We describe the capture, fusion, fission and evaporation residue formation cross sections of superheavy nuclei within the proposed earlier two stages dynamical model. The approaching of the projectile nucleus to the target nucleus is described in the first stage of the model. On the second stage, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by Langevin equations. The transport coefficients of these equations are calculated within the microscopic linear response theory. The mutual orientation of the colliding ions, the tunneling through the Coulomb barrier in the entrance channel and the shell effects in the potential energy on both stages of the calculations are taking into account. The obtained results are compared with the available experimental data and other theoretical predictions.
Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state; the temperature dependence of the location of fission transition points; and the orientation degree of freedom. We see no evidence to suggest that the nuclear viscosity departs from the surface-plus-window dissipation model. The strong increase in the nuclear viscosity above a temperature of ~1 MeV deduced by others is an artifact generated by an inadequate fission model.
We demonstrate that Bayesian machine learning can be used to treat the vast amount of experimental fission data which are noisy, incomplete, discrepant, and correlated. As an example, the two-dimensional cumulative fission yields (CFY) of neutron-induced fission of $^{238}$U are evaluated with energy dependencies and uncertainty qualifications. For independent fission yields (IFY) with very few experimental data, the heterogeneous data fusion of CFY and IFY is employed to interpolate the energy dependence. This work shows that Bayesian data fusion can facilitate the further utilization of impe…
A modified Woods-Saxon potential model is proposed for a unified description of the entrance channel fusion barrier and the fission barrier of fusion-fission reactions based on the Skyrme energy-density functional approach. The fusion excitation functions of 120 reactions have been systematically studied. The fusion (capture) cross sections are well described with the calculated potential and an empirical barrier distribution. Incorporating a statistical model (HIVAP code) for describing the decay of the compound nucleus, the evaporation residue (and fission) cross sections of 51 fusion-fissio…
Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with the fission of fully equilibrated systems with fission lifetime estimates obtained via a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state, the temperature dependence of the location and height of fission transition points, and the orientation degree of freedom. If the standard techniques for calculating fission lifetimes are used, then the calculated excitation-energy dependence of fission lifetimes is incorrect. We see no evi…
We analyzed the experimental data of the pre-scission neutron multiplicity in connection with fission fragments in the reaction $^{58}$Ni+$^{208}$Pb at the incident energy corresponding to the excitation energy of compound nucleus $E^{*}$=185.9 MeV, which was performed by DéMoN group. The relation between the pre-scission neutron multiplicity and each reaction process having different reaction time is investigated. In order to study the fusion-fission process accompanied by neutron emission, the fluctuation-dissipation model combined with a statistical model is employed. It is found that the f…
Consideration of memory of spin and parity in the fissioning compound nucleus by applying the Hauser-Feshbach fission fragment decay model to photonuclear reactions
We present a statistical-model description of fission, in the framework of compound-nucleus decay, which is found to simultaneously reproduce data from both heavy-ion-induced fusion reactions and proton-induced spallation reactions at around 1 GeV. For the spallation reactions, the initial compound-nucleus population is predicted by the Liège Intranuclear Cascade Model. We are able to reproduce experimental fission probabilities and fission-fragment mass distributions in both reactions types with the same parameter sets. However, no unique parameter set was obtained for the fission probability…
The yields of evaporation residues, fusion-fission and quasifission fragments in the $^{48}$Ca+$^{144,154}$Sm and $^{16}$O+$^{186}$W reactions are analyzed in the framework of the combined theoretical method based on the dinuclear system concept and advanced statistical model. The measured yields of evaporation residues for the $^{48}$Ca+$^{154}$Sm reaction can be well reproduced. The measured yields of fission fragments are decomposed into contributions coming from fusion-fission, quasifission, and fast-fission. The decrease in the measured yield of quasifission fragments in $^{48}$Ca+$^{154}…
The prompt fission neutron spectra for neutron-induced fission of 233U for low energy neutrons (below 6 MeV) are calculated using the nuclear evaporation theory with a semi-empirical method, in which the partition of the total excitation energy between the fission fragments for the nth+233U fission reactions are determined with the available experimental and evaluation data. The calculated prompt fission neutron spectra agree well with the experimental data. The proportions of high- energy outgoing neutrons of prompt fission neutron spectrum versus incident neutron energies are investigated wi…
Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time-scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. In the regime $T>1$ MeV, Kramers' theory should be replace…
This dissertation deals with theoretical descriptions of nuclear fission and synthesis of superheavy elements via fusion. The associated shape evolutions are treated using a random-walk approach where both the potential energy and the nuclear level density influence the dynamics. The work in this thesis extends the random-walk model by, in addition to the previous description of fragment mass yields, also simulating how much kinetic energy the fission-fragments obtain and the number of neutrons they emit, as well as how these two quantities are correlated. The thesis also presents studies of h…
Global macroscopic features observed in the fully-damped binary processes in light di-nuclear systems, such as limiting angular momenta, mean total kinetic energies and energy thresholds for fusion-fission processes (''fission thresholds") are presented. Their deduced systematics are consistent with that obtained for heavier systems and follow a fusion-fission picture which can be described by a realistic rotating liquid drop model considering diffuse-surface and finite-nuclear-range effects.
The K-matrix formalism is applied to a schematic model for nuclear fission. The purpose is to explore the dependence of observables on the assumptions made about the configuration space and nucleon interaction in the Hamiltonian of the fissile nucleus. As expected, branching ratios in induced fission are found to depend sensitively on the character of the residual interaction, whether it is pairing in form or taken from a random ensemble. On the other hand, the branching ratio is not much affected by the presence of additional configurations that do not introduce new fission paths.
Some nearly-symmetric fusion reactions are systematically investigated with the improved quantum molecular dynamics (ImQMD) model. By introducing two-body inelastic scattering in the Fermi constraint procedure, the stability of an individual nucleus and the description of fusion cross sections at energies near the Coulomb barrier can be further improved. Simultaneously, the quasi-fission process in $^{154}$Sm+$^{160}$Gd is also investigated with the microscopic dynamics model for the first time. We find that at energies above the Bass barrier, the fusion probability is smaller than $10^{-5}$ f…
The two stages dynamical stochastic model developed earlier for description of fusion-fission reactions is applied to the calculation of mass- and energy-distributions of fission fragments of platinum isotopes in reaction ${\rm ^{36}Ar + ^{142}Nd \to ^{178-x}Pt + xn}$. The first stage of this model is the calculation of the approaching of projectile nucleus to the target nucleus. On the second stage of the model, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by three-dimensional L…
The fusion excitation function is the important quantity in planning experiments for the synthesis of superheavy elements. Its values seem to be determined by the experimental study of the hindrance to complete fusion by the observation of mass, angular and energy distributions of the fissionlike fragments. There is ambiguity in establishment of the reaction mechanism leading to the observed binary fissionlike fragments. The fissionlike fragments can be produced in the quasifission, fast fission, and fusion-fission processes which have overlapping in the mass (angular, kinetic energy) distribu…
Fusion dynamics and the onset of quasi-fission in reactions, leading to production of superheavy nuclei are investigated using the constrained molecular dynamics model. Constraints on the parameters of the nuclear equation of state are derived from experimental fusion probabilities. The obtained constraint on the modulus of incompressibility of nuclear matter K0 = 240 - 260 MeV is consistent with the results of previous study using the Boltzmann-Uehling-Uhlenbeck equation and also with constraints derived using the recent neutron star binary collision event GW170817. Unlike the modulus of inco…
A realistic microscopically-based quantum approach to the competition between fusion and quasi-fission in a heavy fusing system is applied to several reactions leading to $^{256}$No. Fusion and quasi-fission are described in terms of a diffusion process of nuclear shapes through a dynamical collective potential energy landscape which is initially diabatic and gradually becomes adiabatic. The microscopic ingredients of the theory are obtained with a realistic two-center shell model based on Woods-Saxon potentials. The results indicate that (i) the diabatic effects play a very important role in …
Calculations for fission and cluster decay of $^{76}Sr$ are presented for this nucleus to be in its ground-state or formed as an excited compound system in heavy-ion reactions. The predicted mass distribution, for the dynamical collective mass transfer process assumed for fission of $^{76}Sr$, is clearly asymmetric, favouring $α$-nuclei. Cluster decay is studied within a preformed cluster model, both for ground-state to ground-state decays and from excited compound system to the ground-state(s) or excited states(s) of the fragments.
Coulomb fission mechanism may take place if the maximum Coulomb-excitation energy transfer in a reaction exceeds the fission barrier of either the projectile or target. This condition is satisfied by all the reactions used for the earlier blocking measurements except one reaction 208 Pb + Natural Ge crystal, where the measured timescale was below the measuring limit of the blocking measurements < 1 as. Hence, inclusion of the Coulomb fission in the data analysis of the blocking experiments leads us to interpret that the measured time longer than a few attoseconds (about 2-2.5 as) is nothing bu…
Modelling fission with microscopic input: excitation-energy-dependent fission paths for neutron-induced reactions
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔天文与天体物理研究所，布鲁塞尔自由大学）；Brussels Laboratory of the Universe - BLU-ULB（宇宙布鲁塞尔实验室）
The mechanism leading to the formation of the observed products of the collinear cluster tripartition is carried out within the framework of the model based on the dinuclear system concept. The yield of fission products is calculated using the statistical model based on the driving potentials for the fissionable system. The minima of potential energy of the decaying system correspond to the charge numbers of the products which are produced with large probabilities in the sequential fission (partial case of the collinear cluster tripartition) of the compound nucleus. The realization of this mec…
An attempt to unfold the respective influence of the fusion and fission stages on typical fission observables, and namely the neutron pre-scission multiplicity, is proposed. A four-dimensional dynamical stochastic Langevin model is used to calculate the decay by fission of excited compound nuclei produced in a wide set of heavy-ion collisions. The comparison of the results from such a calculation and experimental data is discussed, guided by predictions of the dynamical deterministic HICOL code for the compound-nucleus formation time. While the dependence of the latter on the entrance-channel …
A theory of the competition between fusion and quasi-fission in a heavy fusing system is proposed, which is based on a master equation and the two-center shell model. Fusion and quasi-fission arise from a diffusion process in an ensemble of nuclear shapes, each of which evolves towards the thermal equilibrium. The master equation describes the diffusion of the nuclear shapes due to quantum and thermal fluctuations. Other crucial physical effects like dissipation, ground-state shell effects, diabatic effects and rotational effects are also incorporated into the theory. The fusing system moves i…
Pre-saddle neutron multiplicity has been calculated for several fission reactions induced by heavy ions and light particles. Experimentally, it is impossible to determine the contribution of neutrons being emitted before the saddle point and those emitted between the saddle and the scission points. Determination of the pre-saddle neutron multiplicity in our research is based on the comparison between the experimental anisotropies and those predicted by the standard saddle-point statistical model. Analysis of the results shows that the pre-saddle neutron multiplicity depends on the fission barr…
The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the $^{16}$O+$^{238}$U, $^{19}$F+$^{208}$Pb and $^{32}$S+$^{208}$Pb reactions is studied by analyzing the angular momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of axial symmetry axes of colliding nuclei to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that the deviation of the experimental…
On the occasion of the $75^{th}$ anniversary of the fission phenomenon, we present a surprisingly simple result which highlights the important role of isospin and its conservation in neutron rich fission fragments. We have analysed the fission fragment mass distribution from two recent heavy-ion reactions $^{238}$U($^{18}$O,f) and $^{208}$Pb($^{18}$O,f) as well as a thermal neutron fission reaction $^{245}$Cm(n$^{th}$,f). We find that the conservation of the total isospin explains the overall trend in the observed relative yields of fragment masses in each fission pair partition. The isospin v…
We propose an effective method for the precise investigation of the fusion-fission mechanism in the superheavy-mass region, using the fluctuation-dissipation model. The trajectory calculation with friction is performed in the nuclear deformation space using the Langevin equation. In the reaction $^{48}$Ca+$^{244}$Pu, the trajectories are classified into the fusion-fission process, the quasi-fission process and the deep quasi-fission process. By analyzing the time evolution of each trajectory, the mechanism of each process is clearly revealed, i.e., it is explained why a trajectory takes a char…
We present an evidence of isospin effects in nuclear fission by comparing the fission widths for reactions involving different isospin states of the same compound nucleus (CN). Yadrovsky suggested this possibility in 1975. Yadrovsky obtained the fission widths for two reaction data sets, namely $^{206}$Pb($α$,f) and $^{209}$Bi(p,f), both leading to same CN, and concluded that "a nucleus remembers the isospin value of the nuclear states leading to fission". We obtain the fission decay widths for both the $T_0+1/2$ and $T_0-1/2$ states of CN by using two appropriate reaction data sets. We then c…
Fusion - fission probabilities in the synthesis of heaviest elements are discussed in the context of the latest experimental reports. Cross sections for superheavy nuclei are evaluated using "Fusion by Diffusion" (FBD) model. Predictive power of this approach is shown for experimentally known Lv, Og isotopes and predictions given for Z=119,120. Ground state and saddle point properties as: masses, shell corrections, pairing energies and deformations necessary for cross section estimations are calculated systematically within the multidimensional microscopic - macroscopic method based on the def…
Nucleon exchange mechanism is investigated in the central collisions of ${}^{40}$Ca + ${}^{238}$U and ${}^{48}$Ca + ${}^{238}$U systems near the quasi-fission regime in the framework of the Stochastic Mean-Field (SMF) approach. Sufficiently below the fusion barrier, di-nuclear structure in the collisions is maintained to a large extend. Consequently, it is possible to describe nucleon exchange as a diffusion process familiar from deep-inelastic collisions. Diffusion coefficients for proton and neutron exchange are determined from the microscopic basis of the SMF approach in the semi-classical …
Fusion-fission dynamics is investigated with a special emphasis on fusion reactions at low energy for which shell effects and pairing correlations can play a crucial role leading in particular to multi-modal fission. To follow the dynamical evolution of an excited and rotating nucleus we solve a 2-dimensional Langevin equation taking explicitly light-particle evaporation into account. The confrontation theory-experiment is demonstrated to give interesting information on the model presented, its qualities as well as its shortcomings.
The dependence of fission barriers on the excitation energy of the compound nucleus impacts the survival probability of superheavy nuclei synthesized in heavy-ion fusion reactions. In this work, we investigate the isentropic fission barriers by means of the self-consistent nuclear density functional theory. The relationship between isothermal and isentropic descriptions is demonstrated. Calculations have been carried out for $^{264}$Fm, $^{272}$Ds, $^{278}$112, $^{292}$114, and $^{312}$124. For nuclei around $^{278}$112 produced in "cold fusion" reactions, we predict a more rapid decrease of f…
Focused on the generation and evolution of vast complementary pairs of the primary fission fragments at scission moment, Dinuclear and Statistical Model (DSM) is proposed. (1) It is assumed that the fissile nucleus elongates along a symmetric coaxis until it breaks into two primary fission fragments. (2) Every complementary pair of the primary fission fragments is approximatively described as two ellipsoids with large deformation at scission moment. (3) The kinetic energy in every complementary pair of the primary fragments is mainly provided by Coulomb repulsion, which is explicitly expressed…
Mass-angle correlation of fission fragments has been understood as manifestation of quasifission. We show that this is not so: the effect can originate from correlation between fusion-fission amplitudes with different total spins signifying matter-wave interference in compound nucleus processes. This resolves the well-known puzzle with the mass-angle correlation in the complete fusion sub-barrier reaction $^{16}$O+$^{238}$U. Our finding is important for more reliable predictions of production cross sections for superheavy elements. Matter-wave interference also produces quantum-classical trans…
Compound nucleus effective moment of inertia has been calculated for several fission reaction systems induced by nucleons, light particles, and heavy ions. Determination of this quantity for these systems is based upon the comparison between the experimental data of the fission fragment angular distributions as well as the prediction of the standard saddle-point statistical model (SSPSM). For the systems, the two cases, namely with and without neutron emission corrections were considered. In these calculations, it is assumed that all the neutrons are emitted before reaching the saddle point.It…
The fission fragment mass distributions have been measured in the reactions 16O + 184W and 19F+ 181Ta populating the same compound nucleus 200Pb? at similar excitation energies. It is found that the widths of the mass distribution increases monotonically with excitation energy, indicating the absence of quasi-fission for both reactions. This is contrary to two recent claims of the presence of quasi-fission in the above mentioned reactions.
The angular distributions of fission fragments for the $^{32}$S+$^{184}$W reaction at center-of-mass energies of 118.8, 123.1, 127.3, 131.5, 135.8, 141.1 and 144.4 MeV were measured. The experimental fission excitation function is obtained. The fragment angular anisotropy ($\mathcal{A}_{\rm exp}$) is found by extrapolating the each fission angular distributions. The measured fission cross sections of the $^{32}$S+$^{182,184}$W reaction are decomposed into fusion-fission, quasifission and fast fission contributions by the dinuclear system model. The total evaporation residue excitation function…
The role of spherical quantum shells in the competition between fusion and quasi-fission is studied for reactions forming heavy elements. Measurements of fission fragment mass distributions for different reactions leading to similar compound nuclei have been made near the fusion barrier. In general, more quasi-fission is observed for reactions with non-magic nuclei. However, the $^{40}$Ca+$^{208}$Pb reaction is an exception, showing strong evidence for quasi-fission, though both nuclei are doubly magic. Time-dependent Hartree-Fock calculations predict fast equilibration of $N/Z$ in the two fra…
We analyze reactions of several types that are naively below threshold but can proceed because of the release of binding energy from nuclear fission and occasionally the formation of Coulombic bound states. These reactions include (i) photofission with pion production and (ii) charged current neutrino-nucleus reactions that lead to fission and/or formation of a Coulomb bound state of a $μ^-$ with the nucleus of a fission fragment. We comment on the possible experimental observation of these reactions.
Background: Quasifission and fusion-fission are primary mechanisms to prevent the production of superheavy elements. The recent experimental measurements reveal that the fusion-evaporation cross section in the $3n$ reaction channel of $^{48}$Ca+$^{239}$Pu is 50 times lower than using $^{244}$Pu as target nucleus. However, the precise mechanisms of this remarkable isotopic dependence are not well understood. Purpose: To understand the experimental observation of the rapid decrease of stability of superheavy nuclei as the neutron number decreases, the theoretical studies of quasifission and fusi…
In this contribution, we present the main relations of the Langevin approach to the description of fission or fusion-fission reactions. The results of Langevin calculations are shown for the mass distributions of fission fragments of super-heavy elements and used for the investigation of memory effects in nuclear fission.
The recent availability of precisely measured fusion cross-sections has enabled the extraction of a representation of the distribution of barriers encountered during fusion. These representations, obtained from a variety of reactions, provide a direct observation of how the structure of the fusing nuclei changes the inter-nuclear potential landscape, thus affecting the fusion probability. Recent experiments showing the effects of static quadrupole and hexadecapole deformation, single-- and double-phonon states, transfer of nucleons between two nuclei, and high lying excited states are reviewed…
The effect of the coupling between the neutron multiplicity and the fission competition on the evaporation residue cross sections of the $^{48}$Ca$+^{244}$Pu reaction
New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Nuclear Physics（核物理研究所）
The first solids that form as a white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. Previously [PRL 126, 1311010] we found that these solids might support a nuclear fission chain reaction that could ignite carbon burning and provide a new Type Ia supernova (SN Ia) mechanism involving an {\it isolated} WD. Here we explore this fission mechanism in more detail and calculate the final temperature and density after the chain reaction and discuss a number of open physics questions.
