The decrease in the symmetry energy of hot nuclei populated in $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at beam energies of 30, 40, and 47 MeV/nucleon, as a function of excitation energy is studied. It is observed that this decrease is mainly a consequence of increasing expansion or decreasing density rather than the increasing temperature. The results are in good agreement with the recently reported microscopic calculation based on the Thomas-Fermi approach. An empirical relation to study the symmetry energy of finite nuclei in various mass region is proposed.
The pairing gaps, heat capacities and level densities are calculated within the BCS-based quasiparticle approach including the effect of thermal fluctuations on the pairing field within the pairing model plus noncollective rotation along the z axis for $^{60}$Ni and $^{72}$Ge nuclei. The analysis of the numerical results obtained shows that, in addition to the pairing gap, the heat capacity can also serve as a good observable to detect the appearance of the pairing reentrance in hot rotating nuclei, whereas such signature in the level density is rather weak.
The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.
This article describes calculations of the yield ratio of anti-particles to the yield of particles ($\bar{p}/p$, $\bar{d}/d$,$\overline{^{3}\mathrm{He}}$/$^{3}$He) in proton-proton and nuclear-nuclear interactions using the self-similarity parameter in the central rapidity region. The used approach is based on the study of relativistic nuclear interactions in the four-velocity space. The results of the calculations are compared with the existing experimental data in a wide center-of-mass energy range ($SPS$, $RHIC$, $LHC$). Within this approach the inclusive spectra of pions and kaons and rati…
This review article is focused on the tremendous progress realized during the last fifteen years in the understanding of multifragmentation and its relationship to the liquid-gas phase diagram of nuclei and nuclear matter. The explosion of the whole nucleus, early predicted by Bohr [N. Bohr, Nature 137 (1936) 351], is a very complex and rich subject which continues to fascinate nuclear physicists as well as theoreticians who extend the thermodynamics of phase transitions to finite systems.
A production mechanism of highly excited nuclei formed in violent collisions in the Fermi energy domain is investigated. The collision of two nuclei is decomposed into several stages which are treated separately. Simplified exciton concept is used for the description of pre-equilibrium emission. A modified spectator-participant scenario is used where motion along classical Coulomb trajectories is assumed. The participant and one of the spectator zones undergo incomplete fusion. Excitation energies of both cold and hot fragment are determined. Results of the calculation are compared to recent e…
The ratio of pre-equilibrium neutrons to protons from collisions of neutron-rich nuclei is studied as a function of their kinetic energies. This ratio is found to be sensitive to the density dependence of the nuclear symmetry energy, but is independent of the compressibility of symmetric nuclear matter and the in-medium nucleon-nucleon cross sections. The experimental measurement of this ratio thus provides a novel means for determining the nuclear equation of state of asymmetric nuclear matter.
Simulations based on experimental data obtained from multifragmenting quasifused nuclei produced in central 129Xe + natSn collisions have been used to deduce event by event freeze-out properties on the thermal excitation energy range 4-12 AMeV. From these properties and temperatures deduced from proton transverse momentum fluctuations constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonous behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a first order phase transition for hot nuclei.
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
By using freeze-out properties of multifragmenting hot nuclei produced in quasifusion central $^{129}$Xe+$^{nat}$Sn collisions at different beam energies (32, 39, 45 and 50 AMeV) which were estimated by means of a simulation based on experimental data collected by the $4π$ INDRA multidetector, heat capacity in the thermal excitation energy range 4 - 12.5 AMeV was calculated from total kinetic energies and multiplicities at freeze-out. The microcanonical formulation was employed. Negative heat capacity which indicates a first order phase transition for finite systems is observed and confirms pr…
The production mechanism of highly excited nuclei in the Fermi energy domain is investigated. A phenomenological approach, based on the exciton model, is used for the description of pre-equilibrium emission. A model of deep inelastic transfer is employed for the peripheral collisions in the post-pre-equilibrium stage. An approach to describe more central collisions is proposed. A geometric overlap formula is employed in a way suitable for given energy domain. A simple geometric approach describing the interaction of participant and spectator zones is used to determine the incomplete fusion cha…
The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and sh…
Intermediate energy Coulomb excitation and dissociation is a useful tool for nuclear structure and astrophysics studies. Low-lying strength in nuclei far from stability was discovered by this method. The effective range theory for low-lying strength in one-neutron halo nuclei is summarized and extended to two-neutron halo nuclei. This is of special interest in view of recent rather accurate experimental results on the low-lying electric dipole strength in $^{11}$Li. Another indirect approach to nuclear astrophysics is the Trojan horse method. It is pointed out that it is a suitable tool to inv…
Simulations based on experimental data obtained from multifragmenting quasi-fused nuclei produced in central $^{129}$Xe + $^{nat}$Sn collisions have been used to deduce event by event freeze-out properties in the thermal excitation energy range 4-12 AMeV [Nucl. Phys. A809 (2008) 111]. From these properties and the temperatures deduced from proton transverse momentum fluctuations, constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonic behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a…
We point out that during the supernova II type explosion the thermodynamical condition of stellar matter between the protoneutron star and the shock front corresponds to the nuclear liquid-gas phase coexistence region, which can be investigated in nuclear multifragmentation reactions. We have demonstrated, that neutron-rich hot heavy nuclei can be produced in this region. The production of these nuclei may influence dynamics of the explosion and contribute to the synthesis of heavy elements.
The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. …
The phonon damping model (PDM) is extended to include the effect of angular momentum at finite temperature. The model is applied to the study of damping of giant dipole resonance (GDR) in hot and noncollectively rotating spherical nuclei. The numerical results obtained for Mo88 and Sn106 show that the GDR width increases with both temperature T and angular momentum M. At T > 4 MeV and M<= 60 hbar the increase in the GDR width slows down for Sn106, whereas at M<= 80 hbar the GDR widths in both nuclei nearly saturate. By adopting the nuclear shear viscosity extracted from fission data at T= 0, i…
This article summarizes our present knowledge about nuclear matter at the highest energy densities and its formation in relativistic heavy ion collisions. We review what is known about the structure and properties of the quark-gluon plasma and survey the observables that are used to glean information about it from experimental data.
The number of constituent quarks (NCQ-) scaling of hadrons and the number of constituent nucleons (NCN-) scaling of light nuclei are proposed for nuclear modification factors ($R_{cp}$) of hadrons and light nuclei, respectively, according to the experimental investigations in relativistic heavy-ion collisions. Based on coalescence mechanism the scalings are performed for pions and protons in quark level, and light nuclei $d (\bar d)$ and $^3$He for nucleonic level, respectively, formed in Au + Au and Pb + Pb collisions and nice scaling behaviour emerges. NCQ or NCN scaling law of $R_{cp}$ can …
We have constructed a Lagrangian model (SIG-OM) with coupling of sigma and omega mesons in the relativistic mean-field theory. Properties of finite nuclei and nuclear matter have been explored with the new Lagrangian model. The study shows that with SIG-OM an excellent description of binding energies and charge radii of nuclei over a large range of isospin is achieved. With an incompressibility of nuclear matter K=265 MeV, it is also able to describe the breathing-mode isoscalar giant monopole resonance energies appropriately. It is shown that the high-density behaviour of the equation of stat…
The density profiles of around 750 nuclei are analyzed using the Skyrme energy density functional theory. Among them, more than 350 nuclei are found to be deformed. In addition to rather standard properties of the density, we report a non-trivial behavior of the nuclear diffuseness as the system becomes more and more deformed. Besides the geometric effects expected in rigid body, the diffuseness acquires a rather complex behavior leading to a reduction of the diffuseness along the main axis of deformation simultaneously with an increase of the diffuseness along the other axis. The possible iso…
It is shown that the hole in the centre of $ ^{3}H $, $ ^{3}He $ and $ ^{4}He $, the neutron halos in nuclei, the $ α- $ and other clustering effects in nuclei and the nuclear molecules all basically arise due to the same underlying effect. We shall show that all these ground state properties of nuclei are manifestations of quark effects. The role of triton clustering in very neutron rich nuclei is emphasized. All these require the concept of hidden colour states which arise from confinement ideas of QCD for the multi-quark systems. This provides comprehensive understanding of diverse nuclear …
The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, tr…
An abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation in the Fermi energy domain. On the other hand finite size effects are predicted to strongly reduce this abnormal production. High statistics quasifusion hot nuclei produced in central collisions between Xe and Sn isotopes at 32 and 45 AMeV incident energies have been used to definitively establish, through the experimental measurement of charge correlations, the presence of spinodal instabilities. N/Z influence was als…
We describe a relation between the symmetry energy coefficients c_sym(rho) of nuclear matter and a_sym(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of c_sym(rho). Here we take advantage of this relation to explore the prospects for constraining c_sym(rho) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.
We study 1S0 pairing gaps in neutron and nuclear matter as well as in finite nuclei on the basis of microscopic two-nucleon interactions. Special attention is paid to the consistency of the pairing interaction and normal self-energy contributions. We find that pairing gaps obtained from low-momentum interactions depend only weakly on approximation schemes for the normal self-energy, required in present energy-density functional calculations, while pairing gaps from hard potentials are very sensitive to the effective-mass approximation scheme.
What is the origin of nuclear clustering and how does it emerge from the nuclear interaction? While there is ample experimental evidence for this phenomenon, its theoretical characterization directly from nucleons as degrees of freedom remains a challenge, making it difficult to improve nuclear forces using clustering observables. In this work, a simple ratio of energies based on effective scale arguments is proposed to assess the quality of nuclear forces on alpha clustering (${ {}^{4}\text{He} }$) in bound and narrow ground-state nuclei. The proposed clustering ratio is parameter-free and co…
The formation of $α$-particle clusters on the surface of heavy nuclei is described in a generalized relativistic mean-field model with explicit cluster degrees of freedom. The effects on the size of the neutron skin of Sn nuclei and ${}^{208}$Pb are investigated as a function of the mass number and the isospin-dependent part of the effective interaction, respectively. The correlation of the neutron skin thickness with the difference of the neutron and proton numbers and with the slope of the nuclear symmetry energy is modified as compared to the mean-field calculation without alpha-cluster cor…
In [1,2]the observed decrease in spectral peak energies of IMFs emitted from hot nuclei was interpreted in terms of a breakup density that decreased with increasing energy. Subsequently, Raduta et al. [3] performed MMM simulations that showed decreasing spectral peaks could be obtained at constant density. In this letter we examine this apparent inconsistency.
Slowly extracted relativistic beams of light nuclei and a beam transportation line net system constitute a good base for secondary nuclear beams forming at the LHE accelerator facility. A recent years activity in the field at the Laboratory is connected with a project on study light nuclei structure by means the emulsion technique [1,2]. The paper shortly summarizes results of the work.
The role played by the heaviest fragment in partitions of multifragmenting hot nuclei is emphasized. Its size/charge distribution (mean value, fluctuations and shape) gives information on properties of fragmenting nuclei and on the associated phase transition.
The density of accessible levels at low spin in the (^3He,αγ) reaction has been extracted for the ^{161,162}Dy and ^{171,172}Yb nuclei. The entropy of the even-odd and even-even nuclei has been deduced as a function of excitation energy, and found to reach a maximum of 15 k_B before neutron evaporation. The entropy of one quasi-particle outside an even-even core is found to be 1.70(15) k_B. This quasi-particle picture of hot nuclei is well accounted for within a simple pairing model. The onset of two, four and six quasi-particle excitations in the ^{162}Dy and ^{172}Yb nuclei is discussed and …
Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretica…
The dynamics and thermodynamics of phase transition in hot nuclei are studied through experimental results on multifragmentation of heavy systems (A>200) formed in central heavy ion collisions. Different signals indicative of a phase transition studied in the INDRA collaboration are presented and their consistency is stressed.
Bremsstrahlung of photons emitted during the scattering of $π^{+}$-mesons off nuclei is studied for the first time. Role of interactions between $π^{+}$-mesons and nuclei in the formation of the bremsstrahlung emission is analyzed in details. We discover essential contribution of emitted photons from nuclear part of Johnson-Satchler potential to the full spectrum, in contrast to the optical Woods-Saxon potential. We observe unusual essential influence of the nuclear part of both potentials on the spectrum at high photon energies. This phenomenon opens a new experimental way to study and check …
Obtaining tensor-polarized nuclei with spin $S\ge1$ via spin filtering upon nuclear beam transmission through an unpolarized target (spin dichroism effect)
The dynamics and thermodynamics of phase transition in hot nuclei are studied through experimental results on multifragmentation of heavy systems (A$geq$200) formed in central heavy ion collisions. Different signals indicative of a phase transition studied in the INDRA collaboration are presented and their consistency is stressed.
Nuclear forces and the nuclear many-body problem have been some of Gerry Brown's main topics in his so productive life as a theoretical physicist. In this talk, I outline how Gerry's work laid the foundations of the modern theory of nuclear forces and ab initio calculations of atomic nuclei. I also present some recent developments obtained in the framework of nuclear lattice simulations.
The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $η$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $η/s$ of shear viscosity $η$ to entropy density $s$ is extracted from the experimental systematics of the GDR in copper, tin and lead isotopes at finite temperature $T$. These empirical results are then compared with the predictions by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the r…
In this contribution, the eikonal approximation developed by Roy Glauber to describe high-energy quantum collisions is presented. This approximation has been-and still is-extensively used to analyse reaction measurements performed to study the structure of nuclei far from stability. This presentation focuses more particularly on the application of the eikonal approximation to the study of halo nuclei in modern nuclear physics. To emphasise Roy Glauber's legacy in today's nuclear physics, recent extensions of this model are reviewed.
Heavy mesons in nuclear matter and nuclei are analyzed within different frameworks, paying a special attention to unitarized coupled-channel approaches. Possible experimental signatures of the properties of these mesons in matter are addressed, in particular in connection with the future FAIR facility at GSI.
Recent advancement on the knowledge of multifragmentation and phase transition for hot nuclei is reported. It concerns i) the influence of radial collective energy on fragment partitions and the derivation of general properties of partitions in presence of such a collective energy, ii) a better knowledge of freeze-out properties obtained by means of a simulation based on all the available experimental information and iii) the quantitative study of the bimodal behaviour of the heaviest fragment charge distribution for fragmenting hot heavy quasi-projectiles which allows, for the first time, to …
We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We focus on the links between many-body pairing as it evolves from the underlying nucleon-nucleon interaction and the eventual experimental and theoretical manifestations of superfluidity in infinite nuclear matter and of pairing in finite nuclei. We analyse the nature of pair correlations in nuclei and their potential impact on nuclear structure experiments. We also describe recent experimental evidence that points to a relation betwee…
Thanks to the high detection quality of the INDRA array, signatures related to the dynamics (spinodal decomposition) and thermodynamics (negative microcanonical heat capacity) of a liquid-gas phase transition have been simultaneously studied in multifragmentation events in the Fermi energy domain. The correlation between both types of signals strongly supports the existence of a first order phase transition for hot nuclei.
Recent important progress on the knowledge of multifragmentation and phase transition for hot nuclei, thanks to the high detection quality of the INDRA array, is reported. It concerns i) the radial collective energies involved in hot fragmenting nuclei/sources produced in central and semi- peripheral collisions and their influence on the observed fragment partitions, ii) a better knowledge of freeze-out properties obtained by means of a simulation based on all the available experimental information and iii) the quantitative study of the bimodal behaviour of the heaviest fragment distribution f…
The fragment production in multifragmentation of finite nuclei is affected by the critical temperature of nuclear matter. We show that this temperature can be determined on the basis of the statistical multifragmentation model (SMM) by analyzing the evolution of fragment distributions with the excitation energy. This method can reveal a decrease of the critical temperature that, e.g., is expected for neutron-rich matter. The influence of isospin on fragment distributions is also discussed.
Status and prospects of nuclear clustering studies by dissociation of relativistic nuclei in nuclear track emulsion are presented. The unstable $^{8}$Be and $^{9}$B nuclei are identified in dissociation of the isotopes $^{9}$Be, $^{10}$B, $^{10}$C and $^{11}$C, and the Hoyle state in the cases $^{12}$C and $^{16}$O. On this ground searching for the Hoyle state and more complex $α$-particle states in the dissociation of the heavier nuclei is suggested. A detailed study of a low-density baryonic matter arising in dissociation of the heaviest nuclei is forthcoming long-term problem. An analysis o…
The richness of the data set, collected by the INDRA collaboration during the last twenty years, enabled us to build a set of caloric curves for nuclei of various sizes, by using, for the first time, a single experimental set-up and a single experimental protocol. We will therefore present the different caloric curves ($E^{\ast}-T$) obtained by a new calorimetry, for Quasi-Projectiles produced by symmetric or quasi symmetric reactions at different incident energies (Au+Au, Xe+Sn, Ni+Ni). For all these systems, a clear change of the de-excitation process of hot nuclei is observed but this one i…
Nuclear Lattice Effective Field Theory is a new many-body approach that is firmly rooted in the symmetries of QCD. In particular, it allows for truly ab initio calculations of nuclear structure and reactions. In this talk, I focus on the emergence of alpha-clustering in nuclei based on this approach. I also discuss various recent achievements, the deficiencies of the chiral forces used at present and the prospects to improve upon these and the calculations of nuclear properties and dynamics.
We present results for the $η_c$-nucleus bound state energies for various nuclei using an effective Lagrangians approach. The attractive potentials for the $η_c$ in the nuclear medium originate from the medium-modified intermediate $D D^{*}$ state in the $η_c$ self energy, using the local density approximation. Our results suggest that the $η_c$ should form bound states with all the nuclei considered
When heavy Quarkonia are formed in collisions between between nuclei, their production cross section is modified relative to that in p+p collisions. The physical effects that cause this modification fall into two categories. Hot matter effects are due to the large energy density generated in the nuclear collision, which disrupts the formation of the quarkonium state. Cold nuclear matter effects are due to the fact that the quarkonium state is created in a nuclear target. I will review experimental aspects of quarkonia production due to both hot and cold matter effects.
Synthesis of new elements at the upper border of the charts of nuclei and investigation of their decay properties and nuclear structure has been one of the main research topics in low energy nuclear physics since more than five decades. Main items are the quest for the heaviest nuclei that can exist and the verification of the theoretical predicted spherical proton and neutron shells at Z = 114, 120 or 126 and N = 172 or 184. The scope of the present paper is to illustrate some technical and physical aspects in investigation of the heaviest nuclei ('superheavy nuclei') and to critical discuss …
We use several diverse parameterizations of diffractive parton distributions, extracted in leading twist QCD analyses of the HERA diffractive deep inelastic scattering (DIS) data, to make predictions for leading twist nuclear shadowing of nuclear quark and gluon distributions in DIS on nuclei. We find that the HERA diffractive data are sufficiently precise to allow us to predict large nuclear shadowing for gluons and quarks, unambiguously. We performed detailed studies of nuclear shadowing for up and charm sea quarks and gluons within several scenarios of shadowing and diffractive slopes, as w…
Recent results for the $η_c$- and $J/ψ$-nucleus bound state energies for various nuclei are presented. The attractive potentials for the $η_c$ and $J/ψ$ mesons in the nuclear medium originate, respectively, from the in-medium enhanced $DD^{*}$ and $D\bar{D}$ loops in the $η_c$ and $J/ψ$ self energies. Our results suggest that the $η_c$ and $J/ψ$ mesons should form bound states with all the nuclei considered.
Dissociation of 1.2 A GeV $^{10}$C nuclei in nuclear track emulsionis is studied. It is shown that most precise angular measurements provided by this technique play a crucial role in the restoration of the excitation spectrum of the 2$α$+2p system. Strong contribution of the cascade process $^{10}$C$\rightarrow ^9$B$\rightarrow ^8$Be identified.
Today, we have a variety of reactions at hand that can be used to multi-fragment nuclei. In many of these reactions even several sources of fragments can be discerned and characterized. There is overwhelming evidence that these sources of fragments are hot. It is already less clear whether heat by itself is sufficient to initiate the fragment decay. What causes fragmentation, and when and how are the fragments (pre)formed? These questions have remained as much a challenge as the complementary class of questions to which they are related: What observations derive their significance from the liq…
The average multiplicity of light nuclei and pi-mesons, emitted in HeC and CC interactions at 4.2 A GeV/c were studied as a function of number of identified protons. In both interactions, the behavior of average multiplicity of pi- mesons are in agreement with results coming from the Cascade model. The model could not describe the behavior of average multiplicity of light nuclei produced in HeC interactions. In case of CC interactions the model could describe qualitatively the behavior of the average multiplicity of light nuclei. An essential deviation was observed in some of the most central …
The systematics of the giant dipole resonance (GDR) widths in hot and rotating nuclei are studied in terms of temperature T, angular momentum J and mass A. The different experimental data in the temperature range of 1 - 2 MeV have been compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism using a modified approach to estimate the average values of T, J and A in the decay of the compound nucleus. The values of the ground state GDR widths have been extracted from the TSFM parametrization in the liquid drop limit for the corrected T, J and A for a given system and …
