Description of the two-humped mass distribution of fission fragments of mercury isotopes on the basis of the multidimensional stochastic model

The dynamical model proposed earlier for describing fusion-fission reactions is applied to describing the two-humped mass distribution of fission fragments of mercury isotopes. In this model, the calculation of the time evolution of collective coordinates of the system is broken down into two stages. The first stage is that within which the projectile approaches the target nucleus, while the second is that of the evolution of the system formed after the touching of the projectile and target nuclei. The dynamical evolution of the system within both stages of the calculation is described on the basis of Langevin equations. The shell structure of colliding nuclei is taken into account at either stage of the calculation. Mass distributions are calculated for fragments originating from the fission of the mercury isotopes ^{190, 184}Hg formed in the fusion-fission reactions ⁴⁸Ca + ¹⁴²Nd → ¹⁹⁰Hg and ⁴⁰Ar + ¹⁴⁴Sm → ¹⁸⁴Hg. The process in which the isotope ¹⁸⁰Hg undergoes fission from the ground state is also calculated. The results obtained in this way are compared with the results of previous theoretical calculations and with available experimental data.     

Dynamics of capture and fusion in heavy ion collisions

The effect of entrance channel on decrease of the complete fusion cross sections and on the yield of reaction products are associated with the quasifission which depends on the mass asymmetry and shell structure of colliding nuclei. In reactions of massive projectile and target nuclei, the competition between complete fusion and quasifission appears at the stage of compound nucleus formation, in addition to the increase of the fission probability. It is shown that the yield of quasifission products may be symmetric or asymmetric in dependence on peculiarities of shell structure of reaction fragments. Marima of mass or charge distributions are connected with the peculiarities of shell structure of reaction fragments.     

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.     

Single electron loss in the collisions of C3 + and atomic hydrogen

This paper studies the projectile electron loss cross sections of C3+ colliding with atomic hydrogen in the frame work of extended over-barrier model at intermediate velocities (25 keV/u-600 keV/u). The electron loss is calculated in terms of the interaction between the screened target nucleus and the active projectile electron and of the interaction between projectile electron and target electron. Compared with the convergent close-coupling calculations, screening and anti-screening calculations, this model satisfactorily reproduces the experimentally obtained energy dependence of the electron-impact ionisation cross sections and the single electron loss cross sections over the energy range investigated here.     

Energy losses of fast heavy structure ions in multiple collisions with diatomic molecules

The nonperturbative calculations of the effects of multiple collisions and the orientation of the molecule axis with respect to the projectile motion direction in the energy losses of fast heavy highly charged structure ions colliding with diatomic molecules have been performed with allowance for various excitations and the ionization of both the projectile and target. It has been shown that the effects of multiple collisions gives rise to a significant difference between the energy losses at the parallel and perpendicular orientations of the target; this effect is insignificant for chaotic orientation. Conclusions for the cross sections for the stripping of hydrogen-like ions are similar.     

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。     

Total cross sections for nucleus-nucleus reactions within the Glauber-Sitenko approach for realistic distributions of nuclear matter

The microscopic eikonal phase shifts for nucleus-nucleus collisions and total reaction cross sections are calculated by using the expression previously derived for the profile (thickness) of a realistic distribution of nucleons in the form of a symmetrized Fermi function. If, in addition, the density of the projectile nucleus is approximated by a Gaussian function and if a density profile of arbitrary form is taken for the target nucleus, the phase shift in question reduces to a one-dimensional integral. Questions are considered that are associated with the derivation of density parameters for “pointlike” nucleons in nuclei, with the possibility of approximating realistic densities by Gaussian functions in the region of the nuclear surface, with the dependence of the cross section on the range of nucleon-nucleon interaction and on the nuclear-medium density, and with the role of the distortion of the trajectory. Conclusions on the physics of the process are drawn, and the cross sections calculated on the basis of the present approach without using free parameters are compared with available experimental data.     

Nuclear Potential and Fusion Cross Sections for Synthesizing Super-Heavy Elements in Di-nuclear Systems

A double foMing method with simplified Skyrme-type nucleon nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this method, the potential energy surfaces~ the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.     

Allowance for the shell structure of the 42100 Mo and 46110 Pd nuclei in the synthesis of 84200 Po, 88210 Ra, and 92220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: ₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄¹⁰⁰Po, ₄₂¹⁰⁰Mo + ₄₆¹⁰⁰Pd → ₈₈²¹⁰Ra, and ₄₆¹¹⁰Pd + ₄₆¹¹⁰Pd → ₉₂²²⁰U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.     

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...     

Simple estimates for Fermi jets

The phenomenon of Fermi jets is investigated in the approximation of two colliding potential wells filled with degenerate Fermi gases of nucleons. A model is formulated which largely bypasses the explicit treatment of the relative motion of the nuclei, assumed to be governed by the window friction mechanism. Formulae for the velocity distributions and differential cross sections for neutrons and protons jetting through either target or projectile are derived. The numerical results are investigated systematically over a wide range of nuclear reactions. It is shown that the net linear momentum carried away by Fermi jets accounts for only a rather minor fraction of the observed missing momentum in typical heavy-ion fusion reactions.     

Quantum-mechanical description of the initial stage of fusion reaction

Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated on the basis of the reduced-density-matrix formalism. The effect of dissipation and fluctuations on the capture process is taken into account self-consistently within this model. Cross sections for evaporation-residue formation in asymmetric-fusion reactions are found by using the calculated capture probabilities averaged over all orientations of the deformed projectile or target nucleus.     

Effect of the orientation degree of freedom on the rate and time of fission of highly excited nuclei

The effect of the dimensionality of the dynamical model used on the fission rate and mean time is studied within a multidimensional stochastic approach to fission dynamics. These features of fission of excited compound nuclei are calculated within four-dimensional Langevin dynamics, where the coordinate K, which is the projection of the total angular momentum onto the symmetry axis of the nucleus being considered, is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, a} parametrization. The evolution of this orientation degree of freedom (K mode) is described in terms of the Langevin equation in the overdamped regime. The effect of the orientation degree of freedom on the rate and mean time of fission of compound nuclei is studied. The introduction of the orientation degree of freedom is shown to lead to a substantial decrease in the fission rate and, accordingly, to an increase in the mean fission time upon going over from the three- to the four-dimensional model. The reactions induced by the interaction of ¹⁴N and ¹⁶O projectile ions with ¹⁹⁷Au, ²⁰⁸Pb, ²³²Th, and ²³⁸U nuclei at energies above the Coulomb fusion barrier are considered. The effect of the increase in the fission time because of the introduction of the K mode is so strong that it compensates almost completely for an opposite effect from introducing, in the one-dimensional model, the second and third collective coordinates that take into account, respectively, the evolution of the neck in the nuclear shape and the mass asymmetry. Ultimately, the difference between the results in the four- and one dimensional problems is not more than 5 to 25% for the reactions considered here.     

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.     

Recoil study of multinucleon transfer reactions: Capture of six charges by Nd targets in Ar induced reactions

Multinucleon transfer reactions induced with Ar ions and involving the capture of six charges by the target have been studied. The targets were all the separated isotopes of Nd, and the observed nuclei were ^149gTb, ¹⁵⁰Dy, ¹⁵¹Dy. The experimental technique involved the measurement of the cross sections, angular distributions, and recoil range at each recoil angle, of the heavy residual nuclei. After transformation of the data into the c.m. system, the angular distributions appear to be peaked backwards, close to 180°. This observation suggests that the present reactions are of the same type as the multinucleon transfer reactions studied by other authors for which the angular distribution of the light fragment was peaked forward in the c.m. system. The energy distributions in the c.m. system were used to check the feasibility of various mechanisms which could lead to the production of the observed isotopes. Each mechanism was supposed to be a two-step process: the first step was the exchange, from the projectile to the target, of a number n of nucléons, leading to an excited intermediate nucleus, and the second step the deexcitation of the intermediate nucleus by nuclear evaporation. This analysis indicates that the most probable mechanisms correspond to n close to 12 (6 protons and 6 neutrons), and to an excitation energy of about 60 MeV for the intermediate nucleus. The distribution of cross sections versus the number of nucléons gained by the target is also in accord with this reaction model.     

The validity of the factorization hypothesis for nucleus-nucleus cross sections at high energies

We have calculated nucleus-nucleus cross sections for a variety of projectile and target nuclei and a wide range of energy. Total, reaction and elastic cross sections, as well as the slopes of the elastic diffraction peak, exhibit an approximate factorization property when the nuclei differ by less than 50% in r.m.s. radii. A simple geometrical interpretation is provided for the failure of factorization which occurs when target and projectile differ greatly in size.     

Microscopic approach to calculating cross sections and optical potentials for nucleus-nucleus interaction at intermediate energies

Nucleus-nucleus scattering is considered in the high-energy approximation and on the basis of Glauber-Sitenko microscopic theory in the optical limit. Analytic expressions for eikonal phase shifts are given for the case of Fermi-type realistic potentials and nuclear-density distributions. The effect of taking into account the distortions of the trajectories of the nuclei involved and the nuclear-density dependence of nucleon-nucleon forces on the total reactions cross sections is illustrated. The sensitivity of the reaction cross sections to the choice of model for the ⁶He projectile nucleus, which involves a neutron halo, is explored. Semimicroscopic optical potentials are introduced in order to describe differential cross sections for elastic scattering. The results of the present calculations are compared with available experimental data.     

中子诱发16O双微分截面的理论分析

应用已经发展的轻核反应新模型理论,计算和分析了中子诱发^16O反应截面,比较和分析了出射中子双微分截面的理论计算结果和实验数据,从理论计算结果与实验的符合情况看,这一理论和方法对于计算轻核的双微分截面是成功的。     

140A MeV~(40,48)Ca和~(58,64)Ni炮弹碎裂反应产物的统计擦碎模型计算

用统计擦碎模型计算了140AMeV40,48Ca+9Be和58,64Ni+9Be弹核碎裂反应产物的截面.通过对碎片截面计算结果和实验测量结果的比较发现,采用自由空间的核子-核子反应截面计算时,对非中心反应产物的截面拟合很好,而对中心反应产物的截面有较大高估,而采用饱和密度相关的核子-核子反应截面计算时,对非周边反应产物的截面拟合较好,而对周边反应产物的截面有一定程度的低估.在统计擦碎模型中,对核子-核子反应截面进行细致的介质密度关联,可能会改进计算值与实验值的符合程度.