Multifragmentation reactions are dominating processes for the decomposition of highly excited nuclei leading to the fragment production in heavy-ion collisions. At high energy reactions strange particles are abundantly produced. We present a novel development of the Statistical multifragmentation model (SMM) as its generalization for the hyper-matter which is formed after the hyperon capture. In this way, it is possible to describe its disintegration into normal and hyper-nuclei. Some properties of hyper-nuclei and their binding energies can be determined from the comparison of the isotope yields. The main focus of this method is to investigate strange and multi-strange hypernuclei since their properties are not easy to measure in traditional hyper-nuclei experiments.
In peripheral collisions of relativistic heavy ions highly excited spectators containing Lambda-hyperons can be produced. Such strange spectator matter may undergo a break-up into many fragments (multifragmentation) as it is well established for ordinary nuclear systems. We generalize the statistical multifragmentation model, previously successfully used for the description of experimental data, for the case of hypernuclear systems. We predict relative yields of hypernuclei and the main characteristics of such a break-up. We point at a connection of this phenomenon with a liquid-gas phase tran…
We analyze hypernuclei coming from fragmentation and multifragmentation of spectator residues obtained in relativistic ion collisions. These hypernuclei have a broad distribution in masses and isospin. They reach beyond the neutron and proton drip lines, and they are expected to be stable with respect to neutron and proton emission. This gives us the opportunity to investigate the properties of exotic hypernuclei, as well as the properties of normal nuclei beyond the drip lines, which can be produced after weak decay of such hypernuclei.
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.
We study the formation of single- and double-$Λ$ hypernuclei in antiproton-induced reactions relevant for the forthcoming PANDA experiment at FAIR. We use the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport model with relativistic mean-fields for the description of non-equilibrium dynamics and the statistical multifragmentation model (SMM) for fragment formation. This combined approach describes the dynamical properties of strangeness and fragments in low energy $\bar{p}$-induced reactions fairly well. We then focus on the formation of double-$Λ$ hypernuclei in high energy $\bar{p}$-nucl…
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.
In nuclear reactions induced by hadrons and ions of high energies, nuclei can disintegrate into many fragments during a short time (~100 fm/c). This phenomenon known as nuclear multifragmentation was under intensive investigation last 20 years. It was established that multifragmentation is an universal process taking place in all reactions when the excitation energy transferred to nuclei is high enough, more than 3 MeV per nucleon, independently on the initial dynamical stage of the reactions. Very known compound nucleus decay processes (sequential evaporation and fission), which are usual for…
The shape influence of decaying thermalized source on various characteristics of multifragmentation as well as its interplay with effects of angular momentum and collective expansion are first studied and the most pertinent variables are proposed. The analysis is based on the extension of the statistical microcanonical multifragmentation model.
The process of nuclear multifragmentation has been implemented, together with evaporation and fission channels of the disintegration of excited remnants in nucleus-nucleus collisions using percolation theory and the intranuclear cascade model. Colliding nuclei are treated as face--centered--cubic lattices with nucleons occupying the nodes of the lattice. The site--bond percolation model is used. The code can be applied for calculation of the fragmentation of nuclei in spallation and multifragmentation reactions.
A data-driven idea is presented to test if light nuclei and hypernuclei obey the coalescence-inspired sum rule, i.e., to test if the flow of a light nucleus or hypernucleus is the summed flow of each of its constituents. Here, the mass difference and charge difference among the constituents of light nuclei and hypernuclei are treated appropriately. The idea is applied to the available data for $\sqrt{s_{NN}} = 3$ GeV fixed-target Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), published by the STAR collaboration. It is found that the sum rule for light nuclei is approximately v…
Theoretical calculations are performed to investigate the angular momentum and Coulomb effects on fragmentation and multifragmentation in peripheral heavy-ion collisions at Fermi energies. Inhomogeneous distributions of hot fragments in the freeze-out volume are taken into account by microcanonical Markov chain calculations within the Statistical Multifragmentation Model (SMM). Including an angular momentum and a long-range Coulomb interaction between projectile and target residues leads to new features in the statistical fragmentation picture. In this case, one can obtain specific correlation…
The influence of shape of expanding and rotating source on various characteristics of the multifragmentation process is studied. The analysis is based on the extension of the statistical microcanonical multifragmentation model. The comparison with the data is done for central Xe+Sn collisions at 50 A MeV as measured by INDRA Collaboration.
Two approximate formulae are given for the binding energies in Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller and the Gaussian central potentials. Those easily programmable formulae combine the eigenvalues of the transformed Jacobi eigenequation and an application of the hypervirial theorems.
We present, using the statistical model, an analysis of the production of light nuclei, hypernuclei and their antiparticles in central collisions of heavy nuclei. Based on these studies we provide predictions for the production yields of multiply-strange light nuclei.
The shapes of light normal nuclei and $Λ$ hypernuclei are investigated in the $(β, γ)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $γ$ direction, differ a lot …
Within Fermionic Molecular Dynamics we investigate fragmentation of a compound system which was created in a heavy-ion collision at a beam energy in the Fermi energy domain and the decay of excited iron nuclei. We show that in FMD many-body correlations play an important role in the formation of fragments.
Directed and elliptic flow of light nuclei and hypernuclei in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV: Coalescence vs. Statistical Fragmentation
We simulate the fragmentation processes in the {$α$~$+$~Au~} collisions at a bombarding energy of 5 GeV/u using the simplified RQMD approach plus the statistical decay model. We find from the simulation that the angular-distribution of the intermediate mass fragments has a sideward peak, more strongly in the transverse direction than in the beam-direction, when the intermediate nucleus formed by the dynamical process has an annular eclipse shape, which explains the experimental results.
A prescription to incorporate the effects of nuclear flow on the process of multifragmentation of hot nuclei is proposed in an analytically solvable canonical model. Flow is simulated by the action of an effective negative external pressure. It favors sharpening the signatures of liquid-gas phase transition in finite nuclei with increased multiplicity and a lowered phase transition temperature.
The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Λ$Li. Many more data on low-lying states of $Λ$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Λ$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Λ$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativi…
The production of light nuclei and hypernuclei together with heavy baryons, both hyperons and $Δ$-baryons, in low density matter as found in stellar environments such as supernova or binary mergers is studied within relativistic mean-field models. Five light nuclei were considered together with three light hypernuclei. The presence of both hyperons and $Δ$-baryons shift the dissolution of clusters to larger densities and increase the abundance of clusters. This effect is larger the smaller the charge fraction and the higher the temperature. The couplings of the $Δ$-baryons were chosen imposing…
Nuclear multifragmentation is an important phenomenon, the study of which can throw light on reaction mechanism in heavy ion collisions at intermediate and high energies. Based on statistical and dynamical model studies, this thesis is concentrated mainly on, the following three aspects of nuclear multifragmentation reactions namely (i) production of exotic nuclei which are normally not available in the laboratory (ii) nuclear symmetry energy from heavy ion collisions at intermediate energies and (iii) Nuclear liquid-gas phase transition. In addition to these equivalence of statistical ensembl…
Simultaneous description of ordinary and hypernuclei masses by a single mass formula has been a great challenge in nuclear physics. Hyperon-separation energies of about forty Lambda($Λ$), three Lambda-Lambda($ΛΛ$), one Sigma($Σ$) and seven Cascade($Ξ$) hypernuclei have been experimentally found. Many of these nuclei are of light masses. We prescribe a new mass formula, called BWMH, which describes the normal and hypernuclei on the same footing. It is based on the modified-Bethe-Weizsäcker mass formula (BWM). BWM is basically an extension of the Bethe-Weizsäcker mass formula (BW) for light nucl…
Because of thermal expansion and residual interactions, hot nuclear fragments produced in multifragmentation reactions may have lower nucleon density than the equilibrium density of cold nuclei. In terms of liquid-drop model this effect can be taken into account by reducing the bulk energy of fragments. We study the influence of this change on fragment yields and isotope distributions within the framework of the statistical multifragmentation model. Similarities and differences with previously discussed modifications of symmetry and surface energies of nuclei are analyzed.
Pairing correlations play a very important role in atomic nuclei. Although several effective pairing interactions have been used in mean field calculations for nucleons, little is known about effective pairing interactions for hyperons. Based on the quark model, we propose a relationship between effective pairing interactions for hyperons and for nucleons; e.g., for $Λ$s, the strength of the pairing interaction is 4/9 of that for nucleons. A separable pairing force of finite range which has been widely applied to describing pairing correlations in normal nuclei is used to investigate pairing e…
We investigate the possibility to extract the symmetry energy from multifragmentation data. The applicability of the grandcanonical formula earlier proposed by Ono {\it et al.} [Phys. Rev. C {\bf 68}, 051601(R)] in the case of finite excited nuclei is tested within a microcanonical framework. Relatively good results are obtained except for large residual nuclei, especially when large sources are highly excited. Effects of secondary particle emission and the extent in which relevant information may be inferred from experimental observables are finally discussed.
We point out similarity of thermodynamic conditions reached in intermediate energy nuclear collisions and in supernova explosions. We show that a statistical approach, which has been previously applied for nuclear multifragmentation reactions, can be very useful for description of electro-neutral stellar matter. Then properties of hot unstable nuclei extracted from analysis of multifragmentation data can be used for construction of a realistic equation of state of supernova matter.
The study of hypernuclei in the quark mean-field model are extended from single-$Λ$ hypernuclei to double-$Λ$ hypernuclei as well as $Ξ$ hypernuclei (double strangeness nuclei), with a broken SU(3) symmetry for the quark confinement potential. The strength of the potential for $u,d$ quarks is constrained by the properties of finite nuclei, while the one for $s$ quark is fixed by the single $Λ$-nucleus potential at the nuclear saturation density, which has a slightly different value. Compared to our previous work, we find that the introduction of such symmetry breaking improves efficiently the …
We study the shape of $Λ$ hypernuclei in the full ($β,γ$) deformation plane, including both axially symmetric and triaxial quadrupole deformations. To this end, we use the constrained Skyrme Hartree-Fock+BCS method on the three-dimensional Cartesian mesh. The potential energy surface is analyzed for carbon hypernuclei as well as for sd-shell hypernuclei such as $^{27,29}_Λ$Si and $^{25,27}_Λ$Mg. We show that the potential energy surface in the ($β,γ$) plane is similar to each other between the hypernuclei and the corresponding core nuclei, although the addition of $Λ$ hyperon makes the energy …
A detailed comparison is made between the spin-orbit interactions in $Λ$ hypernuclei and ordinary nuclei. We argue that there are three major contributions to the spin-orbit interaction: 1) a short-range component involving scalar and vector mean fields; 2) a ''wrong-sign'' spin-orbit term generated by the pion exchange tensor force in second order; and 3) a three-body term induced by two-pion exchange with excitation of virtual $Δ(1232)$-isobars (a la Fujita-Miyazawa). For nucleons in nuclei the long-range pieces related to the pion-exchange dynamics tend to cancel, leaving room dominantly fo…
Information on Lambda-7Li, Lambda-9Be, Lambda-10B, Lambda-11B, Lambda-12C, Lambda-15N, and Lambda-16O from the Ge detector array Hyperball is interpreted in terms of shell-model calculations that include both Lambda and Sigma configurations with p-shell cores. It is shown that the data puts strong constraints on the effective Lambda-N interaction.
We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of largest cluster at different …
We study the disintegration of nuclei by strong electromagnetic fields induced by ultrarelativistic heavy ions. The proposed multi-step model includes 1) the absorption of a virtual photon by a nucleus, 2) intranuclear cascades of produced hadrons and 3) statistical decay of the excited residual nucleus. The combined model describes well existing data on projectile fragmentation at energy 200 GeV per nucleon. Electromagnetic multifragmentation of nuclei is predicted to be an important reaction mechanism at RHIC and LHC energies.
Using the quantum molecular dynamics model, we study the role of mass asymmetry of colliding nuclei on the fragmentation at the balance energy and on its mass dependence. The study is done by keeping the total mass of the system fixed as 40, 80, 160, and 240 and by varying the mass asymmetry of the ($η$ = $\frac{A_{T}-A_{P}}{A_{T}+A_{P}}$; where $A_{T}$ and $A_{P}$ are the masses of the target and projectile, respectively) reaction from 0.1 to 0.7. Our results clearly indicate a sizeable effect of the mass asymmetry on the multiplicity of various fragments. The mass asymmetry dependence of var…
We study the properties of the $Θ^+$ in nuclear matter and $Θ^+$ hypernuclei within the quark mean-field (QMF) model, which has been successfully used for the description of ordinary nuclei and $Λ$ hypernuclei. With the assumption that the non-strange mesons couple only to the $u$ and $d$ quarks inside baryons, a sizable attractive potential of the $Θ^+$ in nuclear matter is achieved as a consequence of the cancellation between the attractive scalar potential and the repulsive vector potential. We investigate the $Θ^+$ single-particle energies in light, medium, and heavy nuclei. More bound sta…
We address mixing of different baryonic states in hypernuclei and formation of strange nuclei of various kinds. First, production of neutron-rich Lambda hypernuclei by the (pi-,K+) reaction is considered, and one-step production via baryonic admixtures in the final as well as in the initial state is discussed. Then, the Lambda Lambda - Xi N mixing in p shell Lambda Lambda hypernuclei exemplified by $^{12}_{ΛΛ}$Be is studied. The last topic is devoted to production of Theta pentaquark nuclei (pentanuclei). We suggest a type of reactions with recoilless Theta production.
A model based on chiral SU(3)-symmetry in nonlinear realisation is used for the investigation of nuclei, superheavy nuclei, hypernuclei and multistrange nuclear objects (so called MEMOs). The model works very well in the case of nuclei and hypernuclei with one Lambda-particle and rules out MEMOs. Basic observables which are known for nuclei and hypernuclei are reproduced satisfactorily. The model predicts Z=120 and N=172, 184 and 198 as the next shell closures in the region of superheavy nuclei. The calculations have been performed in self-consistent relativistic mean field approximation assum…
In multifragmentation of hot nuclear matter, properties of fragments embedded in a soup of nucleonic gas and other fragments should be modified as compared with isolated nuclei. Such modifications are studied within a simple model where only nucleons and one kind of heavy nuclei are considered. The interaction between different species is described with a momentum-dependent two-body potential whose parameters are fitted to reproduce properties of cold isolated nuclei. The internal energy of heavy fragments is parametrized according to a liquid-drop model with density and temperature dependent …
We have investigated the properties of $Θ^{+}$ in nuclei within the framework of relativistic mean field. The coupling constants are educed with quark meson coupling model. There is strong attractive interaction for $Θ^{+}$-nucleus and $Θ^{+}$ can be bind in nuclei. The depth of optical potential for $Θ^{+}$ in nuclear matter is estimated.
We present results for the selfenergy of the $Θ^+$ pentaquark in nuclei associated with two sources: the $KN$ decay of the $Θ^+$ and the two meson baryon decay channels of the $Θ^+$ partners in an antidecuplet of baryons. The first source is shown to produce a small potential, unable to bind the $Θ^+$ in nuclei, while the second source gives rise to a large attractive potential. At the same time we show that the width of the $Θ^+$ in nuclei is small, such that, in light and medium nuclei, many bound $Θ^+$ states would appear with a separation between levels appreciably larger than the width of…
The binding energies of a range of nuclei and hypernuclei with atomic number A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron, H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n_f=3 dynamical light quarks using an isotropic clover discretization of the quark-action in three lattice volumes of spatial extent L ~ 3.4 fm, 4.5 fm and …
The $Λ^{\ast}$-hypernuclei, which are bound states of $Λ(1405)$ and nuclei, are discussed as a possible interpretation of the $\bar{K}$-nuclei. The Bonn and Nijmegen potentials are extended and used as a phenomenological potential between $Λ^{\ast}$ and $N$. The $K$-exchange potential is also considered in the $Λ^{\ast}$ and $N$ interaction. The two-body ($Λ^{\ast}N$) and three-body ($Λ^{\ast}NN$) systems are solved by a variational method. It is shown that the spin and isospin of the ground states are assigned as $Λ^{\ast}N(S=1, I=1/2)$ and $Λ^{\ast}NN(S=3/2, I=0)$, respectively. The binding …
Within the statistical multifragmentation model we study modifications of the surface and symmetry energy of primary fragments in the freeze-out volume. The ALADIN experimental data on multifragmentation obtained in reactions induced by high-energy projectiles with different neutron richness are analyzed. We have extracted the isospin dependence of the surface energy coefficient at different degrees of fragmentation. We conclude that the surface energy of hot fragments produced in multifragmentation reactions differs from the values extracted for isolated nuclei at low excitation. At high frag…
Within a combined approach we investigate the main features of the production of hyper-fragments in relativistic heavy-ion collisions. The formation of hyperons is modelled within the UrQMD and HSD transport codes. To describe the hyperon capture by nucleons and nuclear residues a coalescence of baryons (CB) model was developed. We demonstrate that the origin of hypernuclei of various masses can be explained by typical baryon interactions, and that it is similar to processes leading to the production of conventional nuclei. At high beam energies we predict a saturation of the yields of all hyp…
Sequential Clusterization of Light Nuclei and Hypernuclei in Heavy-Ion Collisions within a Wigner Function Coalescence Framework
Central China Normal University（华中师范大学）；University of Heidelberg（海德堡大学）；Johann Wolfgang Goethe University（约翰·沃尔夫冈·歌德大学）；GSI Helmholtz Center for Heavy Ion Research（GSI亥姆霍兹重离子研究中心）
Neutron and proton driplines of single-$Λ$ and double-$Λ$ hypernuclei, $Ξ^{-}$ hypernuclei as well as normal nuclei are studied within a relativistic mean field approach using an extended form of the FSU Gold Lagrangian density. Hyperons are found to produce bound nuclei beyond the normal nuclear driplines. Radii are found to decrease in hypernuclei near the driplines, in line with observations in light $Λ$ hypernuclei near the stability valley, The inclusion of a $Ξ^{-}$ introduces a much larger change in radii than one or more $Λ$'s.
A simultaneous description of non-strange nuclei and hypernuclei is provided by a single mass formula inspired by the spin-flavour SU(6) symmetry breaking. This formula is used to estimate the hyperon binding energies of Lambda, double Lambda, Sigma, Cascade and Theta hypernuclei. The results are found to be in good agreement with the available experimental data on 'bound' nuclei and relativistic as well as quark mean field calculations. This mass formula is useful to estimate binding energies over a wide range of masses including the light mass nuclei. It is not applicable for repulsive poten…
Closed shell charmed hypernuclei $^5_{Λ_c}$Li, $^{17}_{Λ_c}$F, $^{41}_{Λ_c}$Sc, $^{57}_{Λ_c}$Cu, $^{133}_{Λ_c}$Sb and $^{209}_{Λ_c}$Bi are calculated within Hartree-Fock approach by using three different force sets derived from microscopic Brueckner-Hartree-Fock calculations of $Λ$ hypernuclei. Ground state properties (binding energies, $Λ_c$ separation energies, $Λ_c$ single particle energies and $Λ_c$ densities) of charmed nuclei are examined. Due to the Coulomb repulsion between protons and the $Λ_c$ baryon, charmed hypernuclei are most bound for $16\leq$A$\leq 41$, where $^{17}_{Λ_c}$F can…
New experimental data on medium to heavy single Lambda hypernuclei revealed a much larger spin-orbit splitting than observed in older measurements of light hypernuclei. Taking into account particle threshold effects and the density-dependence of in-medium coupling constants the apparent suppression of spin-orbit strength in light hypernuclei as well as the spin-orbit structure observed in medium to heavy nuclei are explained in a unified manner within the density dependent relativistic hadron field theory. It is concluded that the most valuable information on the Lambda spin-orbit dynamics in …
The initial production and dynamical expansion of hot spherical nuclei are examined as the first stage in the projectile-multifragmentation process. The initial temperatures, which are necessary for entering the adiabatic spinodal region, as well as the minimum temperatures and densities, which are reached in the expansion, significantly differ for hard and soft equations of state. Additional initial compression, occurring in central collisions leads most likely to a qualitatively different multifragmentation mechanism. Recent experimental data are discussed in relation to the results of the p…
Shapes of light normal nuclei and $Λ$-hypernuclei are investigated using relativistic mean field approach. The FSUGold parametrization is used for this purpose. The addition of a $Λ$ is found to change the shape of the energy surface towards prolate. The deformation in a $Λ$-hypernucleus, when the hyperon is in the first excited state, is also discussed. The effect of the inclusion of the hyperon on the nuclear radius is generally small with one exception.
Properties of hypernuclei are studied in the context of a chiral Lagrangian which successfully describes ordinary nuclei. Lambda-Sigma^0 mixing arises from nondiagonal vertices in flavor space induced by the vector mesons and by the electromagnetic field. The set of Dirac equations for the coupled hyperon system is discussed. Results are presented for energy spectra and electromagnetic properties of hyperons in the nuclear environment. Simple estimates suggest that flavor mixing can lead to sizable changes in the lifetimes of Lambda hypernuclei.
In highly dissipative collisions between heavy ions, the optimal conditions to investigate different de-excitation channels of hot nuclei such as evaporation, fission or multifragmentation are well known. One crucial issue remains the excitation energy region where fission gives way to multifragmentation. In this paper, the onset of multi-fragment exit channels is investigated in terms of sequential fission. For the first time, the dynamical approach based on solving Langevin transport equations in multidimensional collective coordinate space is used to follow the de-excitation of highly excit…
