Isotopic dependence of fusion cross-sections – linear relationships

A systematic study of isotopic dependence of fusion cross-section is carried out by adding neutrons gradually to N=Z colliding nuclei. We find that fusion barrier position increases and height decreases, both linearly with the increase of N/Z ratio of the compound system. The increase in barrier position is larger compared to decrease in barrier height. In terms of these linear relationships, a parameterized form of fusion cross-sections is given for the neutron-rich colliding nuclei. The fusion cross-sections are also enhanced linearly with the N/Z ratio, and this enhancement is larger for lower incident centre-of-mass energies and independent of the choice of reaction partners. Experimental data and other theoretical studies are called for to verify these results. Received: 27 February 1998 / Revised version: 22 May 1998     

Analytical calculation of fusion cross-sections

We analyse the fusion cross-sections, calculated by using two different analytical parameterisations and compare them with the experimental data. Both the parameterisations are based on ion-ion potentials calculated within the framework of Skyrme energy density formalism. In the first case, the ion-ion potential (including the spin-density term) was parameterised and then, by adding the Coulomb potential, one could compute the fusion barrier analytically. In the second case, the calculated fusion barrier heights and positions were parameterised directly. Both of these (previously) reported parameterisations are used here to calculate the fusion barriers and fusion excitation functions for more than 50 reactions belonging to the s-d and f-shell nuclei. A detailed comparison of these parametrisations with the experimental and several other theoretical results shows that both of these parameterisations are able to reproduce the experimental data equally well. As the (second) direct parameterisation depends only on the charges and masses of colliding nuclei, it is very useful for predicting/ understanding the fusion process in low energy heavy-ion reactions. Received: 24 February 1999 / Accepted: 16 March 2000     

极深垒下熔合反应中扩散过程的研究

基于弹核和靶核接触后的泡利阻塞效应,引入了一个新的扩散因子来描述在极深垒下能区熔合反应中的阻碍现象。在本工作中,熔合截面假定由两部分的乘积构成:克服库仑势垒的隧穿因子和两个反应核接触后的扩散因子。前者可以由耦合道方法来描述,后者则由入射的能量和系统的温度决定。对存在阻碍现象的21个熔合体系进行了详细分析,发现扩散因子在熔合阻碍的实验阈值能量附近起到了重要的作用。此外,以负Q值熔合体系64Ni+64Ni和正Q值熔合体系24Mg+30Si为例,发现熔合截面以及两个重要表象(天体S因子和对数导数)的计算结果与实验数据具有较好的一致性。     

Transfer, breakup, and fusion reactions of 6He with 209Bi near the Coulomb barrier

The fusion of ⁶He with a ²⁰⁹Bi target displays a large enhancement at energies near to and below the Coulomb barrier. Recently, a ⁴He group of remarkable intensity, which dominates the total reaction cross-section, has also been observed in the near-barrier interaction of the same system. It is argued that this transfer/breakup channel acts as a doorway state to fusion. Received: 1 May 2001 / Accepted: 4 December 2001     

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.     

Implication of proton-nucleus scattering for density distributions of unstable nuclei

The use of elastic proton scattering at intermediate and high energies to obtain information about the density distributions of unstable nuclei is investigated. A comparison between the relativistic impulse approximation (RIA) and Glauber model for proton scattering from ¹⁶O, ⁴⁰Ca, ⁴⁴Ca and ⁴⁸Ca at medium energies is performed. We used density distributions derived from the relativistic mean-field theory, employing the recent relativistic force NL-RA1, as well as experimental and phenomenological densities. It is found that the eikonal approximation can describe the cross-section only at small scattering angles and is weakly sensitive to the density distributions, while the RIA nicely produced the experimental cross-sections, even at medium and larger angles, and was very sensitive to the nuclear densities. Furthermore, the RIA better describes the isospin dependence of the cross-section. We used the RIA to investigate the density distribution of ⁵⁸Ca for proton scattering at different energies. It is found that the cross-section strongly depends on the parameters of the density distribution even at a small scattering angle. These results are important in extracting information about the structure of unstable nuclei. We also investigated the RIA and its sensitivity in describing halo nuclei such as ⁶He. We used for ⁶He a no-halo Gaussian density and a realistic-halo density that derived in the cluster orbital shell model approximation and contains the extended distribution of the valence nucleons. Comparison with the recent experimental data at GSI at 717 MeV/nucleon shows that the RIA successfully described the data at all considered range of the momentum transfer and on the other hand favor the halo structure of ⁶He. Received: 1 December 2001 / Accepted: 31 July 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: mrashdan@hotmail.com Communicated by P. Schuck     

超重核熔合中的靶核形变效应

利用额外推力模型研究了⁴⁸Ca+²³⁸U俘获和熔合过程中的靶核形变效应.计算表明,在近垒和垒下能区,靶核形变使俘获截面和熔合截面增强,形成的复合核自旋分布展宽.     

Shell effects and pairing correlations in fission investigated with radioactive beams

The secondary-beam facility at GSI allows to produce a large variety of exotic nuclei at relativistic energies. This technique offers a unique oportunity to investigate systematically fission in inverse kinematics. In the present experiment, the fission properties of more than 70 different actinides and preactinides were investigated at low excitation energy. The elemental yields and kinetic energies of the fission residues present new signatures of shell structure and pairing correlations. Received: 1 May 2001 / Accepted: 4 December 2001     

Combinatorial nuclear level densities based on the Gogny nucleon-nucleon effective interaction

A combinatorial method to calculate total level densities from an arbitrary single-particle level scheme is presented. Parity, angular momentum, pairing correlations as well as collective enhancements are explicitly treated. This method is employed using single-particle level schemes obtained from Hartree-Fock-Bogoliubov calculations based on the Gogny effective interaction. Sixty five even-even nuclei with masses 26 ?A? 250 are considered. Rather good agreements are obtained when comparing our predictions with experimental data for energies of the order of the neutron binding energies and for low excitation energies where discrete levels are experimentally observed. Received: 13 February 2001 / Accepted: 24 September 2001     

Coulomb Potentials between Spherical and Deformed Nuclei

Coulomb potentials for spherical-deformed reaction as well as the conventional formulas. Our results approaches have quite different behaviours in the partners are calculated in terms of the double folding model show that the Coulomb potentials calculated with different internal region of the potential. Because fusion process is sensitive to the barrier height and the internal part of the potential, the fusion excitation function, especially the fusion barrier distribution, should provide a strict test of the interaction potentials. Therefore, we calculate the fusion excitation function and barrier distribution for the ^16O ＋^154Sm system with different versions of the Coulomb potentials, in comparison with the experimental results. It is found that the fusion excitation function and barrier distribution of ^16O＋^154Sm are obviously different for the different versions of the Coulomb potentials. By means of this comparison, we may conclude that the double folding model with the accurate approximate form can provide rather reasonable Coulomb potentials.     

Differences between pairing and zero-range effective interactions for nuclear binding energies

In this paper, we show that, although the spectroscopic properties of the monopole pairing force and a zero-range delta-function interaction are very similar, their saturation properties are quite different. In particular, the predictions for binding energies when filling up a major shell are radically different past mid-shell. This has significant consequences for understanding the masses and binding energies of long isotopic chains of nuclei that will be accessible with advanced exotic beam facilities. Received: 29 November 2001 / Accepted: 13 February 2002     

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。     

Cluster growth processes by direct simulation monte carlo method

Thin films obtained by cluster deposition have attracted strong attention both as a new manufacturing technique to realize high-density magnetic recording media and to create systems with unique magnetic properties. Because the film’s features are influenced by the cluster properties during the flight path, the relevant physical scale to be studied is as large as centimeters. In this paper, a new model of cluster growth processes based on a combination of the Direct Simulation Monte Carlo (DSMC) method and the cluster growth model is introduced to examine the effects of experimental conditions on cluster growth by an adiabatic expansion process. From the macroscopic viewpoint, we simulate the behavior of clusters and inert gas in the flight path under different experimental conditions. The internal energy of the cluster, which consists of rotational and vibrational energies, is limited by the binding energy which depends on the cluster size. These internal and binding energies are used as criteria of the cluster growth. The binding energy is estimated by surface and volume terms. Several types of size distribution of generated clusters under various conditions are obtained by the present model. The results of the present numerical simulations reveal that the size distribution is strongly related to the experimental conditions and can be controlled. Received: 23 January 2001 / Accepted: 3 May 2001 / Published online: 30 August 2001     

Fusion near the Coulomb barrier for the synthesis of heavy and superheavy elements: A theoretical approach

The compound nucleus formation is considered as a two-step process of touching and subsequent tunneling of the projectile into the target. The deep minima in the potential energy curve are due to shell effects in the experimental binding energies and give possible target-projectile combinations for the synthesis of heavy and superheavy elements. The asymmetric channels thus obtained are in remarkable agreement with the known experimental channels. In our model, the colliding partners are first shown to be captured in the pocket behind the outer (touching) barrier and the composite system so formed finally tunnels through the inner (fusion) barrier to form the resulting compound nucleus. These calculations reveal the importance of the fusion barrier, which occur only for the asymmetric target-projectile combinations. The calculated fusion cross-sections show a reasonable comparison with the observed one-neutron evaporation residue cross-sections. An estimate of the excitation energy carried by the compound nucleus is also obtained from our model calculations.     

Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of ¹⁶O with ⁹²Zr, ¹⁴⁴Sm and ²⁰⁸Pb, but fails to reproduce the double peaking of the distribution for the ¹⁴⁴Sm target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights. Received: 6 March 2000 / Accepted: 31 January 2001     

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.     

Quasi-molecular states of neutrons in dinuclear systems and their effect on fusion of heavy atomic nuclei

The evolution of the wave functions of valence neutrons upon collisions of heavy nuclei having energies near the Coulomb barrier has been investigated by numerical solution of the multidimensional time-dependent Schrödinger equation. It is shown that even before overcoming the barrier by nuclei the wave functions of valence neutrons are extended to their volumes with occupation of quasi-molecular states. This process results in a significant effect of neutron transfers on nuclear fusion and, in particular, in a significant increase in the probability of subbarrier fusion for certain combinations of nuclei.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

弱束缚弹核引起的熔合反应

⁶Li, ⁹Be为弱束缚核. 通过弱束缚弹核⁶Li, ⁹Be轰击靶²⁰⁸Pb,²⁰⁸Be的实验熔合激发函数与理论预言的比较, 讨论了弱束缚弹核破裂对熔合过程 的影响. 比较结果显示, 弱束缚弹核与重靶核的完全熔合截面在垒上能区 明显压低. 由部分熔合截面与完全熔合截面之和得到总熔合截面. 研究结果 表明, 破裂对总熔合截面几乎没有影响. 由此可见, 弱束缚核的部分熔合 可能发生在强吸收区域附近. 最后还给出了全熔合截面与部分熔合截面 之间的关系.     

Effects of the entrance channel mass asymmetry in fusion reactions

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei 26Al,30Si,38Ar and 170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model.The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies,the Coulomb barriers and the fusion cross sections.The calculated fusion cross sections agree quantitatively with the experimental data.The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.