超重核合成的同位素依赖探讨

利用二参量Smoluchowski方程计算了54Fe+204Pb,56Fe+206Pb,58Fe+208Pb冷熔合和32,34,36S+238U热熔合的复合核形成截面和蒸发残余截面, 结果清楚地显示出超重核合成截面随同位素的变化。 由于较低的入射道库仑位垒、 较低的不对称裂变谷中的条件鞍点和较小的中子分离能, 一般地说, 丰中子同位素的超重核形成截面明显增强。 The cross sections of the compound nucleus formation and e vaporation residue for the 54Fe+204Pb, 56Fe+206Pb, 58Fe+208Pb cold fusion and 32,34, 36S+238U hot fusion have been calculated by using a two parameter Smoluchowski equation. Our results clearly show the isotope dependence of superheavy nucleus production. The formation cross sections of the neutron rich isotope are, generally speaking, obviously enhanced due to the lower Coloumb barrier , lower height of the conditional saddle point, and smaller neutron separation energy.     

Origin of Unexpected Isotopic Trends in Synthesis of Superheavy Nuclei

We investigate the dependence of the yield of superheavy nuclei with Z = 110, 112, 114 on the neutron excess of the projectile nucleus with a two-parameter Smoluchowski equation. It is confirmed that in some cases, the cold fusion reactions with less neutron excess are more favourable than those with more neutron excess. In order to probe the origin of these unexpected isotopic trends, we also investigate the probabilities of capture, fusion and survival in the cold fusion reactions in detail It is found that the maximal ER cross sections of the superheavy nuclei exponentially increase as a function of Bf - Sn with Bf being the fission barrier and Sn being the neutron separation energy. Although the probabilities of capture and fusion have some influences, the unexpected isotopic trends mainly due to the dependence of the ER cross sections on the Bf - Sn value. Therefore, the reactions with larger Bf - Sn values should be more favourable for synthesis of superheavy nuclei.     

The role of the entrance channel in the fusion of massive nuclei

The role of the entrance channel in the fusion-fission reactions leading to nearly the same superheavy compound nucleus is studied in the framework of dynamic model. The calculations are done for ⁴⁸Ca +²⁴⁴Pu and ^74,76Ge +²⁰⁸Pb reactions which could lead to formation of superheavy element Z = 114. It is shown that for these reactions there is an energy window for the values of the bombarding energy at which a capture probability is sufficiently large. Together with the restriction coming from the intrinsic barrier for fusion, it helps to find an optimal value of the bombarding energy for a given projectile--target combination. Received: 15 July 1998     

Calculation of Interaction Potentials between Spherical and Deformed Nuclei

The interaction potential for spherical-deformed reaction partners is calculated. The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system ^32S＋^154Sm are investigated within the double-folding model of the deformed nuclei. The effective nucleon-nucleon interaction is taken to be the M3Y-Reid potential. The density is considered for three terms of the expansion using the truncated multipole expansion method, which is a deformed Fermi shape With quadrupole and hexadecapole for the density distribution of ^154Sm. It is found for the interaction potential that the height and the position of barrier strongly depend on the deformations, the orientation angle of the deformed nucleus, and hence produce great effects on fusion cross section. The integrated fusion cross section is in good agreement with the experimental data.     

Entrance channel mass asymmetry dependence of compound nucleus formation

The fusion reactions ⁴⁸Ca + ¹⁵⁴Sm and ¹⁶O + ¹⁸⁶W leading to the same compound nucleus ²⁰²Pb are studied within the framework of an 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, Coulomb barriers and fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. We conclude that the compound nucleus formation is favorable for the system with larger mass asymmetry.     

基于双核模型对超重元素合成机制的研究

在双核模型基础上，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁵⁰Ti，⁵⁸Fe+²⁰⁸Pb，²⁰⁹Bi这4个反应系统通过冷熔合反应合成超重元素的激发函数，得到了与实验比较符合的结果.计算了不同入射能量时各角动量分波对熔合概率和超重核存活概率的影响以及对蒸发剩余截面的贡献.这些结果对进一步理解超重核的合成机制有重要意义. 关键词： 超重元素 双核模型 熔合反应 蒸发剩余截面     

Fission process of superheavy nuclei

The process of fusion-fission of superheavy nuclei with Z=102?122 formed in the reactions with ²²Ne, ²⁶Mg, ⁴⁸Ca, ⁵⁸Fe and ⁸⁶Kr ions at energies near and below the Coulomb barrier has been studied. The experiments were carried out at the U-400 accelerator of the Flerov Laboratory of Nuclear Reactions (JINR) using a time-of-flight spectrometer of fission fragments CORSET and a neutron multi-detector DEMON. As a result of the experiments, mass and energy distributions of fission fragments, fission and quasi-fission cross sections, multiplicities of neutrons and gamma rays and their dependence on the mechanism of formation and decay of compound superheavy systems have been studied.     

Effect of the entrance channel on the synthesis of superheavy elements

Cross-sections for the synthesis of superheavy elements were analyzed using the concept of a dinuclear system. Experimental values for the production of elements Z = 104, 108, 110, 111 and 112 by cold fusion reactions with targets of ²⁰⁸Pb and ²⁰⁹Bi were reproduced. The model reveals the importance of entrance channel dynamics and competition between quasi-fission and complete fusion processes. Energy windows were observed which allow capture of the reacting nuclei and formation of the compound nucleus. The quantities were studied which are significant for the interaction dynamics of massive nuclei in the entrance channel.     

基于双核模型对Z = 116~ 121 超重核产生截面的研究(英文)

在双核模型的理论框架下系统研究了超重元素Z = 116 ~121 的蒸发剩余截面,计算过程中核子扩散由主方程描述,同时考虑了全熔合与准裂变的竞争。计算基本再现了利用热熔合反应48Ca+245Cm,48Ca+249Cf 和48Ca+249Bk 产生116~118 号同位素的合成截面。同样,分别以249Bk,249Cf 和243Am 为靶,以48Ca,50Ti 和58Fe 为炮弹,计算了Z = 119~ 121 号同位素的生成截面。结果表明,这些超重核的生成截面随着质子数的增大进一步变小。例如,利用58Fe+243Am 反应合成121 号同位素的最大蒸发剩余截面仅在fb 量级。基于对选择的几个反应系统的系统分析,发现双核系统在熔合蒸发过程中偶Z 奇N 和奇Z 偶N 复合核分别有强的3n 和4n 蒸发道。The production cross sections of superheavy elements with Z = 116~121 have been investigated systematically within the dinuclear system (DNS) concept, where the master equation is solved numerically to obtain the fusion probability. The competition between complete fusion and quasifission, which can strongly affect the cross section of the compound nucleus formation, is taken into account. The evaporation residue cross sections ER calculated for the hot fusion actinide-based reactions (48Ca+245Cm, 48Ca+249Cf and 48Ca+249Bk) are basically in agreement with the known experimental data within one order of magnitude. Similar calculations for the synthesis of superheavy elements up to Z = 121 are performed using the available 249Bk, 249Cf and 243Am as targets and 48Ca, 50Ti and 58Fe as projectiles. Their production cross sections are relatively small,especially for the 58Fe+243Am→301121 reaction. A systematic analysis indicates that the 3n and 4n channelsare respectively the most favorable fusion-evaporation channels in the synthesis of even- and odd-Z superheavy elements.     

Experimental signature of entrance channel effect in heavy mass region via evaporation residue cross section and spin distribution measurements

Evaporation residue (ER) cross sections and gamma multiplicity distributions have been measured for ¹⁶O + ¹⁸⁴W and ¹⁹F + ¹⁸¹Ta systems in the excitation energy range of 50–90 MeV, leading to the same compound nucleus ²⁰⁰Pb^∗. Comparison of experimental results of both the systems shows that ER cross sections and moments of gamma multiplicity distribution of ¹⁶O + ¹⁸⁴W system are significantly higher than those of ¹⁹F + ¹⁸¹Ta system at higher excitation energies. Present measurements directly shows the experimental signature of entrance channel effect even with the systems which are not very different with respect to their entrance channel mass asymmetry. It is further demonstrated that the reduction in the ER cross section and moments of spin distribution for ¹⁹F + ¹⁸¹Ta system is mainly due to the suppression of fusion of higher l values.     

基于相对论平均场理论对超重核冷熔合反应截面的研究

在形变约束的相对论平均场理论框架下计算了合成Z=102—118元素的(可能)冷熔合反应中复合核及蒸发一或两个中子剩余核的位能曲面,得到了复合核和剩余核平衡点和鞍点的性质、静态裂变垒高度和冷熔合反应的最佳入射能;利用壳修正和对修正方法计算了平衡点和鞍点的壳修正能、对修正能和微观能.利用由此得到的壳结构信息,用简单的熔合蒸发唯象模型计算了相应反应的冷熔合截面.结果发现,TM1参数提供的结构性质给出了与实验接近的反应截面.     

Probing Balance Energy Using Momentum- and Isospin-Dependent Potential

Using the momentum- and isospin-dependent Boltmann-Uehling-Uhlenbeck （BUU） model, we investigate the transverse flow and balance energy in two isotopic colliding systems ^48Ca＋^58Fe and ^48Cr＋^58Ni by adopting different symmetry potentials. By comparing the results between the two colliding systems, we find that the difference between the balance energies of two isotopic systems can be considered as a sensitive probe to the density dependence of symmetry energy.     

Weak e+e− lines from internal pair conversion observed in collisions of 238U with heavy nuclei

We present the results of a Doppler-shift correction to the measured e⁺e⁻–sum-energy spectra obtained from e⁺e⁻–coincidence measurements in ²³⁸U +²⁰⁶Pb and ²³⁸U +¹⁸¹Ta collisions at beam energies close to the Coulomb barrier, using an improved experimental setup at the double-Orange spectrometer of GSI. Internal-Pair-Conversion (IPC) e⁺e⁻ pairs from discrete nuclear transitions of a moving emitter have been observed following Coulomb excitation of the 1.844 MeV (E1) transition in ²⁰⁶Pb and neutron transfer to the 1.770 MeV (M1) transition in ²⁰⁷Pb. In the collision system ²³⁸U +¹⁸¹Ta, IPC transitions were observed from the Ta-like as well as from the U-like nuclei. In all systems the Doppler-shift corrected e⁺e⁻–sum-energy spectra show weak lines at the energies expected from the corresponding γ–ray spectra with cross sections being consistent with the measured excitation cross sections of the γ lines and the theoretically predicted IPC coefficients. No other than IPC e⁺e⁻–sum-energy lines were found in the measured spectra. The transfer cross sections show a strong dependence on the distance of closest approach (R_min), thus signaling also a strong dependence on the bombarding energy close to the Coulomb barrier. Received: 22 July 1997 / Revised version: 15 October 1997     

热熔合反应合成超重核产生截面的同位素依赖性

通过在形成超重核的重离子俘获和熔合过程中引入位垒分布函数的方法对双核模型做了进一步发展. 超重核形成过程中的俘获、熔合和蒸发3个阶段分别采用了半经验的耦合道模型、数值求解主方程和统计蒸发模型的方法来描述. 计算了近年来Dubna小组利用热熔合反应⁴⁸Ca(²⁴³Am, 3n—5n)^288—286115和⁴⁸Ca(²⁴⁸Cm, 3n—5n)^293—291116合成超重新核素的蒸发余核激发函数. 系统分析了⁴⁸Ca轰击锕系元素U,Np,Pu,Am,Cm合成超重核Z=112—116产生截面的同位素依赖性. 给出了合成超重新核素最佳的弹靶组合和入射能量, 即有最大的超重核产生截面. 计算说明, 壳修正能和中子分离能是影响超重核生成截面产生同位素依赖性的主要因素.     

Dynamic tunnel effect at low-energy nuclear reactions with neutron-rich nuclei

The probability of neutron transfer between nuclei at close low-energy collisions has been investigated as a function of the energy of the neutron separation, the energy in a center-of-mass system E and the collision impact parameter. The energy dependence of the neutron transfer cross section in the ⁶He + ¹⁹⁷Au reaction has been explained.     

Shell Correction and Pairing Energies in the Dinuclear System Model

We investigate the dependences of the potential energy surfaces （PES） and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy＇s contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding ^208Pb are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.     

Evaluation of Transmutation of ^137Cs（γ, n） 136Cs Using Ultra-Intense Lasers in Solid Targets

Relativistic electrons produced in ultra-intense laser-solid interaction generate highly collimated γ-ray beams through Bremsstrahlung that can be used to induce photonuclear reactions. Photonuclear transmutation （of （% n） type） of ^137 Cs, one of the hazardous nuclear wastes with half-life of 30.17 years which cannot be transmuted practically with neutron bombardment due to its very low neutron capture cross section, has been considered. Nuclear activity of produced 136Cs with half-life of 13.16 days has been evaluated analytically using available experimental data. With irradiating a ^137Cs sample by p-polarized laser light of 10^20 Wcm^-2 and the repetition rate of 10Hz for 30min, the activity of 0.24 Bq is obtained. It is found that intensity has a large effect in yield around 10^21 Wcm^-2. For similar laser with intensity of 5 ×10^21 Wcm^-2, the activity increases with a factor of 10^5.     

How does fusion hindrance show up in medium-light systems? The case of Ca + Ca

The fusion excitation function of ⁴⁸Ca + ⁴⁸Ca has been measured above and well below the Coulomb barrier, thereby largely extending the energy range of a previous experiment down to very low cross sections. This system has a negative Q  -value for compound nucleus formation. The fusion cross section decreases steadily below the barrier with no conspicuous change of slope below ?300 μb$?300\text{μb}$. Coupled-channels calculations using a Woods–Saxon potential indicate that a large diffuseness parameter is needed to reproduce the sub-barrier cross sections. A close analogy with the case of ³⁶S + ⁴⁸Ca, with Q>0$Q>0$, is pointed out. The sign of the Q-value does not influence fusion cross sections down to the 300–600 nb level.     

Strong enhancement of two-neutron transfer in the system 206Pb+118Sn

One and two neutron transfer has been measured in the heaviest asymmetric nuclear system with semi magic nuclei showing superfluid properties, in ²⁰⁶Pb+¹¹⁸Sn collisions at an energy well below the Coulomb barrier with scattering orbits covering the largest angles. Particle-γ coincidence techniques using 5 Euroball-Cluster detectors (EB) combined in a set-up with the Heidelberg-Darmstadt NaI-Crystal Ball (CB) have been used. Transfer channels are identified with EB via their known γ-decays of the lowest excited states. Using the unique feature of the set-up with the CB, transfer to well defined final states with known quantum numbers (without feeding) are selected using the high efficiency multiplicity filter of the CB (no second γ-ray). The data are analysed using the semiclassical approach and transfer probabilities are obtained. The enhancement for the two-neutron transfer populating the low lying superfluid 2⁺ state in ¹²⁰Sn (and ¹¹⁶Sn), while the Pb-branch is in the groundstate is deduced by comparison with the strongest single neutron transfer transition. Large enhancements (EF ≃ 10³) are observed. This is the first direct measurement of enhancement for a heavy nuclear binary system with experimentally separated levels suggesting a strong contribution from superfluid pair transfer. Received: 18 December 1998 / Revised version: 23 February 1999