Ternary fission of actinides probes the state of the nucleus at scission. Light clusters are produced in space and time very close to the scission point. Within the nonequilibrium statistical operator method, a generalized Gibbs distribution is constructed from the information given by the observed yields of isotopes. Using this relevant statistical operator, yields are calculated taking excited states and continuum correlations into account, in accordance with the virial expansion of the equation of state. Clusters with mass number $A \le 10$ are well described using the nonequilibrium generalizations of temperature and chemical potentials. Improving the virial expansion, in-medium effects may become of importance in determining the contribution of weakly bound states and continuum correlations to the intrinsic partition function. Yields of larger clusters, which fail to reach this quasi-equilibrium form of the relevant distribution, are described by nucleation kinetics, and a saddle-to-scission relaxation time of about 7000 fm/c is inferred. Light charged particle emission, described by reaction kinetics and virial expansions, may therefore be regarded as a very important tool to probe the nonequilibrium time evolution of actinide nuclei during fission.
We evaluate the performance of modern nuclear energy density functionals for predicting inner and outer fission barrier heights and energies of fission isomers of even-even actinides. For isomer energies and outer barrier heights, we find that the self-consistent theory at the HFB level is capable of providing quantitative agreement with empirical data.
The current status of the application of covariant density functional theory to the description of fission barriers in actinides and superheavy nuclei is reviewed. The achievements and open problems are discussed.
In this work, we present new experimental data on mass distribution of fission fragments from $^{241}$Am proton-induced fission at $660$ MeV measured at the LNR Phasotron (JINR). The systematic analysis of several measured fragment mass distributions from different fission reactions available in the literature is also presented. The proton-induced fission of $^{241}$Am, $^{237}$Np and $^{238}$U at 26.5, 62.9 and 660 MeV was studied. The proton-induced fission of $^{232}$Th was studied at 26.5, 62.9 and 190 MeV. The fission of $^{208}$Pb also by a proton was investigated at 190, 500 and 1000 Me…
Relativistic mean field theory allowing for triaxial deformations is applied for a systematic study of fission barriers in the actinide region. Different pairing schemes are studied in details and it is shown that covariant density functional theory is able to describe fission barriers on a level of accuracy comparable with non-relativistic calculations, even with the best phenomenological macroscopic+microscopic approaches. Triaxiality in the region of the first saddle plays a crucial role in achieving that.
The double-humped structure of many actinide fission barriers is well established both experimentally and theoretically. There is also evidence, both experimental and theoretical, that some actinide nuclei have barriers with a third minimum, outside the second, fission-isomeric minimum. We perform a large-scale, systematic calculation of actinide fission barriers to identify which actinide nuclei exhibit third minima. We find that only a relatively few nuclei accessible to experiment exhibit third minima in their barriers, approximately nuclei with proton number $Z$ in the range $88 \leq Z \le…
According to the driving potential of a fissile system, we propose a phenomenological fission potential for a description of the pre-neutron emission mass distributions of neutron-induced actinide fission. Based on the nucleus-nucleus potential with the Skyrme energy-density functional, the driving potential of the fissile system is studied considering the deformations of nuclei. The energy dependence of the potential parameters is investigated based on the experimental data for the heights of the peak and valley of the mass distributions. The pre-neutron emission mass distributions for reacti…
Fission-fragment mass distributions are asymmetric in fission of typical actinide nuclei for nucleon number $A$ in the range $228 \lnsim A \lnsim 258$ and proton number $Z$ in the range $90\lnsim Z \lnsim 100$. For somewhat lighter systems it has been observed that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of $^{180}$Hg following electron capture on $^{180}$Tl is asymmetric. We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range $^{178}$Hg--$^{200}$Hg, to investigate the similarities a…
The potential energy of a deformed nucleus has been determined within a Generalized Liquid Drop Model taking into account the proximity energy, the microscopic corrections and compact and necked shapes. Multiple-humped potential barriers appear. A third minimum and third maximum exist in specific exit channels where one fragment is close to a magic spherical nucleus while the other one varies from oblate to prolate shapes. The heights of the fission barriers and half-lives of actinides are in agreement with the experimental results.
In order to describe heavy-ion fusion reactions around the Coulomb barrier with an actinide target nucleus, we propose a model which combines the coupled-channels approach and a fluctuation-dissipation model for dynamical calculations. This model takes into account couplings to the collective states of the interacting nuclei in the penetration of the Coulomb barrier and the subsequent dynamical evolution of a nuclear shape from the contact configuration. In the fluctuation-dissipation model with a Langevin equation, the effect of nuclear orientation at the initial impact on the prolately defor…
The deformation barriers standing in the quasi-molecular shape path have been determined in the actinide region within a macroscopic-microscopic energy derived from a generalized liquid drop model, the algebraic droplet model shell corrections and analytic expressions for the pairing energies. Double and triple-humped fission barriers appear. The second barrier corresponds to the transition from one-body shapes to two touching ellipsoids. The third minimum and third peak, when they exist, come from shell rearrangements in the deformed fragment. The shape of the other almost magic one is close …
Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass-splits. Without quantum shells, which can give extra binding energy to these mass-asymmetric shapes, the nuclei would fission symmetrically. The strongest shell effects are in spherical nuclei, so naturally the spherical "doubly-magic" ${^{132}}$Sn nucleus (${Z=50}$ protons), was expected to play a major role. However, a systematic study of fission has shown that the heavy fragments are distributed around ${Z=52}$ to 56, indicating that ${^{132}}$Sn is not the only driver. Reconciling the strong spherical shell…
The impact of pairing correlations on the fission barriers is investigated in Relativistic Hartree Bogoliubov (RHB) theory and Relativistic Mean Field (RMF)+BCS calculations. It is concluded that the constant gap approximation in the usual RMF+BCS calculations does not provide an adequate description of the barriers. The RHB calculations show that there is a substantial difference in the predicted barrier heights between zero-range and finite range pairing forces even in the case when the pairing strengths of these two forces are adjusted to the same value of the pairing gap at the ground stat…
Fission barriers heights and excitation energies of superdeformed isomeric minima are calculated within the microscopic - macroscopic Woods - Saxon model for 75 actinide nuclei for which the experimental data are known. State - of - the - art methods were used: minimization over many deformation parameters for minima and the imaginary water flow on many - deformation energy grid for saddles, including nonaxial and reflection-asymmetric shapes. We obtain 0.82 - 0.94 MeV rms deviation between the calculated and experimental barriers and 0.53 MeV rms error in the excitation of superdeformed minim…
Isotope-Resolved Ba and Xe Yields in Actinide Fission and Correlated Heavy--Light Fragment Systematics
National Centre for Nuclear Research（国家核研究中心）；China Institute of Atomic Energy（中国原子能科学研究院）；Maria Curie-Skłodowska University（玛丽·居里-斯克沃多夫斯卡大学）；Tsinghua University（清华大学）
The empirical calculations of the prompt neutrons average number for photofission of the 232Th, 233U, 234U, 235U, 236U, 238U, 237Np, 239Pu and 241Am actinides has been done as a function of photon energy, mass and charge of the nuclei, which can be used to evaluate the average number for photo-fission of nuclides for which no or scarce data are available.
We review recent work examining the influence of fission in rapid neutron capture ($r$-process) nucleosynthesis which can take place in astrophysical environments. We briefly discuss the impact of uncertain fission barriers and fission rates on the population of heavy actinide species. We demonstrate the influence of the fission fragment distributions for neutron-rich nuclei and discuss currently available treatments, including recent macroscopic-microscopic calculations. We conclude by comparing our nucleosynthesis results directly with stellar data for metal-poor stars rich in $r$-process el…
A new, rapidly convergent Fourier over spheroid parametrization is developed to describe the shape of a fissioning nucleus: its elongation, non-axiality and left-right asymmetry and neck formation. The 4D Potential Energy Surfaces (PES) of even-even actinide nuclei are evaluated within the macro-micro model. The Langevin trajectories generated on such PESs allow for obtaining the fission fragments' mass and kinetic energy yields. The charge equilibration at the scission configuration and the post-scission neutron emission are also discussed.
We employ density-dependent relativistic mean-field theory to study how the triaxiality and pairing interaction affect the inner fission barriers of actinide nuclei. It was found that triaxiality reduced the inner fission barriers and improved agreement with experimental values for many actinides. However, about 1-2 MeV discrepancy to the experimental values still remained for some of the considered nuclei. Such a discrepancy could be made further smaller by increasing the BCS pairing strength parameter. In this work, we demonstrated that adjusting the paring strength was effective to reproduc…
Background: Fission barriers of actinide nuclei have been mostly and for long been microscopi- cally calculated for even-even fissioning systems. Calculations in the case of odd nuclei have been performed merely within a so-called equal-filling approximation (EFA) as opposed to an approach taking explicitly into account the time reversal breaking properties at the mean field level- and for only one single-particle configuration. Purpose: We study the dependence of the fission barriers on various relevant configurations (e.g. to evaluate the so-called specialization energy). Besides, we want to…
We have studied strength in the BCS pairing force, used as a residual interaction to the relativistic mean-field to reproduce the height of the inner fission barriers for actinide nuclei. It was found that increasing the pairing strength by about 13% makes reproduce the inner fission barriers better over a wide range of actinide nuclei. This result was verified by using the moment-of-inertia of pairing rotational energy, which was introduced to avoid mean-field and odd-mass effects in the pairing interaction to deduce purely the pairing strength. The pairing interaction thus determined could s…
Ternary fission probabilities for thermal neutron induced fission of plutonium are analyzed within the framework of an evaporation-based model where the complexity of time-varying potentials, associated with the neck collapse, are included in a simplistic fashion. If the nuclear temperature at scission and the fission-neck-collapse time are assumed to be ~1.2 MeV and ~10^-22 s, respectively, then calculated relative probabilities of ternary-fission light-charged-particle emission follow the trends seen in the experimental data. The ability of this model to reproduce ternary fission probabiliti…
Monte Carlo calculations of fission of actinides and pre-actinides induced by protons and neutrons in the energy range from 100 MeV to 1 GeV are carried out by means of a recent version of the Liège Intranuclear Cascade Model, INCL++, coupled with two different evaporation-fission codes, GEMINI++ and ABLA07. In order to reproduce experimental fission cross sections, model parameters are usually adjusted on available (p,f) cross sections and used to predict (n,f) cross sections for the same isotopes.
An analysis of the $^{231}$Pa$(d,3n)$$^{230}$U reaction excitation function at energies around the Coulomb barrier has taken into account the pre-equilibrium and compound-nucleus cross sections corrected for the deuteron-breakup decrease of the total reaction cross section, as well as the inelastic breakup enhancement. The analysis reveals the dominance of the deuteron breakup mechanism unlike a former assessment in this respect of the deuteron-induced fission process.
We propose an efficient approach to describe the fission-fragment charge yields for actinides based on the driving potential of fissioning system. Considering the properties of primary fission fragments at their ground states, the driving potential, which represents the potential energies of the system around scission configuration and closely relates to the yields of fragments, can be unambiguously and quickly obtained from the Skyrme energy-density functional together with the Weizsaecker-Skyrme mass model. The fission-fragment charge distributions for thermal-neutroninduced fission and spon…
The systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with $Z=90-120$ from the two-proton up to two-neutron drip lines with proper assessment of systematic theoretical uncertainties has been performed for the first time in the framework of covariant density functional theory (CDFT). These results provide a necessary theoretical input for the r-process modeling in heavy nuclei and, in particular, for the study of fission recycling. Four state-of-the-art globally tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD…
Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separabl…
True ternary fission and Tin-accompanied ternary fission of $^{242}$Pu are studied by using Three Cluster Model. True ternary fission is considered as formation of heavy fragments in the region $28\leq Z_1,Z_2,Z_3\leq 38$, with comparable masses. The possible fission channels are predicted from potential-energy calculations. Interaction potentials, Q-values and relative yields for all possible fragmentations in equatorial and collinear configurations are calculated and compared to each other. It is found out that ternary fission with formation of a double magic nucleus like $^{132}Sn$ is more …
The first solids that form as a cooling white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. This is because the melting points of WD matter scale as $Z^{5/3}$ and actinides have the largest charge $Z$. We estimate that the solids may be so enriched in actinides that they could support a fission chain reaction. This reaction could ignite carbon burning and lead to the explosion of an isolated WD in a thermonuclear supernova (SN Ia). Our mechanism could potentially explain SN Ia with sub-Chandrasekhar ejecta masses and short delay times.
The cold ternary fission of $^{238}$Pu, $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, with $^{4}$He as light charged particle, in equatorial and collinear configuration has been studied within the Unified ternary fission model (UTFM). The fragment combination $^{100}$Zr+$^{4}$He+$^{134}$Te possessing the near doubly magic nuclei $^{134}$Te (N=82, Z=52) gives the highest yield in the alpha accompanied ternary fission of $^{238}$Pu. For the alpha accompanied ternary fission of $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, the highest yield was found for the fragment combination with doubly m…
Fission at low excitation energy is an ideal playground to probe the impact of nuclear structure on nuclear dynamics. While the importance of structural effects in the nascent fragments is well-established in the (trans-)actinide region, the observation of asymmetric fission in several neutron-deficient pre-actinides can be explained by various mechanisms. To deepen our insight into that puzzle, an innovative approach based on inverse kinematics and an enhanced version of the VAMOS++ heavy-ion spectrometer was implemented at the GANIL facility, Caen. Fission of $^{178}$Hg was induced by fusion…
To describe of dynamics of ternary fission of $^{252}$Cf an equation of motion of the tri-nuclear system is calculated. The fission of the $^{70}$Ni+$^{50}$Ca+$^{132}$Sn channel was chosen as one of the more probable channels of true ternary fission of $^{252}$Cf. The collinearity of ternary fission has been checked by analyzing results of the equation of motion. The results show that if initially all nuclei are placed collinearly (potential energy of this position is the smallest) and the component of the middle fragment's initial velocity which is perpendicular to this line, is zero then ter…
Fission-fragment mass distributions were measured for 225,227Pa nuclei formed in fusion reactions of 19F + 206, 208Pb around fusion barrier energies. Mass-angle correlations do not indicate any quasi-fission like events in this bombarding energy range. Mass distributions were fitted by Gaussian distribution and mass variance extracted. At below-barrier energies, the mass variance was found to increase with decrease in energy for both nuclei. Results from present work were compared with existing data for induced fission of 224, 226Th and 228U around barrier energies. Enhancement in mass varianc…
T-odd angular correlations in ternary fission of 233-U and 235-U nuclei by slow polarized neutrons are not related to TRI (time reversal invariance) violation, but are caused by an effective spin-orbit interaction in the final state.
We have calculated the fission probabilities for 237-Np, 233,235,238-U, 232-Th, and nat-Pb following the absorption of photons with energies from 68 MeV to 3.77 GeV using the RELDIS Monte-Carlo code. This code implements the cascade-evaporation-fission model of intermediate-energy photonuclear reactions. It includes multiparticle production in photoreactions on intranuclear nucleons, pre-equilibrium emission, and the statistical decay of excited residual nuclei via competition of evaporation, fission, and multifragmentation processes. The calculations show that in the GeV energy region the fis…
Photonuclear reaction is described with an approach based on the quasideuteron nuclear photoabsorption model followed by the process of competition between light particle evaporation and fission for the excited nucleus. Thus fission process is considered as a decay mode. The evaporation-fission process of the compound nucleus is simulated in a Monte-Carlo framework. Photofission reaction cross sections are analysed in a systematic manner in the energy range $\sim$~50-70 MeV for the actinides $^{232}$Th, $^{233}$U, $^{235}$U, $^{238}$U and $^{237}$Np and the pre-actinide nuclei $^{208}$Pb and $…
The event-by-event fission model FREYA is extended to spontaneous fission of actinides and a variety of neutron observables are studied for spontaneous fission and fission induced by thermal neutrons with a view towards possible applications for detection of special nuclear materials.
Cluster radioactivity is the emission of a fragment heavier than $α$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment a…
Detailed assessments of the ability of recent theoretical approaches to modeling existing experimental data for ternary fission confirm earlier indications that the dominant mode of cluster formation in ternary fission is clusterization in very neutron rich, very low density, essentially chemically equilibrated, nucleonic matter. An extended study and comparison of these approaches applied to ternary fission yields in the thermal neutron induced reaction $^{241}$Pu($n_{\rm th}$,f) has been undertaken to refine the characterization of the source matter. The resonance gas approximation has been …
Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass-yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-…
Experimental data on angular distributions of gamma rays emitted from binary and ternary spontaneous fission of $^{252}{\rm Cf}$ are analyzed. Their difference indicates that the alignment of fragments is higher in ternary fission than in binary one. The consequences of possible relation between the mechanism of ternary fission and the excitation of collective modes during the saddle-to-scission stage are discussed.
The possibilities of the proposed statistical approach are shown in the task of investigating the post-scission transformation of mass and charge yields of fission fragments with considering the emission of different length of chains of elementary particles as the beta particles and neutrons fission. Using as the example the 232 Th isotope, which is located on the border between pre-actinide and actinides nuclei, the changes in the topology of fission fragments yields, the role of emission of nuclear particles in the competition of symmetric and asymmetric modes in fission processes are invest…
A static scission configuration in cold ternary fission has been considered in the framework of two mean field approaches. The virial theorems has been suggested to investigate correlations in the phase space, starting from a kinetic equation. The inverse mean field method is applied to solve single-particle Schredinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system via inverse scattering method in the approximation of reflectless single-particle potentials
We found that a true ternary fission with formation of a heavy third fragment (a new type of radioactivity) is quite possible for superheavy nuclei due to the strong shell effects leading to a three-body clusterization with the two doubly magic tin-like cores. The simplest way to discover this phenomenon in the decay of excited superheavy nuclei is a detection of two tin-like clusters with appropriate kinematics in low-energy collisions of medium mass nuclei with actinide targets. The three-body quasi-fission process could be even more pronounced for giant nuclear systems formed in collisions …
By breaking both the axial and the spatial reflection symmetries, we develop multidimensionally constrained relativistic mean field (MDC-RMF) models. The nuclear shape is assumed to be invariant under the reversion of $x$ and $y$ axes, i.e., the intrinsic symmetry group is $V_{4}$ and all shape degrees of freedom $β_{λμ}$ with even $μ$, such as $β_{20}$, $β_{22}$, $β_{30}$, $β_{32}$, $β_{40}$, $\dots$, are included self-consistently. The Dirac wave functions are expanded in an axially deformed harmonic oscillator basis. The RMF functional can be one of the following four forms: the meson excha…
We compute the final kinetic energies of the fragments emitted in the light charged particle accompanied cold fission of $^{252}$Cf taking into account the ground state quadrupole deformation and the finite-size effects of the fragments and integrating the equations of motion for a three-body system subjected only to Coulomb forces. The initial conditions for the trajectory calculations were derived in the frame of a deformed cluster model which includes also the effect due to the absorbative nuclear part. Although the distributions of initial kinetic energies is rather broad we show that in c…
Comprehensive calculations of cross sections of photon induced reactions on $^{233-238}$U targets for incident photon energies from 3 up to 30 MeV are undertaken with the statistical model code EMPIRE-3.2 Malta. Results are compared with the experimental data from EXFOR and with the current evaluations. The differences and the similarities between the models and parameters used in calculations of photon- and neutron-induced reactions on the same nuclei are discussed with focus on fission. The role of the extended optical model for fission in improving the description of the measured data and i…
Photofission of actinides is studied in the region of nuclear excitation energies that covers the entire giant dipole resonance (GDR) region. A comparative analysis of the behavior of the symmetric and asymmetric modes of photon induced fission as a function of the average excitation energy of the fissioning nucleus is performed. The mass distributions of $^{238}$U photofission fragments are obtained at the endpoint bremsstrahlung energy of 29.1 MeV which corresponds to mean photon energy of 13.7$\pm$0.3 MeV that coincides with GDR peak for $^{238}$U photofission. The integrated yield of $^{23…
Sensitivity of Isotopic Fission Yields in Actinides to the Macroscopic Liquid-Drop Model: LSD vs ISOLDA
National Centre for Nuclear Research（国家核研究中心）；Maria Curie-Skłodowska University（玛丽亚·居里-斯克隆多斯卡大学）；China Institute of Atomic Energy（中国原子能科学研究院）；Tsinghua University（清华大学）
In the frame of proposed statistical method the calculation of fission-fragment yields mass and charge spectra for pre- actinide nuclei on example of natPb isotopes had been conducted.
We have decomposed to symmetric and asymmetric modes the mass-TKE fission fragment distributions calculated by 4-dimensional Langevin approach and observed how the dominant fission mode and symmetric mode change as functions of $Z^2/\sqrt[3]{A}$ of the fissioning system in the actinides and trans-actinide region. As a result, we found that the symmetric mode makes a sudden transition from super-long to super short fission mode around $^{254}$Es. The dominant fission modes on the other hand, are persistently asymmetric except for $^{258}$Fm, $^{259}$Fm and $^{260}$Md when the dominant fission m…
The existence of a new type of cluster decay called "collinear cluster tri-partition" (CCT) is discussed by an analysis of the landscape of the potential energy surface (PES). The total energy of the ternary system is found as a sum the binding energies of fragments and nucleus-nucleus interaction between them. The pre-scission state of the ternary system is assumed to be arranged as a chain of the three fragments along a straight line. Minima and valleys of the PES are determined by variation of the proton and neutron distributions between them. Pre-scission prompt emission of neutrons is ass…
A model for ternary fission is discussed in which a third particle (alpha-particle) is emitted due to non-adiabatic change of the nuclear potential at neck rapture. An expression for energy and angular distribution of alpha-particles is proposed. It is shown that an interaction between spin of fissioning system and orbital momentum of alpha-particle (spin-orbit interaction in the final state) results in recently observed asymmetry of alpha-particle emission, which can be formally related to T-odd correlation. No strong dependence of the asymmetry on the angle of alpha-particle emission with re…
The concept of collinear spontaneous true ternary fission of 252Cf is subject to critical analysis. The conclusion is that the collinear flight of the fragments turns out to be a natural and most probable mode. The collinearity arises in the model on the prescission stage as a result of the account of the principles of the collective Bohr's model. It is partly destroyed at the post-scission stage of spreading of the fragments due to their Coulomb interaction, with the allowance for the spin effects arising at the moment of scission. The final angular distribution of the fragments is calculated…
Based on a recent experimental finding which may suggest the existence of a tri-nuclear molecular structure before the cold ternary fragmentation of $^{252}$Cf takes place, we solved the eigenvalue problem of a certain class of vibrations which are very likely to occur in these molecules. These oscillations are the result of the joined action of rotations of the heavier fragments and the transversal vibrations of the lighter spherical cluster with respect to the fission axis. In the calculation of the interaction between the heavier fragments we took into account higher multipole deformations,…
