Ternary fission within statistical approach

The ternary system with a light nucleus between two heavy fragments is assumed to appear from the binary configuration near scission. The formation of a third light nucleus in the binary system is considered. The calculated charge distributions in spontaneous ternary fission of ²⁵²Cf and in induced ternary fission of ⁵⁶Ni are compared with the available experimental data. The neutron multiplicity from the fission fragments is described. The fine structures of the TKE-mass distribution are predicted.     

Probabilities for the emission of light particles and their energy and angular distributions for true quaternary nuclear fission

On the basis of quantum-mechanical fission theory, the features of true quaternary nuclear fission are studied by treating this fission process as a sequence of three processes following one another in the course of time. The first two processes are the escape of the first and then the second of the two light particles emitted from the neck of a fissioning nucleus because of a nonadiabatic character of the collective deformation motion of this nucleus. Finally, the third process is the separation of the fissioning nucleus into two rather heavy fission fragments. The differences that arise in the emission probabilities and in the angular and energy distributions upon going over from the first emitted to the second emitted prescission third and fourth particles are analyzed by invoking experimental data on the spontaneous and thermalneutron-induced fission of nuclei, and it is shown that these differences are caused by the changes both in the geometric configuration of the fissioning nucleus and in the shell structure of its neck after the first prescission particle is emitted from it.     

Spectroscopic factors and barrier penetrabilities in cluster radioactivity

The cold cluster decay model is presented in the framework of a dinuclear system concept. Spectroscopic factors are extracted from barrier penetrabilities and measured half-lives. The deformation of the light cluster and residual nucleus is shown to affect the nucleus-nucleus potential and decay characteristics. Half-lives are predicted for neutron-deficient actinides and intermediate-mass nuclei. The connection between spontaneous fission and cluster radioactivity is discussed.     

Studies in nuclear macrophysics through fission and fission-like reactions

Recent developments in the study of fission and fission-like reactions are briefly reviewed. After a brief introduction of some of the important features of the fission process, binary fission and fission-like processes in heavy ion-induced reactions are discussed. It is shown that studies of the fission fragment angular distributions which provide a way to determine relative contributions of compound nucleus fission and non-equilibrium fission-like events in heavy ion-induced fission have proved to be quite valuable in investigating the very shortK-equilibration times of the order of 10⁻²⁰ s involved in the nuclear dynamics of the dinuclear complex on its way to compound nucleus formation following nucleus-nucleus collision.     

Interpretation of the low energy fission process in the framework of dinuclear system conception

The possibility of the interpretation of fission of heavy nuclei as the process of formation, evolution and decay of dinuclear system is discussed. The interpretation is based on the nuclear interaction data obtained in heavy-ion nuclear physics investigations.     

Quantum description of quaternary nuclear fission

The quantum theory of binary and ternary fission is generalized to the case of recently observed quaternary nuclear fission. Formulas for the amplitudes of partial fission widths and angular and energy distributions of quaternary fission products are derived with allowance for strong channel coupling. The nonevaporation mechanism for formation of light particles is used to explain the experimentally observed decrease in the probability for emission of light particles (α, α), (α, t), and (t, t) as compared with the product of emission probabilities for the same particles in ternary fission. It is concluded that in quaternary fission, as in ternary fission, light particles escape from the neck of the fissioning nucleus much earlier than scission of the nucleus into heavy fragments occurs.     

Angular Anisotropy of the Fission Fragments in the Dinuclear System Mo del

A theoretical evaluation of the collective excitation spectra of nucleus at large deformations is possible within the framework of the dinuclear system (DNS) model, which treats the wave function of the fissioning nucleus as a superposition of a mononucleus configuration and two-cluster configurations in a dynamical way, permitting exchange of nucleons between clusters. In this work the method of calculation of the potential energy and the collective spectrum of fissioning nucleus at scission point is presented. Combining the DNS model calculations and the statistical model of fission we calculate the angular distribution of fission fragments for the neutron–induced fission of 239Pu.     

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.     

Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.     

Ternary fission of nuclei in the adiabatic approximation

On the basis of a generalization of integral formulas for nuclear-decay widths to the three-body case, the spontaneous and the low-energy induced ternary fission of nuclei are investigated by using the adiabatic approximation. The properties of energy distributions, of partial fission widths, and of the angular distributions of fission fragments are analyzed for the case of ternary fission. Conditions are found under which the angular distributions of two heavy fragments originating from ternary fission are similar to the analogous distributions of fragments originating from binary fission. The features of angular distributions are investigated, along with the parities and angular momenta of the third (light) ternary-fission fragment.     

Centrifugal fragmentation of a dinuclear system in the process of its evolution toward a compound nucleus

The centrifugal fragmentation of a dinuclear system in the process of evolution toward a compound nucleus is examined. If the angular momentum in the collision of primary nuclei is quite high, centrifugal forces become dominant at the final stage of the evolution of the dinuclear system formed, causing the decay of this dinuclear system to two strongly asymmetric nuclear fragments. Experimental data in which this specific nuclear process manifests itself are presented. Centrifugal fragmentation makes it possible to reveal the cluster facet of the evolution of a dinuclear system toward a compound nucleus. The possibility of this fragmentation process is a logical consequence of the concept of a dinuclear system for the complete fusion of nuclei.     

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.     

Spontaneous Fission Barriers Based on a Generalized Liquid Drop Model

The barrier against the spontaneous fission has been determined within the Generalized Liquid Drop Model （GLDM） including the mass and charge asymmetry, and the proximity energy. The shell correction of the spherical parent nucleus is calculated by using the Strutinsky method, and the empirical shape-dependent shell correction is 6mp10yed during the deformation process. A quasi-molecular shape sequence has been defined to describe the whole process from one-body shape to two-body shape system, and a two-touching-ellipsoid is adopted when the superdeformed one-body system reaches the rupture point. On these bases the spontaneous fission barriers are systematically studied for nuclei from 2a~Th to 249 Cm for different possible exiting channels with the different mass and charge asymmetries. The double, and triple bumps are found in the fission potential energy in this region, which roughly agree with the experimental results. It is found that at around Sn-like fragment the outer fission barriers are lower, while the partner of the Sn-like fragment is in the range near l~SRu where the ground-state mass is lowered by allowing axially symmetric shapes. The preferable fission channels are distinctly pronounced, which should be corresponding to the fragment mass distributions.     

Disappearance of shell effects and persistence of an even-odd staggering in the fragment production in nuclear reactions at relativistic energies

The isotopic distributions of fragments produced in the spallation of uranium are strongly influenced by the fission of the excited prefragments, highly fissile nuclei. The competition between fission and evaporation around the doubly-magic nucleus Pb is discussed. The light fragments from Fe beam are produced with a strong enhancement of even-even nuclei compared to the odd-odd in the region of nuclei with equal number of neutrons and protons, N ～ Z. This staggering in the production of light fragments is not observed in the production of heavy fragments, and is in contradiction with the basis of the statistical model of deexcitation of a hot nucleus. Pairing interaction as a function of the excitation energy and as a function of the isospin of the nucleus are questioned.     

Study of Pre-equilibrium Fission Based on Diffusion Model

In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n+²³⁸U reaction and un-fissile nucleus p+²⁰⁸Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equilibrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrium fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.     

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

推广的液滴模型及其应用

简单介绍了近年来在研究重核和超重核衰变性质及熔合反应方面取得的理论成果和面临的挑战,着重阐述推广的液滴模型(GLDM) 理论框架及其应用。基于原子核的质量数、质子数以及反应Q 值,GLDM考虑了质量和电荷的不对称性、形状演化、亲近势和温度等,很好地描述了重核和超重核的质子放射性、 衰变、重离子放射性、自发裂变的半衰期和重离子熔合反应截面,同时也研究了原子核的粒子(质子、 、重离子) 放射性与自发裂变的竞争。Recent theoretical achievements and challenges about the fusion and decay properties of heavy and superheavy nuclei are generally introduced. Especially, the Generalized Liquid Drop Model(GLDM) as well as its application are emphatically described. Based on the mass number, proton number and the reaction Q value, the GLDM has taken the mass and charge asymmetry, the shape evolution, the proximity potential, as well as the temperature of nucleus into account, well described the proton radioactivity, the decay, the heavy particle radioactivity, the half life of spontaneous fission of heavy nuclei and superheavy nuclei, and the cross-sections of heavy ion fusion. The competitions between the spontaneous fission and other decay modes such as proton and heavy particle radioactivity, the alpha decay, and so on are also studied.     

Generation of angular momentum of fission fragments in a cluster model

Based on the dinuclear system concept, the role of bending vibrations in creation of the angular momentum of primary fission fragments is investigated. For ²⁵²Cf spontaneous fission, the angular momenta of the fragments are calculated as a function of the neutron multiplicity and compared with available experimental data. Different cluster compositions of the ²⁵²Cf fission modes at the scission point are considered.     

Fission decay properties of ultra neutron-rich uranium isotopes

The fission decay of highly neutron-rich uranium isotopes is investigated which shows interesting new features in the barrier properties and neutron emission characteristics in the fission process. ²³³U and ²³⁵U are the nuclei in the actinide region in the beta stability valley which are thermally fissile and have been mainly used in reactors for power generation. The possibility of occurrence of thermally fissile members in the chain of neutron-rich uranium isotopes is examined here. The neutron number N = 162 or 164 has been predicted to be magic in numerous theoretical studies carried out over the years. The series of uranium isotopes around it with N = 154–172 are identified to be thermally fissile on the basis of the fission barrier and neutron separation energy systematics; a manifestation of the close shell nature of N = 162 (or 164). We consider here the thermal neutron fission of a typical representative ²⁴⁹U nucleus in the highly neutron-rich region. Semiempirical study of fission barrier height and width shows that ²⁵⁰U nucleus is stable against spontaneous fission due to increase in barrier width arising out of excess neutrons. On the basis of the calculation of the probability of fragment mass yields and the microscopic study in relativistic mean field theory, this nucleus is shown to undergo exotic decay mode of thermal neutron fission (multi-fragmentation fission) whereby a number of prompt scission neutrons are expected to be simultaneously released along with the two heavy fission fragments. Such properties will have important implications in stellar evolution involving r-process nucleosynthesis.