Scaling property in one-nucleon removal reactions induced by exotic nuclei

Assuming a core plus valence nucleon structure, one-nucleon removal reaction is investigated within the framework of few-body Glauber theory. Fermi-type distribution is used for the core density, while the wavefunction of the valence nucleon is calculated by solving the single particle eigeuvalue problem of the SchrSdinger equation with the Woods-Saxon potential. The parallel momentum distribution (P//) of the fragments is calculated for isotopes with 3 < Z < 18. A remarkable scaling property is observed from the dependence of the dimensionless quantity R2v/R2c on the full width at half maximum of the parallel momentum distribution (FWHMp//). R2v/R2c is a measure of the exotic extent of the nuclear halo. Based on the obtained scaling law, FWHMp// can be used as an experimental observable to extract R2v/R2c and measure the exoticextent for the nuclear halo.     

丰中子奇异核17B的实验研究

在兰州重离子加速器国家实验室(HIRFL)放射性次级束流线(RIBLL)上,用束流透射法测量了丰中子奇异核¹⁷B与C靶反应的总截面.假定¹⁷B具有¹⁵B(核芯)＋2n结构,采用Gauss＋HO形式的密度分布和零力程Glauber模型进行计算的结果可以很好地拟合实验数据,并得出¹⁷B的密度分布有一个很大的弥散,表明¹⁷B是双中子晕核. 关键词： 丰中子奇异核 反应总截面 Glauber模型 密度分布     

Production cross sections for exotic nuclei with multinucleon transfer reactions

The main progresses in the multinucleon transfer reactions at energies close to the Coulomb barrier are reviewed. After a short presentation of the experimental progress and theoretical progress, the predicted production cross sections for unknown neutron-rich heavy nuclei and the trans-uranium nuclei are presented.     

Probing the structure of exotic nuclei by transfer reactions

Low energy single nucleon transfer reactions are proposed as a tool to investigate the structure of nuclei far off stability. Experimental concepts and conditions are discussed, in particular high resolution γ-ray spectroscopy after single nucleon pickup reactions. Nuclear structure is described by Skyrme Hartree-Fock calculations including pairing. As representative examples, binding energies, radii and wave functions for Mg and Sn isotopes are calculated. In the neutron deficient Mg isotopes a proton skin is found. At the neutron driplines the Mg and Sn isotopes develop extended neutron skins. The nuclear structure results are used in DWBA and EFR-DWBA transfer calculations. Single nucleon transfer reactions of ^32,36Mg and exotic Sn beams on targets ranging from ²H to ²⁴Mg in inverse kinematics are explored. The one-nucleon transfer cross sections decrease strongly for high-Z targets. An impact parameter analysis shows that the transfer process is selective on the tails of the wave functions. The largest cross sections are obtained for ²H and ⁹Be targets at incident energies of E _lab = 2-5 MeV/u. The energy-momentum dependence is closely related to the special properties of wave functions of weakly bound states. Two-neutron (p,t) stripping reactions are studied for a ⁶He projectile. A strong competition of sequential and direct processes is found at low energies. Received: 1 October 1997 / Revised version: 25 November 1997     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

Momentum Distribution of a Fragment and Nucleon Removal Cross Section in the Reaction of Halo Nuclei

Recently the research on the halo structure of drip-line nuclei has shown some interesting properties of the existence of one or more halo nucleons. In the framework of few-body Glauber model, the momentum distribution of a fragment and nucleon removal cross section in the reaction of halo nuclei is presented and extended to nuclei having more than one halo nucleons. The reaction mechanism is treated with and without taking account of the final-state interaction. The wave function of removal halo nucleons in the continuum state is modified by imposing an orthogonal condition to the bound state. An analytical expression of the longitudinal momentum distribution of the fragment is derived when the bound state wave function of halo nucleons is taken as a Gaussian-type function. This is useful in the further investigation on the structure of halo nuclei.     

Theoretical study on production cross sections of exotic actinide nuclei in multinucleon transfer reactions

Within the dinuclear system(DNS) model, the multinucleon transfer reactions ~(129,136)Xe +~(248)Cm,~(112)Sn+~(238)U, and ~(144)Xe +~(248)Cm are investigated. The production cross sections of primary fragments are calculated with the DNS model. By using a statistical model, we investigate the influence of charged particle evaporation channels on production cross sections of exotic nuclei. It is found that for excited neutron-deficient nuclei the charged particle evaporation competes with neutron emission and plays an important role in the cooling process. The production cross sections of several exotic actinide nuclei are predicted in the reactions ~(112)Sn +~(238)U and ~(136,144)Xe +~(248)Cm.Considering the beam intensities, the collisions of ~(136,144)Xe projectiles with a ~(248)Cm target for producing neutron-rich nuclei with Z =92-96 are investigated.     

Semiclassical description of analyzing powers in one-nucleon transfer reactions induced by 44MeV polarized 7Li ions on 120Sn

Analyzing powers of various ranks for the reaction ${}^{120}\text{Sn(}{}^7\text{L}$, ⁶Li) at E_lab = 44 MeV have been measured as functions of scattering angle and Q-value. The reaction is understood semiclassically as transfer of the neutron from one reaction partner to the other during their relative motion on classical trajectories. An approximate evaluation of transfer amplitudes is presented which takes care of the relative magnitude of amplitudes for various spin quantum numbers and also of the discontinuity of the trajectory angular momentum in the interaction point. Thus simple formulae for analyzing powers are derived. All the characteristic features of the data are reproduced within this model.     

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

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.      

Odd-even effect in fragment angular momentum in low-energy fission of actinides

Quantitative explanation for the odd-even effect on fragment angular momenta in the low-energy fission of actinides have been provided by taking into account the single particle spin of the odd proton at the fragment’s scission point deformation in the case of odd-Z fragments along with the contribution from the population of angular momentum bearing collective vibrations of the fissioning nucleus at scission point. The calculated fragment angular momenta have been found to be in very good agreement with the experimental data for fragments in the mass number region of 130–140. The odd-even effect observed in the fragment angular momenta in the low-energy fission of actinides has been explained quantitatively for the first time.      

Charged-particle pseudorapidity distributions in Au+Au collisions at RHIC

Using the Glauber model, we present the formulas for calculating the numbers of participants,spectators and binary nucleon-nucleon collisions. Based on this work, we get the pseudorapidity distributions of charged particles as the function of the impact parameter in nucleus-nucleus collisions. The theoretical results agree well with the experimental observations made by the BRAHMS Collaboration in Au+Au collisions at √SNN=200 GeV in different centrality bins over the whole pseudorapidity range.     

放射性束引起的重离子碰撞中敏感于对称能的几个观测量

利用同位旋与动量相关的强子输运模型，我们研究了放射性束引起的中能重离子碰撞中几个观测量的对称能效应。我们发现自由核子发射的非对称度的快度分布，中快度中－质比的横动量分布，的动能分布，以及同位旋相分化（fractionation）的时间演化都敏感于对称能。     

Pseudorapidity distribution of multiplicity in Au Au collisions at (S_(NN))~(1/2)=200 GeV

Using the Glauber model,we discuss the number of binary nucleon-nucleon collisions in heavy-ion collisions.Based on the latter,after considering the effect of energy loss of the nucleons in multiple colli- sions,we derive the pseudorapidity distribution of the multiplicity as a function of the impact parameter in nucleus-nucleus collisions.Using this,we analyze the experimental measurements carried out by the BRAHMS Collaboration in Au Au collisions at Pseudorapidity distribution of multiplicity in Au Au collisions at (S_(NN))~(1/2)=200 GeV)=200 GeV.The results are in good agreement with the experi- mental observations.     

Big deformation in 17C

Reaction and interaction cross sections of 17C on a carbon target have been re-analyzed using the modified Glauber model. The analysis with a deformed Woods-Saxon density/potential suggests a big deformation structure for 17C. The existence of a tail in the density distribution supports the possibility of it being a one-neutron halo structure. Under a deformed core plus a single-particle assumption, analysis shows a dominant d-wave of the valence neutron in 17C.     

Charged-particle pseudorapidity distributions in Au+Au collisions at RHIC

Using the Glauber model, we present the formulas for calculating the numbers of participants, spectators and binary nucleon-nucleon collisions. Based on this work, we get the pseudorapidity distributions of charged particles as the function of the impact parameter in nucleus-nucleus collisions. The theoretical results agree well with the experimental observations made by the BRAHMS Collaboration in Au＋Au collisions at √^SNN=200 GeV in different centrality bins over the whole pseudorapidity range.     

Big deformation in ~(17)C

Reaction and interaction cross sections of ¹⁷C on a carbon target have been re-analyzed using the modified Glauber model. The analysis with a deformed Woods-Saxon density/potential suggests a big deformation structure for ¹⁷C. The existence of a tail in the density distribution supports the possibility of it being a one-neutron halo structure. Under a deformed core plus a single-particle assumption, analysis shows a dominant d-wave of the valence neutron in ¹⁷C.     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Degree and wealth distribution in a network induced by wealth

A network induced by wealth is a social network model in which wealth induces individuals to participate as nodes, and every node in the network produces and accumulates wealth utilizing its links. More specifically, at every time step a new node is added to the network, and a link is created between one of the existing nodes and the new node. Innate wealth-producing ability is randomly assigned to every new node, and the node to be connected to the new node is chosen randomly, with odds proportional to the accumulated wealth of each existing node. Analyzing this network using the mean value and continuous flow approaches, we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node. From this relation, we show that the degree distribution of the network induced by wealth is scale-free. We also show that the wealth distribution has a power-law tail and satisfies the 80/20 rule. We also show that, over the whole range, the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the Bouchaud-Mèzard model, even though the mechanism for producing wealth is quite different in our model. Further, we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log-normal distribution, while for the richest, the cumulative wealth distribution has a power-law behavior.