X‐ray spectrometry: a powerful tool for the measurement of complete fusion of weakly bound nuclei

We describe how the method of detection of delayed K x‐rays produced by the electron capture decay of the residual nuclei can be a powerful tool in the investigation of the effect of the breakup process on the complete fusion (CF) cross‐section of weakly bound nuclei at energies close to the Coulomb barrier. This is presently one of the most interesting subjects under investigation in the field of low‐energy nuclear reactions, and the difficult experimental task of separating CF from the incomplete fusion (ICF) of one of the breakup fragments can be achieved by the x‐ray spectrometry method. We present results for the fusion of the ⁹Be + ¹⁴⁴Sm system. Copyright © 2008 John Wiley & Sons, Ltd.     

用QMD模型研究晕核 11 Be+208Pb的熔合机制

通过用QMD模型研究晕核^11Be ^208Pb的近垒熔合反应,发现晕核引起的熔合反应中,并存着两种相互竞争的机制：一方面当入射晕核^11Be靠近靶核时,由于^11Be是弱束缚体系,与靶核的相互作用可使其很容易破裂或少数核子被靶核俘获形成核子转移反应,从而对于熔合表现出压制;另一方面当^11Be的少数中子进入靶核并与靶核相互作用而使得靶核有些激发,而使局部半径增大,导致熔合势垒降低,熔合截面增强。用QMD模型计算出的熔合截面与实验值基本符合,垒附近表现出增强效应。     

On the information value of angular distributions in elastic scattering of heavy ions

A method is developed for computing the total cross section σ_F of complete and incomplete fusion, quasifission, and deep-inelastic collisions, as well as the total cross section σ_D of peripheral reactions, on the basis of analysis of angular distributions for elastic scattering of heavy ions. The method makes it possible, on a unified basis, to explain the mechanism of formation of σ_F and σ_D both for strongly and for weakly bound ions. The method permits the calculation of quantitative characteristics of fusion enhancement (and, accordingly, suppression of peripheral reactions) for strongly bound ions and, conversely, the suppression of fusion (and, accordingly, enhancement of peripheral reactions) for weakly bound ions. The potential of the method is demonstrated for two systems, ¹⁶O+²⁰⁸Pb and ⁹Be+²⁸Si, the projectile ion being strongly bound in the former system and weakly bound in the latter one.     

A systematic study of the fission and evaporation residue excitation functions in complete fusion reactions with weakly bound stable nuclei

We carry out a systematic study on the fusion-fission and evaporation residue excitation functions for the reactions of ^6,7Li, ⁹Be, ^10,11B + ²⁰⁹Bi and ^6,9Li, ⁹Be + ²⁰⁸Pb, in which the projectiles are loosely bound and have low threshold energies against breakup. The fusion cross sections are calculated by the coupled-channel model. The compound nuclei decay are analyzed with the standard statistical model. The fission and evaporation residue excitation functions are well reproduced by our calculations, proving the validity of the standard statistical model in describing the compound nuclei decay in these characteristic reactions. For the compound nuclei with A=215-220 and Z=86-88, the liquid drop fission barriers need to be scaled by 0.80-1.02 to reproduce the experimental data. And a decreasing trend of the scaling factor with increasing fissionability parameter Z²/(50A) is found.     

Structure effects on reaction mechanisms in collisions induced by radioactive ion beams

The present paper concerns the study of reactions induced by radioactive beams of halo and weakly bound nuclei at energies around and above the Coulomb barrier. The results obtained for the reaction induced by the halo nucleus ⁶He on ⁶⁴Zn have been compared with the results for the reaction induced by ⁴He on the same target. The results of the reaction induced by the weakly bound unstable ¹³N on the weakly bound ⁹Be have been compared with those for the reaction ¹⁰B + ¹²C. The text was submitted by the authors in English.     

7Li quasi-free scattering off the α-cluster in 9Be nucleus

Spectra of coincident charged particles from the reactions induced by a 52 MeV ⁷Li beam incident on a beryllium target were measured. Strong contributions of the ⁷Li quasi-free scattering off the α-cluster in ⁹Be nucleus were observed. This observation supports the conclusions from the study of complete fusion of weakly bound light nuclei at low energies that the “fragility” of the nuclei makes their fusion less probable. Received: 1 June 1998     

Disentangling the reaction mechanisms of weakly bound nuclei

Complete and incomplete fusion cross sections for the ⁹Be + ¹⁴⁴Sm reaction have been measured at near-barrier energies, using the delayed X-ray detection technique. At above-barrier energies these show a suppression of complete fusion for this weakly bound projectile on an intermediate mass target. The suppression factor, attributed to ⁹Be break-up, was deduced from a comparison of complete fusion yields with coupled-channels calculations, and appears consistent with measured incomplete fusion product yields. At ∼10%, it is considerably smaller than the value of ∼30% previously found for a ²⁰⁸Pb target. Simultaneous measurements of elastic and inelastic scattering permit a clearer picture of the reaction mechanisms.     

Light charged particle decay in the reaction7Li+16O

Angular distributions and excitation functions for the emission of a large number of proton, deuteron, triton, and-particle groups in⁷Li+¹⁶O reactions have been measured in the vicinity of the Coulomb barrier. Within the framework of the statistical reaction model, two approaches are presented that can reproduce the only weakly anisotropic shape of the angular distributions and the absolute cross section for those groups of ejectiles where contributions from direct reaction modes are small. When a standard Woods-Saxon potential deduced from elastic scattering is used, the entrance channel angular momentum distribution must be limited to values below critical angular momental _cr which are smaller than the grazing angular momental _gr if fusion is to be described. A global proximity potential with a parameter set that has been adjusted to reproduce the fusion reactions of a variety of p- and sd-shell nuclei yields very similar results when applied to⁷Li+¹⁶O. The proximity potential effectively introduces a similar angular-momentum limitation. This analysis proves the existence of a fusion cross section limitation and the importance of strong direct reaction modes (transfer and possibly inelastic processes) in⁷Li+¹⁶O reactions at energies close to and even below the Coulomb barrier. Another aspect of⁷Li+¹⁶O is addressed briefly. The resonance-like structure observed in the heavy-ion radiative capture reaction⁷Li(¹⁶O, ₀₊₁)²³Na atE _x (²³Na)=25.4 MeV is not observed in the particle decay channels investigated in the present work.The authors would like to acknowledge the help received from B. Bellenberg, B. Dechant, H. Hemmert, T. Krischak, E. Kuhlmann, H. Putsch, and C. Scholz during the experiments.     

Reaction mechanisms in collisions induced by halo and/or weakly bound radioactive nuclei around the barrier

In this paper a brief review of the status of theory and experiments concerning the study of reaction mechanisms, in particular fusion, with halo and loosely bound nuclei at energies around the Coulomb barrier is made. The data of the reactions ^4,6He+⁶⁴Zn and ¹³N+⁹Be are discussed in more detail.     

Radiative capture reactions with the participation of weakly bound light nuclei

Reactions of radiative capture of weakly bound light nuclei are investigated in the scope of the potential model. The applicability of the approach is demonstrated with an analysis of the cross section for the ⁶Li(p, ??)⁷Be reaction. Good agreement with the available experimental data is shown. The radiative capture cross section for the ⁶He(p, ??)⁷Li reaction in the region of low sub-barrier energies is evaluated. It is concluded that reactions involving ⁶He could also play a noteworthy part in stellar nucleosynthesis processes.     

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems ⁶Li + ²⁰⁸Pb, ⁹Be + ²⁰⁹Bi have been determined. The effect of breakup on fusion for weakly bound projectiles ⁶Li and ⁹Be incident on ²⁰⁸Pb or ²⁰⁹Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.     

Fusion-fission and neutron-evaporation-residue cross-sections in 40Ar- and 50Ti-induced fusion reactions

For the reactions ⁴⁰Ar+ ¹⁶⁵Ho. ¹⁶⁹Tm, ¹⁷⁴Yb. ¹¹⁵Lu, ^176–180Hf, ¹⁸¹Ta, ²⁰⁸Pb and ⁵⁰Ti + ²⁰⁸Pb, ²⁰⁹Bi the cross sections for the fusion-fission process were determined by measuring energy and time-of-flight of the reaction products. In addition, the neutron-evaporation-residue cross sections were measured by using the velocity filter SHIP. A σ versus 1/E analysis of the fusion-fission cross sections is used to determine fusion barriers and fusion radii. The evaporation- residue cross sections are used to extract in an approximate way barriers for compound-nucleus formation. These barriers are found to agree with the fusion barriers determined from the fission cross sections. For all systems investigated the neutron-evaporation-residue cross sections reach their maximum close to the fusion barrier as calculated from the Bass potential.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998     

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

Fusion of halo nuclei

The sub-barrier fusion of halo nuclei such as ¹¹Be and ¹¹Li with heavy target nuclei is discussed. The couplings to the soft dipole mode as well as to the break-up channels are taken into account. At barrier energies, the fusion cross section was found to be more than one order of magnitude smaller than that corresponding to the uncoupled problem. At sub-barrier energies, it was shown to be larger.     

Elastic scattering for the system 11Be + 209Bi at Coulomb barrier energies

The elastic scattering process for ¹¹Be ions impinging on a ²⁰⁹Bi target was studied in the energy range around the Coulomb barrier. The angular distributions of the ¹¹Be scattered particles were analyzed within the optical model framework in order to evaluate the reaction cross section, which turned out to be much larger than the fusion one, especially in the sub-barrier region. The comparison with the system ⁹Be + ²⁰⁹Bi showed that the reaction cross section is larger for the reaction ¹¹Be + ²⁰⁹Bi in the energy range around the Coulomb barrier, while they are rather similar at higher bombarding energies. This result suggests that direct processes related to the ¹¹Be halo structure and lower binding energy are more relevant at near-barrier energies.     

弱束缚原子核引起的熔合反应机制研究

弱束缚原子核引起的熔合反应机制研究是近几十年中实验核物理研究的重要课题之一。相比于放射性核束,加速器提供的稳定弱束缚原子核束流的强度要高几个数量级,利用稳定弱束缚原子核作为弹核进行反应机制的研究,可以在保证统计性和准确性的基础上,深入研究原子核的破裂、转移等反应道对熔合过程的耦合作用。已有很多实验数据表明,在库仑位垒附近,弱束缚原子核引发的熔合反应有很多有趣的现象,例如完全熔合截面的“垒下增强”和“垒上压低”。本文主要回顾近年来弱束缚原子核“垒上压低”的研究结果,并探讨造成“垒上压低”的可能原因。完全熔合截面“垒上压低”的主要原因是弱束缚原子核在进入熔合位垒之前发生破裂,从而降低了完全熔合反应道的入射通量。同时,实验研究表明完全熔合截面压低的程度可能与靶核质量数以及靶核结构相关。目前,在实验上对弱束缚原子核引起的熔合反应研究主要有3种测量方法,分别为$\gamma$射线测量方法、带电粒子测量方法以及带电粒子-$\gamma$射线符合测量的方法。其中,带电粒子-$\gamma$射线符合测量的方法在反应道鉴别方面具有明显的优势。本文对这3种测量方法进行了概要介绍,并就国内外对运用这3种方法开展的研究进行了介绍,包括本研究组在此方面的研究工作。此外,对弱束缚原子核引起的熔合反应近期在理论方面的研究工作也做了些介绍。     

Excitation functions of <Superscript>6</Superscript>Li incomplete fusion reactions with Pt nuclei

Experimentally determined excitation functions of the transfer reactions producing ^194–199Au and ^197m Hg isotopes during the interaction of ⁶Li with Pt nuclei are presented. An analysis of the experimental data as compared to EMPIRE-2.18 model calculations and experimental results on the d + ^natPt and α + ^natPt reactions allow determination of the interaction channels of d- and α-clusters in ⁶Li with the target nucleus. The results from model calculations of the reaction cross sections appear considerably lower than the experimental data. This discrepancy in describing the reactions with weakly bound nuclei is probably associated with the incomplete consideration of various interaction channels in the EMPERE-2.18 software. It is clear that a complete understanding of the interaction pattern in these processes requires consideration of the direct channels of ⁶Li nucleus cluster transfer during ⁶Li breakup near the Coulomb barrier.