Fissioning nuclei and fission fragments, nuclear fragments emerging from energetic collisions, or nuclei probed with various external fields can emit one or more pre-equilibrium neutrons, protons, and potentially other heavier nuclear fragments. I describe a formalism which can be used to evaluate the pre-equilibrium neutron emission probabilities and the excitation energies of the remnant fragments.
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.
Fortran subroutines have been written to simulate the production of fission neutrons from the spontaneous fission of 252Cf and 240Pu, and from the thermal neutron induced fission of 239Pu and 235U. The names of these four subroutines are getnv252, getnv240, getnv239, and getnv235, respectively. These subroutines reproduce measured first, second, and third moments of the neutron multiplicity distributions, measured neutron-fission correlation data for the spontaneous fission of 252Cf, and measured neutron-neutron correlation data for both the spontaneous fission of 252Cf and the thermal neutron…
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…
We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium isotopes, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three c…
Post-neutron emission fission product mass distributions are calculated by using pre-neutron emission fission product yields (FPYs) and neutron multiplicity. A semi-empirical model is used to calculate the pre-neutron FPY, first. Then the neutron multiplicity for each fission fragment mass is used to convert the pre-neutron FPY to the post-neutron FPY. In doing so, assumptions are made for the probability for a pre-emission fission fragment with a mass number $A^*$ to decay to a post-emission fragment with a mass number $A$. The resulting post-neutron FPYs are compared with the data available.…
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…
The series of Uranium isotopes with $N=154 \sim 172$ around the magic number N=162/164 are identified to be thermally fissile. The thermal neutron fission of a typical representative $^{249}$U of this region amenable to synthesis in the radioactive ion beam facilities is considered here. Semiempirical study of fission barrier height and width shows this nucleus to be infinitely stable against spontaneous fission due to increase in barrier width arising out of excess neutrons. Calculation of probability of fragment mass yields and microscopic study in relativistic mean field theory, show this n…
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…
Recent measurements of reactor-produced antineutrino fluxes and energy spectra are inconsistent with models based on measured thermal fission beta spectra. In this paper, we examine the dependence of antineutrino production on fission neutron energy. In particular, the variation of fission product yields with neutron energy has been considered as a possible source of the discrepancies between antineutrino observations and models. In simulations of low-enriched and highly-enriched reactor core designs, we find a substantial fraction of fissions (from 5% to more than 40%) are caused by non-therm…
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 …
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…
Neutron star (NS) merger ejecta offer a viable site for the production of heavy r-process elements with nuclear mass numbers A >140. The crucial role of fission recycling is responsible for the robustness of this site against many astrophysical uncertainties. Here, we introduce new improvements to our scission-point model, called SPY, to derive the fission fragment distribution for all neutron-rich fissioning nuclei of relevance in r-process calculations. These improvements include a phenomenological modification of the scission distance and a smoothing procedure of the distribution. Such corr…
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…
Mean field calculations, based on the D1S, D1N and D1M parametrizations of the Gogny energy density functional, have been carried out to obtain the potential energy surfaces relevant to fission in several Ra isotopes with the neutron number 144 $\le$ N $\le$ 176. Inner and outer barrier heights as well as first and second isomer excitation energies are given. The existence of a well developed third minimum along the fission paths of Ra nuclei, is analyzed in terms of the energetics of the "fragments" defining such elongated configuration. The masses and charges of the fission fragments are stu…
A comparative study of fission of actinides specially $^{238}$U, by proton and bremsstrahlung photon is performed. Relative mass distribution of $^{238}$U fission fragments have been explored theoretically for both proton and photon induced fission. The integrated yield along with charge distribution of the products are calculated to find out the neutron richness in comparison to the nuclei produced by r-process in nucleosynthesis. Some r-process nuclei in intermediate mass range for symmetric fission mode are found to be produced almost two order of magnitude more for proton induced fission t…
This pedagogical review presents the Shell Correction Method (SCM) and variants thereof, appropriate for describing shape deformations and electronic shell effects, energetics and decay pathways of metal-cluster fragmentation processes (e.g., monomer/dimer dissociation and fission). The experimental trends are compared to the theoretical SCM interpretations, and in addition theoretical results for fission from first-principles molecular-dynamics simulations are discussed. Some latest insights concerning the importance of electronic-entropy and finite-temperature effects are given special atten…
We have, recently, shown that the general trends of partition-wise fission fragment mass distribution in heavy ion (HI) induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using the concept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [1, 2, 3, 4]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-induced CN fission reaction, 245Cm(nth, f). As earlier, we use Kelson's conjectures [5] to assign isospin to …
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…
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…
A theoretical model of one-body nuclear friction which was developed earlier, namely the chaos-weighted wall formula, is applied to a dynamical description of compound nuclear decay in the framework of the Langevin equation coupled with statistical evaporation of light particles and photons. We have used both the usual wall formula friction and its chaos-weighted version in the Langevin equation to calculate the fission probability and prescission neutron multiplicity for the compound nuclei $^{178}$W, $^{188}$Pt, $^{200}$Pb, $^{213}$Fr, $^{224}$Th, and $^{251}$Es. We have also obtained the co…
The neutron and proton density distributions obtained in constrained Hartree-Fock-Bogolyubov calculations with the Gogny force along the fission paths of 232Th, 236U, 238U and 240Pu are analyzed. Significant differences in the multipole deformations of neutron and proton densities are found. The effect on potential energy surfaces and on barrier heights of an additional constraint imposing similar spatial distributions to neutrons and protons, as assumed in macroscopic-microscopic models, is studied.
We discuss the fission barrier height of neutron-rich nuclei in a r-process site at highly excited state, which is resulted from the beta-decay or the neutron-capture processes. We particularly investigate the sensitivity of the fission barrier height to the temperature, including the effect of pairing phase transition from superfluid to normal fluid phases. To this end, we use the finite-temperature Skyrme-Hartree-Fock-Bogolubov method with a zero-range pairing interaction. We also discuss the temperature dependence of the fission decay rate.
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…
We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in $^{208}$Pb ($^{18}$O, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. We take into account a range of isospin values allowed by the isospin algebra and assume that the fission fragments are formed in Isobaric Analog States. We also take into account the neutron multiplicity data for various neutron-emission channels in each partition, and use them to obtain the weight factors in calculating the yields. We then calculate th…
Transients in the fission of highly excited nuclei are studied in the framework of the Langevin equation. Time-dependent fission widths are calculated which show that after the initial transients, a steady flow towards the scission point is established not only for nuclei which have fission barriers but also for nuclei which have no fission barrier. It is shown from a comparison of the transient time and the fission life time that fission changes from a diffusive to a transient dominated process over a certain transition region as a function of the spin of the fissioning nucleus. Multiplicitie…
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…
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）
A consistent framework for treating the energy dependence of fission-fragment neutron multiplicities is presented. The shape evolution of the compound nucleus towards scission is treated in the strong damping limit using the Metropolis walk method. The available excitation energy at scission is then divided statistically between the two fragments using microscopic level densities. Deformation energies, which contribute to the excitation energy when the fragments relax to their ground-state shapes, are also computed. From the total fragment excitation energies, the number of emitted neutrons is…
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…
Consideration of memory of spin and parity in the fissioning compound nucleus by applying the Hauser-Feshbach fission fragment decay model to photonuclear reactions
After constructing yield tensors with three dimensions for 851 fission products and filling the tensors with the independent yield data from the ENDF/B-VIII.0 database, the tensor decomposition algorithm is applied to predict the independent isotopic yield in fission, which resulting in the Fission Yield Tensor Decomposition (FYTD) model. The fission yields of 235U and 239Pu are set as missing values and then predicted. The predictions for235U fissions by the FYTD model agree with the ENDF/B-VIII.0 data and are better than those by the Talys and BNN+Talys models. Furthermore, we predict not on…
The anatomy of neck configuration in the fission decay of Uranium and Thorium isotopes is investigated in a microscopic study using Relativistic mean field theory. The study includes $^{236}U$ and $^{232}Th$ in the valley of stability and exotic neutron rich isotopes $^{250}U$, $^{256}U$, $^{260}U$, $^{240}Th$, $^{250}Th$, $^{256}Th$ likely to play important role in the r-process nucleosynthesis in stellar evolution. Following the static fission path, the neck configurations are generated and their composition in terms of the number of neutrons and protons are obtained showing the progressive …
Following upon our earlier paper [1] containing some initial results, we present detailed discussion and complete results in this paper, which provide the first direct evidence for the validity of isospin as a nearly good quantum number in neutron-rich systems. The evidence comes from the reproduction of the general features of the partition-wise relative yields of neutron-rich fission fragments produced in two heavy-ion induced fusion fission reactions, namely $^{208}$Pb ($^{18}$O, f) and $^{238}$U ($^{18}$O, f), by using the concept of isospin conservation. To fix the isospin values and use …
The dynamics of fission has been studied by solving Euler-Lagrange equation with dissipation generated through one and two body nuclear friction. The average kinetic energies of the fission fragments, prescission neutron multiplicities and the mean energies of the prescission neutrons have been calculated and compared with experimental values and they agree quite well. A single value of friction coefficient has been used to reproduce the experimental data for both symmetric and asymmetric splitting of the fissioning systems over a wide range of masses and excitation energies. It has been obser…
We calculate neutron multiplicities from fission fragments with specified mass numbers for events having a specified total fragment kinetic energy. The shape evolution from the initial compound nucleus to the scission configurations is obtained with the Metropolis walk method on the five-dimensional potential-energy landscape, calculated with the macroscopic-microscopic method for the three-quadratic-surface shape family. Shape-dependent microscopic level densities are used to guide the random walk, to partition the intrinsic excitation energy between the two proto-fragments at scission, and t…
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…
For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = …
Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of few intermediate-mass fragments can also be observed. We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions. We find that the formation of few IMF's can be confused with asymmetric fission when relying on yield observables, but it can not be assimilated to the statist…
The effect of the right-left asymmetry is considered in the angular distribution of gamma quanta from fission of U-235 by polarised thermal neutrons, which depends on the polarisation of the neutrons with respect to the gamma-fission plane. Electric dipole radiation from fission fragments arising due to the Strutinsky-Denisov induced polarisation mechanism may give rise to such an effect. Earlier, this mechanism was shown to fit the non-statistical part observed in the gamma spectrum from spontaneous fission of Cf-252. The calculated value of the magnitude of the asymmetry parameter is on the …
The structures observed in the sub-threshold neutron-induced fission of ^{232}Th were investigated employing a recent developed model. Theoretical single-particle excitations of a phenomenological two-humped barrier are determined by solving a system of coupled differential equations for the motion along the optimal fission path. A rather good agreement with experimental data was obtained using a small number of independent parameters. It is predicted that the structure at 1.4 and 1.6 MeV is mainly dominated by spin 3/2 partial cross-section with small admixture of spin 1/2, while the structur…
In the present paper, we explore the idea of isospin conservation in new situations and contexts based on the directions provided by our earlier works. We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in fast neutron-induced fission, 238U (n, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. Our results successfully reproduced the gross features of partition wise fission fragments distribution of 238U (n, fission). This confirms that in all kinds of fission, isospin remains p…
Nuclear Science Division, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室核科学部）；NAPC, Nuclear Data Section, International Atomic Energy Agency（国际原子能机构核数据处）；Suncoast Data Evaluation（太阳海岸数据评估）；Physics Division, Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室物理分部）；Physics Department, University of California, Davis（加州大学戴维斯分校物理系）
A new type of decay corresponding to the neutronless $^{10}$Be-accompanied fragmentation of $^{252}$Cf is studied. We employ a cluster model similar to the model used for the description of cluster radioactivity. No preformation factors were considered. The ternary relative isotopic yields were calculated as the ratio of the penetrability of a given ternary fragmentation over the sum of penetrabilities of all possible ternary neutronless fragmentations. The corresponding barriers between the light and heavy fragment and between the $^{10}$Be cluster and the two heavier fragments were computed …
The Coulomb effects hypothesis is used to interpret even-odd effects of maximum total kinetic energy as a function of mass and charge of fragments from thermal neutron induced fission of 235U. Assuming spherical fragments at scission, the Coulomb interaction energy between fragments (C_sph) is higher than the Q-value, the available energy. Therefore at scission the fragments must be deformed, so that the Coulomb interaction energy does not exceed the Q-value. The fact that the even-odd effects in the maximum total kinetic energy as a function of the charge and mass, respectively, are lower tha…
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 …
Several sources of angular anisotropy for fission fragments and prompt neutrons have been studied in neutron-induced fission reactions. These include kinematic recoils of the target from the incident neutron beam and the fragments from the emission of the prompt neutrons, preferential directions of the emission of the fission fragments with respect to the beam axis due to the population of particular transition states at the fission barrier, and forward-peaked angular distributions of pre-equilibrium neutrons which are emitted before the formation of a compound nucleus. In addition, there are …
A correlation is established between the neutron multiplicity and the neutrons number in the fission state of Curium and Californium isotopes within a microscopic study using relativistic mean field formalism. The study includes the isotopes of Cm and Cf nuclei near the valley of stability, and hence is likely to play an important role in the artificial synthesis of superheavy nuclei. The static fission path, the neutron$-$proton asymmetry, the evolution of the neck and their composition in terms of nucleon numbers are also estimated. We find a maximum ratio for average neutron to proton densi…
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…
The $(n,γf)$ process is reviewed in light of modern nuclear reaction calculations in both slow and fast neutron-induced fission reactions on $^{235}$U and $^{239}$Pu. Observed fluctuations of the average prompt fission neutron multiplicity and average total $γ$-ray energy below 100 eV incident neutron energy are interpreted in this framework. The surprisingly large contribution of the M1 transitions to the pre-fission $γ$-ray spectrum of $^{239}$Pu is explained by the dominant fission probabilities of 0$^+$ and $2^+$ transition states, which can only be accessed from compound nucleus states fo…
Incident neutron energy dependence of delayed neutron yields of uranium and plutonium isotopes is investigated. A summation calculation of decay and fission yield data is employed, and the energy dependence of the latter part is considered in a phenomenological way. Our calculation systematically reproduces the energy dependence of delayed neutron yields by introducing an energy dependence of the most probable charge and the odd-even effect. The calculated fission yields are assessed by comparison with JENDL/FPY-2011, delayed neutron activities, and decay heats. Although the fission yields in …
Decay of $^{210}$Po compound nucleus formed in light and heavy-ion induced fusion reactions has been analyzed simultaneously using a consistent prescription for fission barrier and nuclear level density incorporating shell correction and its damping with excitation energy. Good description of all the excitation functions have been achieved with a fission barrier of 21.9 $\pm$ 0.2 MeV. For this barrier height, the predicted statistical pre-fission neutrons in heavy-ion fusion-fission are much smaller than the experimental values, implying the presence of dynamical neutrons due to dissipation ev…
The recent advent of experimental techniques in which the dynamical characteristics of fission fragments are determined more accurately, prompted us to investigate the angular momentum acquired by fragments in a model which describes the cold(neutronless) fission of $^{252}$Cf as the decay of a giant nuclear molecule. The molecular configuration is a consequence of the interplay between the attractive nuclear part and the repulsive Coulomb+nuclear forces. The basic ideea of the present approach is to separate the radial(fission) modes describing the decay of the molecule from the modes associa…
Selected aspects of the description of neutron-induced fission in 240Pu in the framework of the nuclear energy density functional theory at finite temperature are presented. In particular, we discuss aspects pertaining to the choice of thermodynamic state variables, the evolution of fission barriers as function of the incident neutron energy, and the temperatures of the fission fragments.
