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.     

Fusion cross sections for superheavy nuclei in the dinuclear system concept

Using the dinuclear system concept we present calculations of production cross sections for the heaviest nuclei. The obtained results are in a good agreement with the experimental data. The experimentally observed rapid fall-off of the cross sections of the cold fusion with increasing charge number Z of the compound nucleus is explained. Optimal reactions for the synthesis of the superheavy nuclei are suggested.     

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.     

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.     

Inverse Quasifission in <Superscript>156,160</Superscript>Gd + <Superscript>186</Superscript>W Reactions

To investigate the impact shell effects have in the formation of neutron-rich fragments in multinucleon transfer reactions, a series of experiments to explore the binary channel in ^156,160Gd + ¹⁸⁶W reactions at energies near and above the Coulomb barrier is performed at the Flerov Laboratory’s U-400 accelerator using the CORSET setup. These experiments are aimed mainly at obtaining the production cross sections of leadlike fragments in the process of inverse quasifission. The mass, energy, and angular distributions of the binary reaction products are measured at energies of 860 and 935 MeV of ¹⁶⁰Gd ions and 878MeV in the case of ¹⁵⁶Gd ions. The excitation energies of primary fragments are estimated using their measured mass–energy distributions. Enhanced yields of products with masses of 200–215 amu are observed for both reactions. At energies above the barrier for side-to-side collisions (935 MeV), the yield of lead-like fragments is an order of magnitude larger than at energies near the Coulomb barrier, due possibly to the influence of orientation effects. The enhancement observed in the yield of reaction products with masses heavier than the target mass confirms that multinucleon transfer reactions can be used to obtain new neutron-rich isotopes, and to synthesize new superheavy elements.     

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.     

Near-Barrier Proton Transfer in Reactions with <Superscript>3</Superscript>He Nucleus

Calculations of production cross sections for isotopes ¹⁹⁴Au in the ³He + ¹⁹⁴Pt reaction and ⁴⁵Ti in the ³He + ⁴⁵Sc reaction are performed, based on the solution to a time-dependent Schrödinger equation in combination with calculations in the statistical model using the computational code of the NRV data base. The experimental differences in the near-barrier energy dependences of the isotope production cross sections in these reactions are explained by the difference between the proton and neutron shells of the target nuclei, and by the different evolutions of the probability density for protons of the projectile nucleus and neutrons of the target nuclei in collisions.     

不同理论模型预言合成超重核Z=119~122研究进展

通过双核系统模型与其他模型对$Z\leqslant$118元素的计算结果与实验数据的比较，证明了不同模型预测超重核的产生截面是可靠的。对比分析了不同模型对Z=119和Z=120超重核的预言结果，我们认为合成超重核Z=119和Z=120的最佳弹靶组合分别为反应$^{48}{\rm{Ca}} + ^{{\rm{252}}}{\rm{Es}}$和$^{40}{\rm{Ca}} + ^{{\rm{257}}}{\rm{Fm}}$，并且Z=119新核素很有可能会先于Z=120新核素在实验上被合成。由于实验上Z>100锕系靶的限制，人们正尝试寻找比48Ca更重的弹核来合成超重核Z=121和Z=122，超重核Z=121可以通过反应V+Cf来合成，而超重核Z=122的产生截面已经非常小，要求将来在实验上提高探测及鉴别技术。希望本文的讨论可以在将来为实验及理论核物理工作者们提供一些参考。     

Description of quasifission reactions in the dinuclear system model

The formation and evolution of dinuclear systems in quasifission reactions are investigated. The process of formation of reaction products is analyzed based on the concept of a dinuclear system. Isotopic trends of cross sections of production of superheavy nuclei in quasifission reactions are discussed. The yields of new neutron-rich isotopes of nuclei with Z = 64–80 in quasifission reactions are predicted. The mechanism of production of complex fragments in complete fusion and quasifission reactions is analyzed.     

Predictions of synthesizing element 119 and 120

The evaporation residue cross sections of synthesizing superheavy nuclei Z=119, 120 are calculated by different sets of master equations with different dynamical variables. Two methods basically predicted similar results that the Ca induced hot fusion can 48 produce element 119 easier than produce 120, and the evaporation residue cross sections for 119 are detectable by current advanced techniques, while the evaporation residue cross sections are below 0.1 pb for producing element 120.     

Study of fusion and nucleon transfer channels in the <Superscript>197</Superscript>Au + <Superscript>6</Superscript>He reaction in an energy range of <Superscript>6</Superscript>He to 20 Mev/A

New data on the cross sections of reactions occurring during the interaction of ⁶He nuclei with ¹⁹⁷Au at energies of ⁶He from 40 to 120 MeV are presented. The experiments were performed in the ACCULINNA secondary beam separator of the Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research. To identify the reaction products, the activation method for measuring the gamma activity of the target assembly of thin foils was used. The excitation functions for fusion reactions involving the evaporation of up to ten neutrons from the compound nucleus as well as reactions with the emission of charged particles and nucleon transfer in the investigated energy region are obtained. Data analysis was carried out using two codes: ALICE-MP and NRV. The cross sections for the (⁶He, xn) reactions occurring through the compound nucleus are mostly in agreement with the results of model calculations based on the statistical approach. It is shown that, up to the energies of 114 MeV, the cross-section drop in the complete fusion reactions is negligible. The experimental excitation functions of reactions leading to the formation of isotopes of mercury and gold (transfer reaction) indicate that the main contribution to their formation is made by direct processes and that evaporation reactions (⁶He, pxn) and (⁶He, αxn) play a minor role, as is evidenced by a comparison of the measured cross sections with the calculation results.     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

Effect of the structure of neutron-rich <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li isotopes on the characteristics of proton elastic scattering

The differential cross sections of proton elastic scattering from ⁸Li and ⁹Li nuclei in inverse kinematics have been calculated. The cross sections were determined within the Glauber diffraction theory with the wave functions of nuclei in the three-particle α-t-n, α-t-2n, and ⁷Li-n-n models. Comparison with the existing experimental data for E = 700 and 60 MeV/nucleon made it possible to draw a conclusion about the quality of the wave functions and the adequacy of the potentials used for their calculations.     

New approximations to the energy dependences of the total cross sections for the proton-induced fission of <Superscript>197</Superscript>Au, <Superscript>203</Superscript>Tl, <Superscript>nat</Superscript>Pb,and <Superscript>209</Superscript>Bi nuclei

The total cross sections for ¹⁹⁷Au and ²⁰³Tl fission induced by protons of energy varied from about 200 to 1000 MeV with a step of about 100 MeV are measured. New approximations to the energy dependences of the cross sections for the proton-induced fission of ¹⁹⁷Au, ²⁰³Tl, natPb, and ²⁰⁹Bi nuclei are presented and discussed. For all of these nuclei, exponential functions are used as approximations.     

Data on photoneutron reactions from various experiments for <Superscript>133</Superscript>Cs, <Superscript>138</Superscript>Ba and <Superscript>209</Superscript>Bi nuclei

Basic methods for determining cross sections for photoneutron partial reactions are examined. They are obtained directly in experiments with quasimonoeneregetic annihilation photons or from the cross section for the (γ, xn) = (γ, 1n) + 2(γ, 2n) + 3(γ, 3n) +... neutron-yield reaction in experiments with bremsstrahlung photons by introducing corrections based on statistical nuclear-reaction theory. The difference in the conditions of these experiments, which leads to discrepancies between their results because of sizable systematic errors, is analyzed. Physical criteria are used to study the reliability of data on the photodisintegration of ¹³³Cs, ¹³⁸Ba, and ²⁰⁹Bi nuclei. The cross sections for partial and total reactions satisfying the reliability criteria are evaluated within the experimental–theoretical method (σ^eval(γ, in) = F_i^theor × σ^expt(γ, xn)) on the basis of the experimental cross sections σ^expt(γ, xn) and the results of the calculations within the combined model of photonuclear reactions.     

Diffractive scattering of <Superscript>7</Superscript>Be and <Superscript>8</Superscript>B nuclei by <Superscript>12</Superscript>C nuclei

A theory of the diffractive scattering of loosely bound three-cluster nuclei by nuclei was developed with allowance for Coulomb interaction. The differential cross sections for the scattering of projectile exotic nuclei ⁷Be and ⁸B by ¹²C nuclei at an energy of 40 MeV per nucleon were calculated within the proposed formalism. The results describe satisfactorily relevant experimental data.     

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

Use of (<Superscript>3</Superscript>He, <Emphasis Type="Italic">t</Emphasis>) charge-exchange reactions in determining radii of excited states of nuclei

A method for determining the radii of excited states of nuclei by means of (³He, t) charge-exchange reactions was proposed. Two versions of a comparison of differential cross sections for (³He, t) reactions were considered. The first relies on a comparison with cross sections for inelastic-scattering processes leading to the formation of isobaric analog states, while the second involves (³He, t) reactions leading to the production of the ground state. The two versions in question yield similar results and make it possible to determine the radius of the first excited state of the ¹³N nucleus. This state has the excitation energy of E* = 2.37 MeV, lying above the proton-emission threshold. The resulting radius proved to be enhanced in relation to the ground state and is close to the radius of the 3.09-MeV isobaric analog state of the ¹³С nucleus, which has a neutron halo. This permitted drawing the conclusion that the ¹³N nucleus in the 2.37-MeV state has a proton halo. The possibility of revealing a proton halo in other states of light nuclei is considered.     

The analysis of reactions leading to synthesis of super heavy elements within the dinuclear system concept

The dinuclear system concept of complete fusion of nuclei has been applied to the analysis of superheavy elements synthesis. The optimal excitation energy of compound nuclei and production cross sections in the cold synthesis of heavy elements with charge Z=102–112 have been calculated. The possibility of synthesizing the element with magic number Z=114 in cold and hot fusion reactions has been considered.     

Pro duction of Exotic Nuclei in Low-Energy Multi-Nucleon Transfer Reactions

Multinucleon transfer processes in low-energy heavy ion collisions open a new field of research in nuclear physics, namely, production and studying properties of heavy neutron rich nuclei. This not-yet-explored area of the nuclear map is extremely important for understanding the astrophysical nucleosynthesis and the origin of heavy elements. Beams of very heavy U-like ions are needed to produce new long-living isotopes of transfermium and superheavy elements located very close to the island of stability.The calculated cross sections are high enough to perform the experiments at available accelerators.Beams of medium-mass ions (such as 136Xe, 192Os, 198Pt) can be used for the production of neutron rich nuclei located along the neutron closed shell N = 126 (the last waiting point) having the largest impact on the astrophysical r-process. The Low-energy multinucleon transfer reactions is a very efficient tool also for the production and spectroscopic study of light exotic nuclei. The corresponding cross sections are 2 or 3 orders of magnitude larger as compared with high energy fragmentation reactions.