Probing the nuclear symmetry energy with heavy-ion reactions induced by neutron-rich nuclei

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 theoretical progress on probing the high density behaviors of the nuclear symmetry energy in heavy-ion reactions induced by high energy radioactive beams.      

γ-Spectroscopy of light neutron-rich nuclei after secondary reactions at relativistic energies

After the fragmentation reaction of ⁵⁰Ti on ⁹Be at 330 MeV/u, more than 30 neutron-rich isotopes from B to Ca were selected by the fragment separator FRS at GSI. Peripheral collisions with a secondary Pb target at relativistic energies were used to study the excited states of these isotopes. De-excitation γ-rays were detected with the Darmstadt-Heidelberg Crystal Ball spectrometer. The first results demonstrate the feasibility of in-beam γ-spectroscopy at relativistic energies.     

Fragmentation of light nuclei by intermediate energy photons

New data on the fragmentation of carbon nuclei by photons with energies from 800 to 1500 MeV, obtained in the collaboration GRAAL, are presented. These data include the yields of heavier fragments than nucleons. Comparison of new results with literature data, obtained with real and virtual photons in reactions with electrons and relativistic ions (Coulomb dissociation) is done using a general approach in frame of the Weizsäcker–Williams model. Possible reasons for the observed differences between them are discussed.     

Effects of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy-ion collisions.     

Isotopic distributions of fragments in intermediate energy heavy ion reactions

We use measured isotopic yields of fragments produced in the reaction ⁴⁰Ar on ⁶⁸Zn at 27.6 MeV/nucleon in order to see whether these quantities may constitute a test which allows to gain some insight into the projectile fragmentation process. We compare the experimental distributions to those obtained with the multisequential decay model which we developed previously, the projectile break-up model proposed by Friedman and abrasion-ablation model calculations.     

Emission order of light particles and light fragments from hot nuclei followed by binary fission

Emission orders of light charged particles and Li fragments from highly excited fissioning nuclei in the reaction of ⁴⁰Ar+¹⁹⁷Au at E _beam /A=25 MeV have been studied by measuring difference velocity distributions of two correlated particles at small relative angles in coincidence with two fission fragments. By comparing the data with three-body trajectory calculations, we found that high velocity deuterons are emitted prior to high velocity Li fragments but low velocity deuterons are emitted after low velocity Li fragments. On the other hand, no preferential emission was observed among light particles, such as protons and deuterons. Furthermore, the emission orders are found to depend only weakly on the mass asymmetry of fission fragments. Received: 3 June 1997 / Revised version: 23 July 1997     

Phenomenological analysis of intermediate mass fragments emission in alpha induced reactions

Intermediate mass fragment emission in induced reactions on Al and Ti at 60 and 104 MeV, respectively has been analysed using phenomenological moving source model. Fragment emission at backward angles is found to be well explained by a single fusion-like source, whereas for forward angles an additional intermediate velocity source is required to explain the data. The relative contribution of the intermediate velocity source decreases sharply with angle for lower energies and it extends significantly to larger angles in the higher energy reaction. The fractional momentum transfer for the fusion-like source is in agreement with the corresponding Viola systematics value in the case of +Al reaction, whereas for +Ti reaction, it is larger than that obtained from the Viola systematics. The degree of incompleteness (in momentum transfer) is found to be fragment dependent; incompleteness being more for lighter fragments and vice-versa.     

Structure of light neutron-rich nuclei and mechanism of elastic proton scattering

Differential cross sections for elastic p ⁶He, p ⁸Li, and p ⁹Li scattering at two energies of 70 and 700 MeV per nucleon were calculated within the Glauber theory of multiple diffractive scattering. Threeparticle wave functions (α-n-n for ⁶He, α-t-n for ⁸Li, and ⁷Li-n-n for ⁹Li) were used for realistic potentials of intercluster interactions. The sensitivity of elastic scattering to proton-nucleus interaction and to the structure of nuclei was explored. In particular, the dependence of the differential cross section on the contribution of higher order collisions, on scattering on the core and peripheral nucleons, and on the contribution of small wave-function components and their asymptotic behavior was determined. A comparison with available experimental data and with the results of calculations within different formalisms was performed.     

Yield of fission fragments from the photofission of actinide nuclei

Yields of the ¹⁰¹Mo, ¹³⁵I, and ^135m Cs isotopes from the photofission of the actinide nuclei ²³²Th ²³⁸U, and ²³⁷Np are measured. These fission fragments have specific nuclear structure features or are of practical use. The measurements are performed in the bremsstrahlung from the microtron of the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research (JINR) at an electron energy of 22 MeV. The yields of the fragments are measured by the activation method using a γ radiation HPGe detector.     

A theory of intermediate structure,overlapping resonances and photonuclear reactions in light nuclei

Starting from a many body Hamiltonian a general theory involving intermediate structures and overlapping resonances in nuclear reaction has been worked out. This treatment, based on Trefftz's work on dielectronic recombination in atomic physics, avoids explicit use of projection operators and all relevant quantities like decay widths and energy shifts are explicitly expressed in terms of two body matrix elements. In particular, attention has been focused on the interaction of bound states among themselves and then on the coupling of the continuum with these interacting bound states. For the case of overlapping resonances, it is shown that in general one cannot take a simple energy average of the resonant amplitudes, and explicit equations for this case have been obtained. This microscopic theory also provides a justification of the model of Duke, Malik, and Firk in explaining the intermediate structure in giant dipole resonance region of ¹⁶O and ²⁸Si. However, the formalism is a general one and is suitable for the study of intermediate structure involving isolated and overlapping resonances for many types of reactions.     

Correlations of projectile-like fragments in heavy-ion reactions at Fermi energy

Correlations between pairs of projectile-like fragments, emitted by the system ¹⁶O$ + $¹⁹⁷Au at the laboratory bombarding energy of 515MeV, have been studied under two stipulated conditions: 1) at least one member of the pair is emitted at an angle less than the grazing angle for the system, 2) both the members of the pair are emitted at angles larger than the grazing angle. A surprisingly large difference, by more than an order of magnitude, is found between the correlations for the two cases. This observation could be explained on the basis of a simple semi-classical break-up model. Further analysis of the variation of the charge correlation function with the difference in the nuclear charges of the correlated pair showed trends which are consistent with an “inelastic break-up process”, in which the projectile breaks up at the radius of contact, in such a way that, one fragment (preferably the lighter) is emitted to one side within the grazing angle, while the other orbits around the target nucleus for a while and emerges on the other side, at a negative scattering angle, much like in a deep inelastic scattering.     

Quasielastic knockout of light fragments from 12C and 16O nuclei by intermediate-energy pions

Quasielastic deuteron and triton knockout from ¹²C and ¹⁶O nuclei has been studied infull kinematics using a 0.72-GeV/c pion beam. The momentum distributions of the intranuclear quasideuteron motion, excitation-energy spectra of the residual nuclei, and the effective numbers N _d ^eff of quasideuterons are determined. The parameters of the quasideuteron intranuclear motion are in reasonable agreement with the results obtained in other beams. The N _d ^eff in the nuclei from ⁶Li to ¹⁶O measured in full kinematics are virtually independent of the atomic number in contrast to the analogous values in the inclusive deuteron-knockout reaction induced by protons. The phenomenon of triton knockout from these nuclei is observed, which makes possible estimation of the cross section of backward pion-triton elastic scattering in yet unexplored regions of energy and momentum transfer.     

Symmetry energy from neutron-rich fragments in heavy-ion collisions, and its dependence on incident energy, and impact parameters

The yields of fragments produced in the 60Ni+ 12C reactions at 80 A and 140 A MeV, and with maximum impact parameters of 1.5, 2 and 7.3 fm at 80 A MeV are calculated by the statistical abrasion-ablation model. The yields of fragments are analyzed by the isobaric yield ratio (IYR) method to extract the coefficient of symmetry energy to temperature (asym/T ). The incident energy is found to influence asym/T very little. It’s found that asym/T of fragments with the same neutron-excess I = N-Z increases when A increases, while asym/T of isobars decreases when A increases. The asym/T of prefragments is rather smaller than that of the final fragments, and the asym/T of fragments in small impact parameters is smaller than that of the larger impact parameters, which both indicate that asym/T decreases when the temperature increases. The choice of the reference IYRs is found to have influence on the extracted a sym /T of fragments, especially on the results of the more neutron-rich fragments. The surface-symmetry energy coefficient (bs/T ) and the volume-symmetry energy coefficient (bv/T) are also extracted, and the bs/bv is found to coincide with the theoretical results.     

Polarized recoil nuclei from nuclear reactions induced by polarized lithium ions

The production of vector polarized recoil nuclei was investigated for nuclear reactions initiated by vector polarized⁶Li and⁷Li beams of energies up to 20 MeV. The vector polarization was detected by theβ-asymmetry of the decaying recoil nuclei implanted into various stopper materials. Considerable polarization values were observed for⁸Li produced in the systems⁷Li+⁹Be,⁷Li+⁷Li and⁶Li+⁷Li, and for¹²B in the systems⁷Li+⁷Li and⁶Li+¹¹B. However, no polarization has been observed for heavier nuclei with unknown nuclear moments. The relaxation of the vector polarization of⁸Li implanted into various stopper materials at room temperature was investigated in detail. For a gold stopper it was found to be much larger when compared to earlier results.     

Production of fast fragments by bombarding light nuclei with intermediate-energy protons

The high-energy parts of the spectra of ³H, ³He and ⁴He nuclei obtained in bombarding Li, Be and C targets with 665 MeV protons as well as the spectra of fast deuterons as a function of the proton energy (from 380 to 665 MeV) at a lab angle of 5.5° have been measured. The mechanisms of the interactions of intermediate-energy protons with light nuclei are discussed. It is found that the production of fast nuclear fragments at a small angle can be explained to a large extent by direct nuclear reactions of two types, i.e. quasielastic scattering and pion production processes on clusters.     

中能重离子碰撞中晕核反应动力学

基于同位旋相关量子分子动力学研究了中子晕核和质子晕核的核反应动力学，着重研究了松散的晕结构对于重离子碰撞中的碎裂和动量耗散中的特殊作用. 为了突出晕核松散结构在反应动力学中的特殊作用. 同时计算了在完全相同入射道条件下相等质量稳定弹核引起核反应. 通过对晕核和稳定核核反应动力学结果的对比分析，发现晕核的松散结构对核反应动力学的作用和影响是重要的. 如这种松散结构明显的增加了碎裂多重性；相反, 减小了原子核阻止(动量耗散). 关键词： 中子晕核 质子晕核 重离子碰撞 核反应动力学     

Isomer ratios of products from photonuclear reactions on silver and indium nuclei at γ ray energies above 35 MeV

The paper reports the results of measuring and calculating isomer ratios of products from photonuclear reactions with multiple emission of particles occurring on silver and indium nuclei at γ ray energies higher than energies of the giant dipole resonance. The technique of measuring the induced activity of irradiated samples by a semiconductor spectrometer with detector of highly pure germanium was used to obtain the isomer ratios. The TALYS code was employed to analyze agreement of the theoretical calculations and the experimental data.     

A microscopic calculation of angular and energy distributions of light fragments in deeply inelastic heavy-ion reactions

A random-matrix model for the form factors connecting channels corresponding to high intrinsic excitation energy of either fragment is used to calculate energy-averaged cross sections in deeply inelastic heavy-ion reactions. The distribution of the form factors is determined microscopically. The calculation yields differential cross sections without any fit parameters. Results for Kr- and Bi-induced reactions are compared with the data.