Critical temperature for the nuclear liquid-gas phase transition (from multifragmentation and fission)
V. A. Karnaukhov, H. Oeschler, A. Budzanowski, S. P. Avdeyev, A. S. Botvina, E. A. Cherepanov, W. Karcz, V. V. Kirakosyan, P. A. Rukoyatkin, I. Skwirczynska, E. Norbeck
Critical temperature Tc for the nuclear liquid-gas phase transition is stimated both from the multifragmentation and fission data. In the first case,the critical temperature is obtained by analysis of the IMF yields in p(8.1 GeV)+Au collisions within the statistical model of multifragmentation (SMM). In the second case, the experimental fission probability for excited 188Os is compared with the calculated one with Tc as a free parameter. It is concluded for both cases that the critical temperature is higher than 16 MeV.
A correlation between the production and kinematic properties of the fragments issued of fission and multifragmentation is established in the study of the reaction 136Xe+hydrogen at 1 GeV per nucleon, measured in inverse kinematics at the FRagment Separator (GSI, Darmstadt). Such observables are analysed in a comprehensive study, selected as a function of the decay mode, and related to the isotopic properties of the fragments in the intermediate-mass region. Valuable information can be deduced on the characteristics of the heaviest product in the reaction, which has been considered a fundament…
Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid--fog phase transition deep inside the spinodal region. The experimental data for p(8.1GeV) + Au collisions are analyzed. It is concluded that the decay process of hot nuclei is characterized by two size parameters: transition state and freeze-out volumes. The similarity between dynamics of fragmentation and ordinary fission is discussed. The IMF emission time is related to the mean rupture time at the multi-scission point, which corresponds to the kinetic freeze-out configuration.
Mostly for the purpose of applications for the energy and the environment and for the design of sources of neutrons or exotic nuclides, intense research has been dedicated to spallation, induced by protons or light projectiles at incident energies of around 1 GeV. In this energy range, while multifragmentation has still a minor share in the total reaction cross section, it was observed to have, together with fission, a prominent role in the production and the kinematics of intermediate-mass fragments, so as to condition the whole production of light and heavy nuclides. The experimental observa…
Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid-fog phase transition. The charge distributions of the intermediate mass fragments produced in p(3.6 GeV) + Au and p(8.1 GeV) + Au collisions are analyzed within the statistical multifragmentation model with the critical temperature for the nuclear liquid-gas phase transition Tc as a free parameter. The analysis presented here provides strong support for a value of Tc > 15 MeV.
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…
In Xe+Sn central collisions from 12 to 20 MeV/A measured with the INDRA 4$π$ multidetector, the three-fragment exit channel occurs with a significant cross section. In this contribution, we show that these fragments arise from two successive binary splittings of a heavy composite system. Strong Coulomb proximity effects are observed in the three-fragment final state. By comparison with Coulomb trajectory calculations, we show that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming compatible with quasi-simultaneous multifragmentation above 18…
Two roads are presently being followed in order to establish the existence of a liquid-gas phase transition in finite nuclear systems from nuclear reactions at high energy. The clean experiment of observing the thermodynamic properties of a finite number of nucleons in a container is presently only possible with the computer. Performed with advanced nuclear transport models, it has revealed the first-order character of the transition and allowed the extraction of the pertinent thermodynamic parameters. The validity of the applied theory is being confirmed by comparing its predictions for heavy…
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…
Multifragmentation is the dominant decay mode of heavy nuclear systems with excitation energies near their binding energies and is characterized by a multiple production of nuclear fragments with intermediate mass. At relativistic bombarding energies, multifragmentation may be observed in peripheral collisions of heavy symmetric systems or more central collisions of mass asymmetric systems. The decay properties indicate a high degree of equilibration and are well described by statistical multifragmentation models. Multifragmentation has been linked to the liquid-gas phase transition in finite …
An extensive study of GeV light-ion-induced multifragmentation and its possible interpretation in terms of a nuclear liquid-gas phase transition has been performed with the Indiana Silicon Sphere (ISiS)4 pi detector array. Measurements were performed with 5-15 GeV/c p, pbar, and pion beams incident on $^{197}$Au and 2-5 GeV $^3$He incident on $^{nat}$Ag and $^{197}$Au targets. Both the reaction dynamics and the subsequent decay of the heavy residues have been explored. The data provide evidence for a dramatic change in the reaction observables near an excitation energy of E*/A = 4-5 MeV per re…
The distribution of fragments produced in events involving the multifragmentation of excited sources is studied for peripheral Au + Au reactions at 35 A.MeV. The Quasi-Projectile has been reconstructed from its de-excitation products. An isotropic emission in its rest frame has been observed, indicating that an equilibrated system has been formed. The excitation energy of the Quasi-Projectile has been determined via calorimetry. A new event by event effective thermometer is proposed based on the energy balance. A peak in the energy fluctuations is observed related to the heat capacity, suggest…
The equation of state of nuclear matter suggests that at suitable beam energies the disassembling hot system formed in heavy ion collisions will pass through a liquid-gas coexistence region. Searching for the signatures of the phase transition has been a very important focal point of experimental endeavours in heavy ion collisions, in the last fifteen years. Simultaneously theoretical models have been developed to provide information about the equation of state and reaction mechanisms consistent with the experimental observables. This article is a review of this endeavour.
Thermal multifragmentation of hot nuclei is interpreted as the nuclear liquid-fog phase transition inside the spinodal region. The experimental data for p(8.1GeV) + Au collisions are analyzed within the framework of the statistical multifragmentation model (SMM) for the events with emission of at least two IMFs. It is found that the partition of hot nuclei is specified after expansion to a volume equal to Vt = (2.6+-0.3) Vo, with Vo as the volume at normal density. However, the freeze-out volume is found to be twice as large: Vf = (5+-1) Vo.
An overview of the recent progress in the studies of nuclear multifragmentation is presented. Special emphasis is put on the exploration of isotopic trends in nuclear multifragmentation and the possibilities to extract physical information related to the nuclear equation of state. Relevant experimental methods of isotope identification are described. The isotopic composition of fragments is used to extract the values of thermodynamical observables of the system undergoing multifragmentation such as temperature and chemical potentials. Various methods for extraction of thermodynamical variables…
Recent analyses of multifragmentation in terms of Fisher's model and the related construction of a phase diagram brings forth the problem of the true existence of the vapor phase and the meaning of its associated pressure. Our analysis shows that a thermal emission picture is equivalent to a Fisher-like equilibrium description which avoids the problem of the vapor and explains the recently observed Boltzmann-like distribution of the emission times. In this picture a simple Fermi gas thermometric relation is naturally justified. Low energy compound nucleus emission of intermediate mass fragment…
For nuclei in five different mass regions the critical temperatures, at which the surface tension vanishes, are derived from information on the liquid branch of the coexistence curve. These critical temperatures increase with increasing mass and, for higher masses are well above recently reported critical temperatures obtained from Fisher Droplet model and percolation model analyses. However, for the lowest mass region nuclei, with 30<A<60, this analysis indicates that nucleonic matter has been produced essentially at the critical point, characterized by Tc and rho_c.
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…
Isotopic distributions for light particles and intermediate mass fragments have been measured for 112Sn+112Sn, 112Sn+124Sn, 124Sn+112Sn and 124Sn+124Sn collisions at E/A=50 MeV. Isotope, isotone and isobar yield ratios are utilized to obtain an estimate of the isotopic composition of the gas phase, i.e., the relative abundance of free neutrons and protons at breakup. Within the context of equilibrium calculations, these analyses indicate that the gas phase is enriched in neutrons relative to the liquid phase represented by bound nuclei.
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.
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 brief description of the IntraNuclear cascade, preequilibrium, evaporation, fission, coalescence, and Fermi breakup models used by the last versions of our CEM and LAQGSM event generators is presented, with a focus on our latest development of all these models. The recently developed "S" and "G" versions of our codes, that consider multifragmentation of nuclei formed after the preequilibrium stage of reactions when their excitation energy is above 2A MeV using the Statistical Multifragmentation Model (SMM) code by Botvina et al. ("S" stands for SMM) and the fission-like binary-decay model GE…
For the past decade, intense experimental effort has been devoted to the search for a liquid-gas phase transition in highly excited nuclei. Now, synthesis of the large body of existing multifragmentation data provides a strong case for identification of this phenomenon. In this presentation we discuss several salient features of the data that support their interpretation in terms of a spinodal liquid-gas phase transition.
A systematic analysis of the multifragmentation (MF) in fully reconstructed events from 1A GeV Au, La and Kr collisions with C has been performed. This data is used to provide a definitive test of the variable volume version of the statistical multifragmentation model (SMM). A single set of SMM parameters directly determined by the data and the semi-empiricalmass formula are used after the adjustable inverse level density parameter, $ε_{o}$ is determined by the fragment distributions. The results from SMM for second stage multiplicity, size of the biggest fragment and the intermediate mass fra…
The charge distribution of the intermediate mass fragments produced in p (8.1 GeV) + Au collisions is analyzed in the framework of the statistical multifragmentation model with the critical temperature for the nuclear liquid-gas phase transition $T_c$ as a free parameter. It is found that $T_c=20\pm3$ MeV (90% CL).
Longitudinal ternary and binary fission barriers of $^{36}$Ar, $^{56}$Ni and $^{252}$Cf nuclei have been determined within a rotational liquid drop model taking into account the nuclear proximity energy. For the light nuclei the heights of the ternary fission barriers become competitive with the binary ones at high angular momenta since the maximum lies at an outer position and has a much higher moment of inertia.
We have demonstrated that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au197, Sn124, La124 and Kr78 at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent tau with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have demonstrated that nuclear multifragmentat…
Isotopic effects in spectator fragmentations following heavy-ion collisions at relativistic energies are investigated using data from recent exclusive experiments with SIS beams at GSI. Reactions of 12C on 112,124Sn at incident energies 300 and 600 MeV per nucleon were studied with the INDRA multidetector while the fragmentation of stable 124Sn and radioactive 107Sn and 124La projectiles was studied with the ALADIN spectrometer. The global characteristics of the reactions are very similar. This includes the rise and fall of fragment production and deduced observables as, e.g., the breakup temp…
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.
We have demonstrated that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au197, Sn124, La124 and Kr78 at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent tau with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have demonstrated that nuclear multifragmentat…
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.
The study of liquid-gas phase transition in heavy ion collisions has generated a lot of interest amongst the nuclear physicists in the recent years. In heavy ion collisions, there is no direct way of measuring the state variables like entropy, pressure, energy and hence unambiguous characterization of phase transition becomes difficult. This work proposes new signatures of phase transition that can be extracted from the observables which are easily accessible in experiments. It is observed that the temperature dependence of the first order derivative of the order parameters in nuclear liquid g…
A simple model is proposed to examine the isotopic yields of the fragments from binary fission. For a given charge partition the peaks and widths in the isotope distributions are studied both with the liquid-drop model and with shell modifications. The basis for isoscaling is also explored. The symmetry energy plays a dominant role in both the distributions and the isoscaling behavior. A systematic increase in the isoscaling parameter, $α$, with the proton number of the fragment element is predicted in the context of the liquid-drop model. Deviations arising from shell corrections are explored…
Fission excitation functions of He-3 and He-4 induced compound nuclei are shown to scale exactly according to the Bohr-Wheeler transition state prediction once the shell effects are accounted for. The presented method furthermore allows one to model-independently extract values for the shell effects which are in good agreement to those obtained from liquid-drop model calculations. The fact that no deviations from the transition state method have been observed within the experimentally investigated excitation energy regime allows one to assign an upper limit for the transient time of 10 zs.
Charge partitions and distributions of fragments emitted in multifragmentation of fused systems produced in central collisions are studied over the incident energy range 32-50 MeV per nucleon. Most of the charged products are well identified thanks to the high performances of the INDRA 4pi array. Supported by dynamical calculations, charge correlations are used t$ evidence, or not, spinodal instabilities and consequently the liquid-gas coexistence region over the considered incident energy range. It was claimed in the last few years that mass/charge distributions should follow a power law beha…
Reactions of nuclear multifragmentation of excited finite nuclei can be interpreted as manifestation of the nuclear liquid-gas phase transition. During this process the matter at subnuclear density clusterizes into hot primary fragments, which are located in the vicinity of other nuclear species. In recent experiments there were found evidences that the symmetry and surface energies of primary fragments change considerably as compared to isolated cold or low-excited nuclei. The new modified properties of primary fragments should be taken into account during their secondary de-excitation.
Analyses of multifragmentation in terms of the Fisher droplet model (FDM) and the associated construction of a nuclear phase diagram bring forth the problem of the actual existence of the nuclear vapor phase and the meaning of its associated pressure. We present here a physical picture of fragment production from excited nuclei that solves this problem and establishes the relationship between the FDM and the standard compound nucleus decay rate for rare particles emitted in first-chance decay. The compound thermal emission picture is formally equivalent to a FDM-like equilibrium description an…
For many years it has been speculated that excited nuclei would undergo a liquid to vapor phase transition. For even longer, it has been known that clusterization in a vapor carries direct information on the liquid- vapor equilibrium according to Fisher's droplet model. Now the thermal component of the 8 GeV/c pion + 197Au multifragmentation data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model, thus providing the strongest evidence yet of the liquid to vapor phase transition.
A natural nuclear fission reactor with a power output of 3- 10 terawatt at the center of the earth has been proposed as the energy source of the earth's magnetic field. The proposal can be directly tested by a massive liquid scintillation detector that can detect the signature spectrum of antineutrinos from the geo-reactor as well as the direction of the antineutrino source. Such detectors are now in operation or under construction in Japan/Europe. However, the clarity of both types of measurements may be limited by background from antineutrinos from surface power reactors. Future U. S. detect…
ALADIN multifragmentation data show features characteristic of a critical behavior, which are very well reproduced by a bond percolation model. This suggests, in the context of the lattice gas model, that fragments are formed at nearly normal nuclear densities and temperatures corresponding to the Kertesz line. Calculations performed with a lattice gas model have shown that similarly good reproduction of the data can also be achieved at lower densities, particularly in the liquid-gas coexistence region.
Fragment production in central collisions of Xe+Sn has been systematically studied with the INDRA multidetector from 25 to 150 AMeV. The predominant role of collision dynamics is evidenced in multiple intermediate mass fragment production even at the lowest energies, around the so-called "multifragmentation threshold". For beam energies 50 AMeV and above, a promising agreement with suitably modified Antisymmetrised Molecular Dynamics calculations has been achieved. Intriguingly the same reactions have recently been interpreted as evidence for a liquid-gas phase transition in thermodynamically …
The study of liquid gas phase transition in fragmentation of nuclei in heavy ion collisions has been extended to the strangeness sector using the statistical model for multifragmentation. Helmholtz's free energy, specific heat and few other thermodynamic observables have been analyzed in order to examine the occurence of phase transition in the strange matter. The bimodal behaviour of the largest cluster formed in fragmentation also strongly indicates coexistence of both the phases. The presence of hyperons strengthens the signals and also shifts the transition temperature to lower values.
