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 with the theoretical spectra, and the results are consistent with the systematics. We conclude that the semi-empirical method is sound, and it could be a useful tool for prompt fission neutron spectra evaluation.
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.
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}…
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…
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…
Following the formation of an excited muonic atom, inner shell transitions may proceed without photon emission by inverse internal conversion, i.e. the muonic excitation energy is transferred to the nucleus. In actinides, the 2p -> 1s and the 3d -> 1s muonic transitions result in excitation of the nuclear giant dipole and giant quadrupole resonances, respectively, which act as doorway states for fission. The nuclear excitation energy is typically 6.5 - 10 MeV. Because the muon lifetime is long compared to the timescale of prompt nuclear fission, the motion of the muon in the Coulomb field of t…
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 Hauser-Feshbach Fission Fragment Decay (HF$^3$D) model is extended to calculate the prompt fission neutron spectrum (PFNS) for the thermal neutron induced fission on $^{235}$U, where the evaporated neutrons from all possible fission fragment pairs are aggregated. By studying model parameter sensitivities on the calculated PFNS, as well as non-statistical behavior of low-lying discrete level spin distribution, we conclude that discrepancies between the aggregation calculation and the experimental PFNS seen at higher neutron emission energies can be attributed to both the primary fission fra…
Earlier studies of 239Pu(n, f) have been extended to incident neutron energies up to 20 MeV within the framework of the event-by-event fission model FREYA, into which we have incorporated multichance fission and pre-equilibrium neutron emission. The main parameters controlling prompt fission neutron evaporation have been identified and the prompt fission neutron spectrum has been analyzed by fitting those parameters to the average neutron multiplicity nubar from ENDF-B/VII.0, including the energy-energy correlations in nubar(E) obtained by fitting to the experimental nubar data used in the END…
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.
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…
This study addresses, for the first time, the total prompt energy release and its components for the fission of 235-U, 238-U, and 239-Pu as a function of the kinetic energy of the neutron inducing the fission. The components are extracted from experimental measurements, where they exist, together with model-dependent calculation, interpolation, and extrapolation. While the components display clear dependencies upon the incident neutron energy, their sums display only weak, yet definite, energy dependencies. Also addressed is the total prompt energy deposition in fission for the same three syst…
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…
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…
We solve the time-dependent Dirac equation for a muon which is initially bound to a fissioning actinide nucleus. The computations are carried out on a 3-D cartesian lattice utilizing the Basis-Spline collocation method. The muon dynamics is sensitive to the nuclear energy dissipation between the outer fission barrier and the scission point. From a comparison with experimental data we find a dissipated energy of about 10 MeV and a fission time delay due to friction of order $2 \times 10^{-21}$ s.
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…
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…
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 CGMF code implements the Hauser-Feshbach statistical nuclear reaction model to follow the de-excitation of fission fragments by successive emissions of prompt neutrons and $γ$ rays. The Monte Carlo technique is used to facilitate the analysis of complex distributions and correlations among the prompt fission observables. Starting from initial configurations for the fission fragments in mass, charge, kinetic energy, excitation energy, spin, and parity, $Y(A,Z,KE,U,J,π)$, CGMF samples neutron and $γ$-ray probability distributions at each stage of the decay process, conserving energy, spin an…
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…
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…
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 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…
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 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…
Employing a recently developed Monte Carlo model, we study the fission of 240Pu induced by neutrons with energies from thermal to just below the threshold for second chance fission. Current measurements of the mean number of prompt neutrons emitted in fission, together with less accurate measurements of the neutron energy spectra, place remarkably fine constraints on predictions of microscopic calculations. In particular, the total excitation energy of the nascent fragments must be specified to within 1 MeV to avoid disagreement with measurements of the mean neutron multiplicity. The combinati…
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 …
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…
The Hauser-Feshbach statistical model is applied to the de-excitation of primary fission fragments using input mass yields calculated with macroscopic-microscopic models of the potential energy surface. We test the sensitivity of the prompt fission observables to the input mass yields for two important reactions, $^{235}$U$(n_\mathrm{th},f)$ and $^{239}$Pu$(n_\mathrm{th},f)$, for which good experimental data exist. General traits of the mass yields, such as the location of the peaks and their widths, can impact both the prompt neutron and $γ$-ray multiplicities, as well as their spectra. Speci…
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 present a self-consistency analysis of fission product yield evaluations. Anomalous yields are determined using a series of simple conservation checks and comparing charge distributions with common parameterizations. The total prompt neutron multiplicity as a function of product mass $\barν_T(A)$ is derived directly from the independent fission product yields using average charge conservation. This method is checked against Monte Carlo simulations of the de-excitation of the fission fragments in a Hauser-Feshbach statistical decay framework. The derived $\barν_T(A)$ is compared with experim…
The present work concerns two successful models used today: Point by Point (PbP) and the Monte Carlo approaches. The description of the PbP model and of the extended Los Alamos model for higher energies that takes into account the secondary chains and ways is given in Chapter II. In this chapter are given also examples of PbP and most probable fragmentation approach calculations for various quantities which characterize prompt emission: multi-parametric matrices, quantities as a function of fragment mass, quantities as a function of the TKE and total average quantities, for different spontaneo…
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.
We perform energy dependent calculations of independent and cumulative fission product yields for $^{235}$U, $^{238}$U, and $^{239}$Pu in the first chance fission region. Starting with the primary fission fragment distributions taken from available experimental data and analytical functions based on assumptions for the excitation energy and spin-parity distributions, the Hauser-Feshbach statistical decay treatment for fission fragment de-excitation is applied to more than 1,000 fission fragments for the incident neutron energies up to 5 MeV. The calculated independent fission product yields ar…
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…
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.
The Hauser-Feshbach fission fragment decay model, $\mathtt{HF^3D}$, which calculates the statistical decay of fission fragments, has been expanded to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input pre-scission quantities - fission probabilities and the average energy causing fission - and post-scission quantities - yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculatio…
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.
A simplified, though realistic, model describing two receding and accelerating fission fragments, due to their mutual Coulomb repulsion, shows that fission fragments share excitation energy well after they ceased to exchange nucleons. This mechanism leads to a lower total kinetic energy of the fission fragments, particularly if the pygmy resonances in the fission fragments are excited. Even though the emphasis here is on fission, similar arguments apply to fragments in heavy-ion reactions.
