Analytic description of the fusion and fission processes through compact quasi-molecular shapes

Recent studies have shown that the characteristics of the entrance and exit channels through compact quasi-molecular shapes are compatible with the experimental data on fusion, fission and cluster radioactivity when the deformation energy is determined within a generalized liquid drop model. Analytic expressions allowing to calculate rapidly the main characteristics of this deformation path through necked shapes with quasi-spherical ends are presented now; namely formulas for the fusion and fission barrier heights, the fusion barrier radius, the symmetric fission barriers and the proximity energy.     

Microscopic analysis of the fission barriers in <Superscript>256</Superscript>Fm and <Superscript>258</Superscript>Fm

The fission barriers of ²⁵⁶Fm and ²⁵⁸Fm have been analyzed in the HFB theory. The potential energy and the effective inertia parameter have been calculated in the two-dimensional deformation space of quadrupole and octupole moments. Fission paths for various octupole moments of the exit point from the fission barrier have been determined. The half-life along each path has been calculated. The shortest half-lives have been obtained for the paths with reflection symmetric shapes of nuclei in both the considered isotopes.     

Three-Parameter Liquid-Drop Model Describing a Large-Amplitude Collective Nuclear Motion

In this paper, the liquid-drop model with three parameters {c, h,a} is used to describe symmetric or asymmetric fission process. The analytical expression of the effective moment of inertia is given. The inertial and frictional tensors of nucleus are evaluated by the Werner-Wheeler method. Based on a standard liquid-drop model, the Coulomb energy and surface energy are accurately calculated. The scission point of the fissioning nucleus is defined by energy criteria. The salient features of the dynamical coefficients are discussed.     

有限温度下三分裂的三种模式比较

用一个球到多个球重叠到分离的几何形状来描述裂片相互以120°方向形变(品字型),相互沿一条直线的拉长三体形变,以及先非对称后对称的级联三分裂的形变过程。方便比较只用了一个形变参数。基于液滴模型计算了表面能和库仑能,加入了新生碎片之间的核势,局域壳效应的壳能,给出三种三分裂模式的形变势能比较。考虑热核的各种温度效应,计算了在有限温度下这三种模式的位垒穿透概率,给出高温核位垒高度下降甚至位垒消失,定性给出三分裂的最可能的裂变方式。 关键词：     

~(236)U Multi-modal Fission Paths on a Five-dimensional Deformation Surface

In this paper, we develop a new path search algorithm which considers all the degrees of freedom and apply it on our calculated five-dimensional potential energy surface(PES) of~(236) U. Asymmetric and symmetric fission paths and barriers are obtained.     

FISSION MEASUREMENT ON 5.5 TO 21.7MeV/A 28Si+197Au SYSTEM (Ⅱ) ANGULAR DISTRIBUTION OF ICF AND SF

According to the distribution of linear momentum transfer (lmt) obtained from the correlation measurement of fission partner,the events of Incomplete Fusion Fission (ICF) and Sequential Fission (SF) were distinguished.The fission angular distributions of both ICF and SF were obtained,respectively.
With calculating the moment of inertia by Cassinian Ovaloid as the fission shape, the angular distributions were fitted by current procedure.The spins of fission nuclei corresponding to ICF and SF are extracted.The relation between spins and bombarding energy is discussed.Besides,the angular distribution in coincidence with complex particles is discussed.     

Rotational energy and limits to fusion reactions between two nuclei

The energy balance of the fusion process between two nuclei is discussed with respect to the rotational energy. Two energy regimes are obtained. In the first regime the increase of rotational energy of the compound system as function of incident energy is governed by the moment of inertia of the two-fragment system at the barrier configuration. The faster increase of rotational energy of the compound system is furnished by theQ-value. In a sliding collision only part of theQ-value can be converted into rotational energy. Therefore, the Yrast limit in the population of the compound nucleus cannot be reached. When this source of energy is exhausted at a certain angular momentum, a second regime is obtained; then the increase of angular momentum and rotational energy as function of incident energy must be determined by the moment of inertia of the compound system.     

Non-axial shapes in spontaneous fission of superheavy nuclei

We test the importance of non-axial nuclear shapes in spontaneous fission of heavy and superheavy even-even nuclei from the region around a hypothetical doubly magic nucleus ²⁹⁸114. Fission half-lives are calculated by finding dynamical fission paths as dictated by the least WKB action principle with the macroscopic-microscopic energy and the cranking inertial parameters. Results show that the effects of non-axial shapes on the fission process are weakened by the inertia tensor and become important only for the heaviest elements with Z ⩾ 120.     

Quantummechanical treatment of the penetration through a two-dimensional fission barrier

The collective Hamiltonian is idealized by making a harmonic approximation for the motion perpendicular to the fission path. This is done within a properly defined set of coordinates. The frequency for the transverse oscillations depends on the fission coordinate which leads to a coupling between the two degrees of freedom. Its influence is discussed within the language of scattering theory. Using the Born approximation, formulas for the transmission amplitudes are deduced. These formulas are applied to a simple example. All calculations are done analytically, taking into account the variation of the inertia for the fission mode.     

多维Kramers公式的研究

本文研究了鞍点附近多维的位能曲面及鞍点所在位置;并用Werner Wheeler及无旋液体等两种方法计算了多维的质量系数与粘滞系数,然后用多维Kramers公式计算了裂变速率.发现裂变速率随着维数的增加而适当增大.不同的形变参量以及不同的计算质量和粘滞系数方法对计算核裂变速率影响不大.从结果看,采用三维计算裂变几率已足够准确.     

中子星的转动惯量与表面红移的研究

在温度、密度及同位旋相关的核物质状态方程的基础上,通过求解Tolman–Oppenheimer–Volkoff方程,得到了中子星的转动惯量与表面红移.计算结果表明,中子星的转动惯量较强地依赖于核物质的不可压缩系数与对称能强度系数,而对核子有效质量不太敏感;中子星的表面红移却对对称能强度系数不太敏感,而较强地依赖于不可压缩系数与核子有效质量.     

Some dynamical aspects of the fission process

The properties of the nuclear mass parameter and its influence on the fission process are discussed. In particular, correlations between dynamical and statical paths to fission are considered. The least action trajectories idea is used for finding the dynamical path to fission. Ritz method for the action integral minimalization is applied. An example of the nucleus ²⁵²Fm is considered.     

Fragment angular distributions from fission of238U,209Bi and197Au by 140-MeV4He Ions

The fission fragment angular distributions from reactions of 140-MeV⁴He ions with²³⁸U,²⁰⁹Bi and¹⁹⁷Au have been studied. From the anisotropies in the angular distributions, values for? _eff, the effective moment of inertia at the fission saddle point, have been estimated and compared with results obtained at lower bombarding energies. The derivation of? _eff values has included corrections for the effects of incomplete fusion mechanisms on the orbital angular momentum distribution of the fissioning nuclei and for neutron evaporation prior to fission. The results are also compared with heavy-ion-induced fission data for systems of similar fissility. Also, examination of the forward-backward symmetry of the²³⁸U angular distribution substantiates other results which show that the fraction of fission reactions which follow complete fusion of the target and projectile is less than 0.5 for 140-MeV⁴He-ion bombardment of²³⁸U.     

Statistical emission of large fragments: A general theoretical approach

A theory for the statistical emission of large fragments is developed. In analogy with the fission saddle point, a ridge line in the potential energy surface is defined which controls the decay width of the system into any two given fragments. The normal modes at the ridge are separated into three classes: decay modes, amplifying modes, and non-amplifying modes. Amplifying modes are those whose thermal fluctuations are amplified and lead to a broadening of the kinetic energy distribution. Analytical expressions for the kinetic energy distributions are developed for various combinations of amplifying and non-amplifying modes. The limit for large amplifications is a Gaussian kinetic energy distribution. The limit for no amplification is a Maxwellian-like distribution. Thus the formalism comprehends the fission decay on one hand and the neutron evaporation on the other. The angular distributions are evaluated in terms of the ridge line principal moments of inertia. A general analytical expression has been derived which predicts, correctly in both limits, the angular distributions of the evaporated neutrons and of the fission fragments.     

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.     

Calculation of the real part of the interaction potential between two heavy ions in the sudden approximation

We have calculated the interaction potential between two heavy ions using the energy density formalism and Fermi distributions for the nuclear densities. The experimental fusion barriers are rather well reproduced. The conditions for the observation of fusion between two heavy ions are discussed. As far as the nuclear part of the interaction potential is concerned, the proximity scaling is investigated in detail. It is found that the proximity theorem is satisfied to a good extent. However, as far as the neutron excess is concerned, disagreement with the proximity potential is observed.     

Macroscopic potential-energy surfaces for symmetric fission and heavy-ion reactions

We calculate the macroscopic potential energy of deformation for symmetric configurations of interest in fission and heavy-ion reactions. The shape of the system is characterized in terms of two moments of the matter distribution. These moments correspond to the distance between the centers of mass of the two halves of the system and to the elongation of each half about its center of mass. The configurations studied include a continuous sequence of shapes from the sphere to two-, three-, and four-fragment scission lines. Beyond the scission lines and prior to the line of first contact in heavy-ion reactions we represent the system in terms of separated oblate and prolate spheroids. The macroscopic energy is calculated as the sum of a Coulomb energy and a nuclear macroscopic energy that takes into account the finite range of the nuclear force. For systems throughout the periodic table we display the calculated energy as a function of the two moments in the form of contour maps. Some important features of the contour maps are the binary, ternary, and quaternary saddle points, the fission and fusion (or two-fragment) valleys, and the three- and four-fragment valleys. The maps illustrate how the topography of the potential energy changes as a function of the nuclear system considered. For example, as we move from lighter to heavier nuclear systems the binary saddle point moves from outside the point of first contact in heavy-ion reactions to inside the contact point. Because of this, the formation of a heavy compound nucleus requires additional energy relative to the maximum in a one-dimensional interaction barrier. The maps also illustrate for moderately heavy systems the presence of separate valleys for binary fission and fusion. For still heavier systems the ternary and quaternary saddle points are no longer present. This means that the ternary and quaternary valleys are accessible by paths that decrease monotonically in energy beyond the binary saddle point. Finally, for nuclear systems heavier than about ³⁰⁰120, the binary saddle point itself disappears, which in the absence of single-particle effects precludes altogether the formation of a compound system.     

Nucleon transport processes in fission and heavy ion reactions

The nucleon exchange process between two nuclei in close proximity and its application to an explanation of fragment mass and charge distributions in fission and in heavy ion deep inelastic collisions are reviewed. An analysis of the measured correlations between the energy loss from relative motion and the fragment mass and charge variances in the heavy ion deep inelastic collisions is presented. The recent data on fragment mass and charge variances as a function of the fragment kinetic energy in thermal neutron induced fission of²³⁵U, lends added support to the hypothesis that the nucleon transport process plays a similar role both in fission and in heavy ion deep inelastic collisions.