ$ hyperon. The nucleonic mean-fields are computed from a zero-range density functional, whereas the pion-nucleon interactions are treated to leading order in chiral perturbation theory. We sho…
We investigate nuclear matter equations of state in neutron star with kaon condensation. It is generally known that the existence of kaons in neutron star makes the equation of state soft so that the maximum mass of neutron star is not likely to be greater than 2.0 $M_{\odot}$, the maximum mass constrained by current observations. With existing Skyrme force model parameters, we calculate nuclear equations of state and check the possibility of kaon condensation in the core of neutron stars. The results show that even with the kaon condensation, the nuclear equation of state satisfies both the m…
A unified treatment of normal nuclear matter described by Walecka's mean field theory and kaon condensed matter described by chiral perturbation theory is proposed in terms of mean fields of an effective chiral Lagrangian. The BR scaling is found to play a key role in making the link between the ground state properties of nuclear matter and the fluctuation into the strangeness-flavor direction. A simple prediction for kaon condensation is presented.
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (B…
The Bose-Einstein condensation of $α$ partciles in the multicomponent environment of dilute, warm nuclear matter is studied. We consider the cases of matter composed of light clusters with mass numbers $A\leq 4$ and matter that in addition these clusters contains $\isotope[56]{Fe}$ nuclei. We apply the quasiparticle gas model which treats clusters as bound states with infinite life-time and binding energies independent of temperature and density. We show that the $α$ particles can form a condensate at low temperature $T\le 2$ MeV in such matter in the first case. When the $\isotope[56]{Fe}$ nu…
We study dilute gases with short range interactions and large two-body scattering lengths. At temperatures between the condensation temperature and the scale set by therange of the potential there is a high degree of universality. The first two terms in the expansion of thermodynamic functions in powers of the fugacity $z$, which measures the diluteness of the system, are determined by the scattering length only. The term proportional to $z^3$ depends only on one new parameter describing the three-body physics. We compute the third term of the expansion and show that, for many values of this n…
Enhancement of nuclear pasta formation due to multi-nucleus simultaneous collision is presented based on time-dependent density functional calculations with periodic boundary condition. This calculation corresponds to the situation with density lower than the known low-density existence limit of the nuclear pasta phase. In order to evaluate the contribution from three-nucleus simultaneous collisions inside the cosmic matter, the possibility of multi-nucleus simultaneous collisions is examined by a systematic Monte-Carlo calculation, and the mean free path of a nucleus is obtained. Consequently…
On-shell kaon-nucleon scattering, kaonic atom and kaon condensation are treated on the same footing by means of a chiral perturbation expansion to the next-to-next-to-leading order (``N$^2$LO"). Constraining the low-energy constants in the chiral Lagrangian by on-shell $KN$ scattering lengths and kaonic atom data, the off-shell s-wave scattering amplitude up to one-loop order corresponding to N$^2$LO and the critical density of kaon condensation up to in-medium two-loop order are computed. The effects on kaon-proton scattering of the quasi-bound $Λ(1405)$ and on kaonic atoms and kaon condensat…
