重离子熔合反应形成超重核的截面研究

在双核系统框架下,通过数值法解主方程计算了双核间的核子跃迁全熔合几率.两碰撞核内部激发能由相对运动能损提供,因此能够将核子转移过程与相对运动耦合起来.对一些以Pb为靶的形成超重核的冷熔合反应,计算了最佳激发能、形成双核系统的俘获截面、复合核形成几率及存活几率等,所得到的形成超重核蒸发剩余截面与已知实验值符合较好. In the concept of Dinuclear system (DNS) the complete fusion probability of two touch nuclei via nucleon transfer is described by numerically solving the Master equation. The excitation energy of two colliding nuclei is supplied by the energy dissipation of their relative motion, thus the nucleon transfer process and the relative motion are coupled. For Pb based cold fusion reactions to form super heavy nuclei, the optimal excitation energy, the capture cross section to form a DNS ...     

Production of super-heavy nuclei in cold fusion reactions

A model for cold-fusion reactions related to the synthesis of super-heavy nuclei in collisions of heavy projectile-nuclei with a ²⁰⁸Pb target nucleus is discussed.In the framework of this model,the production of the com-pound nucleus by two paths,the di-nuclear system path and the fusion path,are taken into account simultaneously.The formation of the compound nucleus in the framework of the di-nuclear system is related to the transfer of nucle-ons from the light nucleus to the heavy one.The fusion path is linked to the sequential evolution of the nuclear shape from the system of contacting nuclei to the compound nucleus.It is shown that the compound nucleus is mainly formed by the fusion path in cold-fusion reactions.The landscape of the potential energy related to the fusion path is discussed in detail.This landscape for very heavy nucleus-nucleus systems has an intermediate state,which is linked to the formation of both the compound nucleus and the quasi-fission fragments.The decay of the intermediate state is taken into account in the calculation of the compound nucleus production cross sections and the quasi-fission cross sections.The values of the cold-fusion cross sections obtained in the model agree well with the experimental data.     

Symmetry energy at subsaturation densities and the neutron skin thickness of ~(208)Pb

The mass-dependent symmetry energy coefficients asym(A) has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work.Taking advantage of the obtained symmetry energy coefficient asym(A) and the density profiles obtained by switching off the Coulomb interaction in208 Pb,we calculated the slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3.The calculated L0.11 ranges from 40.5 Me V to 60.3 Me V.The slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of208 Pb,which is the difference of the neutron and proton rms radii of the nucleus.With the linear relation the neutron skin thickness Rn pof208 Pb is predicted to be 0.15–0.21 fm.     

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.     

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.     

Branching Ratios of α Decay for Nuclei near Deformed Shell Closures

The generalized liquid drop model （GLDM） is extended to the region around deformed shell closure ^270Hs by taking into account the excitation energy EI＋ of the residual daughter nucleus and the centrifugal potential energy Vcen（r）. The branching ratios of a decays from the ground state of a parent nucleus to the ground state 0^＋ of its deformed daughter nucleus and to the first excited state 2^＋ are calculated in the framework of the GLDM. The results support the proposal that a measurement of a spectroscopy is a feasible method to extract information on nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

Influence of Nuclear Deformation on the Potential Energy Surface in Di—Nuclear Model

Influence of the nuclear deformation on the potential energy surface(PES) in a di-nuclear system is studied in details.It is found that the PES shape changes greatly due to the deformation effect.The top point of the PES could be reduced significantly,which implies that the optimum excitation energy could also be reduced greatly and may enhance the fromation probability of the compound nucleus.The dynamical deformaiton as a function of the reaction time in the reaction process is dramatic.The Z/N ratios of fragments tend to follow that of the compound nucleus during the nucleon exchange process,but to fluctuate.     

重离子熔合反应与双核模型

简单介绍了兰州-北京-吉森合作组对合成超重核的重离子反应进行的初步研究。研究的重点是熔合阶段的反应机制。在原有双核模型的基础上做了一些改进，把耗散相对运动过程与核子转移过程耦合起来，从更微观的角度来描写双核系统向全熔合复合核的演化。在双核过程中的每一步求解主方程，不对驱动势做谐振子近似。同时，还探讨了原子核形变与相对取向对驱动势的影响，存活几率与复合核蒸发中子的奇偶效应，以及入射道中原子核非弹性激发对俘获截面的影响等。In recent years, the Lanzou-Beijing-Giessen collaboration has studied the heavy ion reactions which are lead to the formation of super-heavy nuclei. The study emphases the mechanism of the fusion stage of the reactions. Based on the so called Di-nuclear System Model, some improvements have been made. The main points are the coupling of the dissipation of relative motion energy, angular momentum with nucleon transfer, and solving the Master equation in every step of the nucleon transfer with exact driving potentials, in order to describe the evolution of the system more microscopically. At the same time, we also discussed the effects of nuclear deformation and their relative orientation on the driving potentials, and studied the survive probability of the compound nuclei and its old-even effects, as well as the influence of inelastic excitations of nuclei in entrance channels to the capture cross sections.     

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.     

重离子碰撞中超重核的形成机制(英文)

在双核模型框架下,用数值解主方程方法计算了超重核的熔合几率。 明确描述了包含能量、角动量和碎片形变弛豫的相对运动，并与核子扩散过程相耦合。因此，用微观方法推导出的核子跃迁几率是与时间相关的。所计算的以Pb为靶的冷熔合超重核形成截面和以48Ca为弹核的热熔合超重核形成激发函数与已知的实验值在合理的范围内符合。In the dinuclear system conception, the master equation is solved numerically to calculate the fusion probabilities of super heavy nuclei. The relative motion concerning the energy, the angular momentum and the fragment deformation relaxations is explicitly treated to couple with the diffusion process. The nucleon transition probabilities, which are derived microscopically, are related with the energy dissipation of the relative motion, thus they are time dependent. The formation cross sections of the super heavy nuclei from Pb based cold fusion and excitation functions from 48Ca induced hot fusion are reasonably consistent with known experimental data.     

Emission of heavy clusters in nuclear reactions at low collision energies

A survey of theoretical and experimental investigations of the process involving the emission of heavy clusters from excited nuclear systems produced in heavy-ion reactions at low collision energies is given. The dinuclear system (DNS) model for calculating cross sections for the formation of heavy clusters in complete-fusion and quasifission reactions is described in detail. The results of respective calculations are compared with relevant experimental data and with the results obtained on the basis of different models. The role of the angular momentum, the asymmetry of the entrance channel, the N/Z ratio, and the excitation energy in the formation of final reaction products is studied within the proposed approach. A method is developed for calculating cross sections for evaporation-residue formation. This method takes into account both channels of light-particle emission and channels of heavy-cluster emission. The possibility for the formation of Rn, Fr, and Ra isotopes in channels of heavy-cluster emission from the excited compound nucleus of Pu is demonstrated for the first time. The calculated cross sections and isotopic distributions for residual nuclei arising upon the emission of heavy clusters from an excited compound nucleus of Pu are in good agreement with experimental data. The model developed in the present study permits finding optimum experimental conditions (projectile-target combination and bombarding energy) for studying processes involving the emission of specific complex fragments.     

Modeling fast heavy ion induced amorphization in pure metals

Bombardment of metallic targets with heavy, GeV energy ions results in electronic excitation beyond a threshold value of stopping power. Due to the spatial homogeneity of ion tracks, the projectile homogeneously deposits its energy onto all atoms within a cylinder. The radius of such an ionization cylinder is calculated, thereafter the amount of energy transferred to each single atom in the cylinder is evaluated: n ionization events per atoms occur, which change the atomic configuration from (Z) to (Z-n). Ionized atoms are ejected out of the ionization cylinder, and they interact with matrix atoms inside a damage cylinder. Locally a starting compound [(Z) (Z-n)] is formed. Segregation at the matrix-damage cylinder interface of one component of the starting compound gives rise to a non-equilibrium compositional profile. Relaxation to metastable equilibrium of the associated non-equilibrium electronic density is simulated via charge transfer reactions, each of which involves a matrix atom and an ionized atom. The reaction product is a dimer, considered a nucleus of an effective compound. The energy cost to introduce in the matrix an effective compound dimer is calculated, together with the surface properties of starting and effective compounds. Qualitative differences are found between compounds which form in metals amorphized or, respectively crystallized under fast heavy ion irradiation.     

Self-consistent calculations for highly excited compound nuclei

A method for self-consistently calculating average nuclear properties at high excitation energies is derived. Calculations using this formalism have been performed for a double-magic and a deformed nucleus employing the Skyrme force for the nucleon-nucleon interaction. The effects of excitation energy on the nuclear structure are discussed and a comparison of self-consistently calculated level densities with those obtained in the usual statistical method is made. The calculations for the deformed nucleus show the transition from the deformed to a spherical shape with increasing excitation.     

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.     

Complete inclusion of parity-dependent level densities in the statistical description of astrophysical reaction rates

Microscopic calculations show a strong parity dependence of the nuclear level density at low excitation energy of a nucleus. Previously, this dependence has either been neglected or only implemented in the initial and final channels of Hauser–Feshbach calculations. We present an indirect way to account for a full parity dependence in all steps of a reaction, including the one of the compound nucleus formed in a reaction. To illustrate the impact on astrophysical reaction rates, we present rates for neutron captures in isotopic chains of Ni and Sn. Comparing with the standard assumption of equipartition of both parities, we find noticeable differences in the energy regime of astrophysical interest caused by the parity dependence of the nuclear level density found in the compound nucleus even at sizeable excitation energies.     

Remarks on a quantum mechanical treatment of internal excitation in low energy nuclear fission

Internal excitations of the fissioning nucleus are usually described phenomenologically by friction terms. In the present paper an approach is discussed which is in principle based on a correct quantum mechanical treatment taking the projection form of the Schrödinger equation as a starting point. Considering nuclear fission as an almost adiabatic process an estimate for the friction energy is made. In this very crude estimate only 10–15% of the collective energy gain in going from the saddle to the scission point is transformed into internal excitation energy. This is in agreement with experimental data showing pronounced substructure effects which would be destroyed in the presence of a larger friction. As compared to other microscopic calculations, in the present work the total Hamiltonian is split in such a way that the only perturbation term being responsible for the deformation is essentially the Coulomb energy. By this assumption the calculation of transition probabilities to intrinsically excited states becomes rather insensitive to the exact excitation energy spectrum of the compound nucleus.     

Properties of products originating from the interaction of 35-MeV/nucleon <Superscript>7</Superscript>Li ions with Pb nuclei

The results are presented that were obtained by measuring and analyzing the yields and kinematical features of radioactive products of the reactions initiated in a lead target by lithium ions accelerated to an energy of 35M eV per nucleon. The cross sections, charge and mass distributions, and kinematical and energy features of various reaction products associated with the fission and the evaporation channels of the decay of excited nuclei are determined. Quantities that are calculated in the present study include the momenta and kinetic energies of residual nuclei, as well as the momentum transfer and the excitation energy of intermediate nuclear systems formed upon complete and incomplete fusion. On the basis of an analysis of data obtained in our experiment, the total cross section for nuclear interaction and partial widths with respect to various channels of the decay of intermediate compound nuclei are determined in the energy range being investigated.