Probing Shell Correction at High Spin by Neutron Emission of Doubly Magic Nuclei 208Pb and 132Sn

Shell effects in particle emission for two doubly magic nuclei ^132Sn and ^208pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shelle ffects in the emission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.     

Statistical properties of excited fissioning nuclei

The phenomenon of the disappearance of the shell effects on the thermodynamic properties of nuclei with increasing excitation energy has been examined quantitatively on the basis of numerical calculations based on realistic shell model single particle level schemes. It is shown that shell effects disappear at moderate excitation energies and above these excitation energies, the thermodynamic behaviour of the nucleus is identical to that of the equivalent liquid drop model nucleus. Implications of the above feature in the interpretation of some aspects of fission of excited nuclei such as mass-asymmetry and angular anisotropy are examined. The relationship of the phenomenon of washing out of shell effects at high excitation energies with the temperature smearing method of determining ground state shell correction energies is also outlined.     

Fusion hindrance and roles of shell effects in superheavy mass region

We present the first attempt of systematically investigating the effects of shell correction energy for a dynamical process, which includes fusion, fusion–fission and quasi-fission processes. In the superheavy mass region, for the fusion process, shell correction energy plays a very important role and enhances the fusion probability when the colliding partner has a strong shell structure. By analyzing the trajectory in three-dimensional coordinate space with the Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by ‘cold fusion valleys’. The temperature dependence of shell correction energy is considered.     

入射粒子与靶相互作用中电子能损的高阶修正

研究了在较高能入射离子（He离子、 12_C离子）与靶相互作用中电子能量损失的物理机制, 分别探讨了电子能量损失中的相对论修正、 壳修正、 密度修正以及Barkas效应和Bloch效应等修正的贡献, 发现壳修正、 Barkas效应修正和Bloch效应修正在能量小于100 MeV时是重要的, 而相对论修正和密度修正是在能量大于100 MeV时起作用。 加入各种修正项之后, 电子阻止本领的计算结果和实验值（ICRU49）符合更好。 The mechanisms of electronic energy loss in the process of incident particles interaction with Si and Al₂O₃ at proper energies are investigated. The contribution to the electronic energy loss from high order corrections, such as the relativistic correction, the shell correction, the density correction, the Barkas effect correction and the Bloch effect correction are discussed respectively. It is found that the shell correction, the Barkas effect correction and the Bloch effect correction are important at low energies, the relativistic correction and the density correction are important at high energies. The calculated results with these higher order corrections are in good agreement with the experiment data (ICRU49).     

Microscopic transport theory of heavy-ion collisions

Effects from shell structure on mass transport coefficients are studied in a schematic model. The diffusion coefficient is slightly reduced by shell effects, the reduction being less than 20% for realistic cases and reasonably high excitation energies. A much stronger effect results for the drift coefficient. This is due to the rapid variation of the shell correction energy as function of the fragmentation variable. The influence of shell effects on the time-dependent mass distributions is illustrated.     

Shell-structure inertia for slow collective motion

The modified shell correction method is suggested for the calculation of transport coefficients in a slow nuclear collective dynamics. For the multipole low-lying vibrations near the spherical shape of a nucleus, the smooth transport coefficients corresponding to the extended Thomas-Fermi approach are used as a macroscopic background. The time-dependent mean field is approximated through the infinitely deep square-well potential for the calculation of the shell corrections. Significant shell effects in stiffness and inertia are found at small temperatures. These effects disappear approximately at the same large enough temperature as in the free energy. It is shown that the collective inertia is substantially larger than that of irrotational flow owing to the consistency condition of particle density and potential variations. The collective vibration energies and reduced friction and effective damping coefficients with accounting for the shell effects are in better agreement with allowance data than that found from the hydrodynamic model. The text was submitted by the authors in English.     

Shell effect and capture cross sections in the synthesis of superheavy nuclei

The shell effect is included in the improved isospin dependent quantum molecular dynamics model in which the shell correction energy of the system is calculated by using the deformed two-center shell model.A switch function is introduced to connect the shell correction energy of the projectile and the target with that of the compound nucleus during the dynamical fusion process.It is found that the calculated capture cross sections reproduce the experimental data quantitatively at the energy near the Coulomb...     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

锕系原子核自发裂变性质的理论研究

运用推广的液滴模型（GLDM）来确定锕系原子核的自发裂变势垒, 采用量子力学中的WKB近似方法对相应自发裂变的半衰期进行了研究。 在GLDM中, 首次考虑了微观Strutinsky壳修正对裂变势垒的影响。 理论计算的锕系区重核自发裂变半衰期与实验值符合得很好, 表明包括微观壳修正的GLDM可以成功研究重核的自发裂变性质。 The spontaneous fission half lives of the actinides are calculated by the WKB approximation and the potential barriers are constructed by a General Liquid Drop Model (GLDM) including the proximity energy, the mass and charge asymmetry, and an accurate nucleus radius. The microscopic shell correction which plays a key role for the spontaneous fission barrier is considered for the first time. The two parameter quasi molecular shape and the proximity are described in details within the GLDM. The effects of the microscopic shell correction and proximity energy for fission barrier are discussed separately. The calcula ted spontaneous fission half lives for the actinides reasonably accord with the experimental data, implying the present GLDM combined with the microscopic shell correction can be used to study the spontaneous fission properties of heavy nuclei successfully.     

The equivalence of the Strutinsky type smoothing and the temperature averaging method

The Fermi gas model of the nucleus at high temperatures can be used to define a ground state shell correction. We demonstrate analytically that the shell correction so obtained is the same as that obtained from the Strutinsky type method.     

Barkas effect,shell correction,screening and correlation in collisional energy-loss straggling of an ion beam

Collisional electronic energy-loss straggling has been treated theoretically on the basis of the binary theory of electronic stopping. In view of the absence of a Bloch correction in straggling the range of validity of the theory includes both the classical and the Born regime. The theory incorporates Barkas effect and projectile screening. Shell correction and electron bunching are added on. In the absence of shell corrections the Barkas effect has a dominating influence on straggling, but much of this is wiped out when the shell correction is included. Weak projectile screening tends to noticeably reduce collisional straggling. Sizable bunching effects are found in particular for heavy ions. Comparisons are made with selected results of the experimental and theoretical literature. Received 24 September 2002 / Received in final form 1st December 2002 Published online 4 February 2003     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

重离子碰撞中熔合位垒的研究

熔合位垒的研究对熔合反应以及超重核合成有重要的意义。在改进的同位旋相关的量子分子动力学(ImIQMD)模型框架下,提取了熔合反应体系40Ca+40Ca,48Ca+208Pb,48Ca+204Pb和16O+154Sm的熔合位垒。研究了壳修正能对熔合位垒的影响、动力学位垒的能量依赖性、同位旋效应以及形变核的方向效应。计算发现壳修正能降低了熔合反应的位垒。在研究动力学位垒的能量依赖性时,发现位垒高度和位垒半径表现出相反的能量依赖行为。在动力学反应中,当两个核距离接近时,缺中子体系的库仑势同样表现出一定的能量依赖性。对于丰中子体系,由于中子屏蔽作用,库仑势基本没有能量依赖性。     

Strutinsky smoothing and the partition function approach

The Strutinsky shell correction is analytically shown to be equivalent to the shell correction obtained from the partition function approach, provided certain restrictions on the Strutinsky smoothing parameter are met.     

超重核合成截面计算中几个问题的探讨

讨论了超重核形成截面计算中的耦合道效应、壳效应的阻尼效应、能级密度的集体运动增强因子以及蒸发残余核的自旋分布等几个重要问题,并给出相应的实验结果.因这些因素都可能对截面有数量级的影响,正确处理与否直接关系到超重核合成截面理论预言的可靠性. .Several important aspects in the cross section calculations for the synthesis of superheavy nuclei have been inquired. They are the effects of the coupled channels, the damping of shell correction energy, the collective enhancements in the level density and the spin distributions of evaporation residues. The channel coupling of relative motion with internal degrees of freedom will enhance significantly the capture cross section at sub barrier energies. However, recent measurements of spin distributions for ...     

Shell effects in a paired nucleus for finite excitation energies

Shell effects are considered as functions of the excitation energy of the nucleus. The effects of pairing are included and studied in the BCS approximation. Some numerical results, based on the single-particle spectrum of a Woods-Saxon potential, are given. In the limit of zero excitation the shell correction to the energy is compared with the results obtained by the Strutinsky method.     

Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of ^296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.     

Angular momentum and energy dependence of fission andn,p,4He emission from194Hg compound nucleus

Spin and temperature dependence of the fission and particle emission is studied for¹⁹⁴Hg. The compound nucleus is described using the Strutinsky shell correction approach extended for finite angular momenta and temperature. The shell corrections to the potential energy, free energy and the angular momentum are calculated using the Woods-Saxon average field. Results are compared with the experimental data and show a good qualitative agreement. It is found that the inclusion of the shell effects is necessary to understand the decay properties of¹⁹⁴Hg even for temperatures as high as 1.5–2.0 MeV.     

Correlation between muonic levels and nuclear structure in muonic atoms

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A “kink” appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the β-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.