Energy Of Fission Fragments Research Articles

Calculation of the energy dependence of fission fragments yields and kinetic energy distributions for neutron-induced 235U fission* *Supported by the National Natural Science Foundation of China (12075105), the NSFC-Nuclear Technology Innovation Joint Fund (U2167203), the Major Science and Technology Projects of Gansu Province (22ZD6GB020), the Fundamental Research Funds for the Central Universities of China (lzujbky-2022-ey14, lzujbky-2022- kb07)

Fission fragments yields and average total kinetic energy are fundamental nuclear data for nuclear energy applications and the study of nuclear devices. Certain fission products, such as 95Zr, 99Mo, 140Ba, 144Ce, and 147Nd, serve as burnup monitors, assessing the number of fissions induced by neutrons on 235U. However, current experimental data for these fission products worldwide are inconsistent, introducing significant uncertainty into related scientific research. In this study, we employed the Potential-driving Model to calculate the independent yields of 235U and evaluate its advantages in such calculations. Additionally, we investigated the energy dependence of independent yields to select important products. Furthermore, we calculated the cumulative yields of 95Zr, 99Mo, 140Ba, 144Ce, and 147Nd, and compared them with existing literature data to explore the energy dependence of fission products for 235U. Given the lack of fission product yield data above 14.8 MeV, we extended our calculated incident neutron energy to 20 MeV, aiming to support future scientific research. The Geant4 physical model does not consider the influence of incident neutron energy on the average total kinetic energy of fission fragments; thus, we introduced the excitation function of the total kinetic energy of fission fragments recommended by Madland et al., which effectively describes the experimental data of the average total kinetic energy of fragments formed in 235U fission. In this paper, we comprehensively discuss the energy dependence of fission product yields and average total kinetic energy.

Characteristics of the fission fragments in the three-body model of binary fission

The evaluated nuclide yields, fragment mass and charge distributions, and averaged total kinetic energy of fission fragments for the neutroninduced fission of 30 actinide nuclei are well described in the new model, which considers the fissioning scission system consisting of two heavy fragments and an α-particle between them. The α-particle has its origin in the neck nucleons. The yield of fission fragments in the model is linked to the number of states over the barrier of the saddle point, which is between the contacting and well-separated fission fragments. The α-particle is fused with the nearest heavy fragment after passing the saddle point, therefore, two final fragments appear during fission. The quadrupole deformations of heavy fragments are taken into account in the model. The fragment yields depend on the heights of corresponding saddle points and the values of the equilibrium quadrupole deformation of fragments.

Total Kinetic Energy of Fission Fragments based on Fission Product Data

Total kinetic energy (TKE) is the physical quantity that must be acquired during a nuclear fission reaction. This energy is used for various purposes, primarily to determine the spectrum of the second proton. This spectrum is advantageous in the design of nuclear reactors. Various techniques for calculating TKE, from microscopic to macroscopic, have been carried out, from statistical to quantum reviews. This whole technique is solely for obtaining TKE accurately. This paper will review the TKE calculation based on the fission products' experimental results. This fission product data can be in the form of raw experimental data or evaluated data. The calculations are carried out within a macroscopic and statistical review framework. The macroscopic view is a liquid drop model, while the statistics use the random number technique. Because the liquid drop model and the random number technique are very standard, this paper does not review them.

Fission dynamics of excited compound nuclei in a wide range of fissile parameters produced in O16,18+X reactions within a stochastic approach

A stochastic approach based on four-dimensional Langevin equations has been used to simulate the fission dynamics of the excited compound nuclei $^{256}\mathrm{Fm}, ^{254}\mathrm{Fm}, ^{224}\mathrm{Th}, ^{215}\mathrm{Fr}, ^{213}\mathrm{Fr}, ^{200}\mathrm{Pb}, ^{187}\mathrm{Ir}, ^{172}\mathrm{Yb}, ^{170}\mathrm{Yb}, ^{162}\mathrm{Yb}, ^{142}\mathrm{Ce}$, and $^{125}\mathrm{Cs}$ produced in ${}^{16,18}\mathrm{O}+X$ reactions with projectile energies 158.8 and 288 MeV. The effect of nuclear dissipation was investigated in the dynamical simulation of fission process of these nuclei. The average prescission neutron multiplicity, the fission time, the average total kinetic energy of fission fragments, the mass and energy distribution of fission fragments, and the variation of the prescission neutron multiplicity with total kinetic energy of fission fragments have been calculated for these nuclei. The dynamical calculations have taken into account not only three shape collective coordinates introduced on the basis of the ``funny hills'' shape parameters but also orientation degree of freedom (spin about the symmetry axis), and in the dynamical calculations dissipation generated through the chaos-weighted wall and window friction formula and also the sum of the chaos-weighted wall and window friction formula with the two-body nuclear friction. Furthermore, the effect of dissipation coefficient of $K, {\ensuremath{\gamma}}_{K}$, were also considered in the dynamical calculations. Comparison of the theoretical results with the experimental data shows that the experimental data for compound nuclei produced with the projectile energy 158.8 MeV can be reproduced satisfactorily with the results of calculations by using the chaos-weighted wall and window friction formula, although the results of calculations of the average prescission neutron multiplicity, the fission time, and the variation of the pre-scission neutron multiplicity with total kinetic energy of fission fragments lie somewhat below the experimental data for heavy nuclei produced in reactions with projectile energy ${E}_{\mathrm{lab}}=158.8\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and also for compound nuclei produced with the projectile energy 288 MeV. It was also shown that for reproducing experimental data for heavy nuclei produced in reactions with projectile energy ${E}_{\mathrm{lab}}=158.8\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ and also for nuclei produced with projectile energy ${E}_{\mathrm{lab}}=288\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ is suitable to use the sum of the chaos-weighted wall and window friction formula with the two-body nuclear friction in the Langevin equations. In other words, for simulations of fission dynamics of nuclei at high excitation energies and also for heavy nuclei it is suitable to use the sum of the chaos-weighted wall and window friction formula with the two-body nuclear friction in the Langevin equations.

Pre-neutron emission average total kinetic energy of fission fragments

A new expression for a calculation of the pre-neutron emission average total kinetic energy of fission fragments (TKE), which takes into account the dependence of TKE on both Z2/A1/3 and the excitation energy of the fissioning nuclei, is found using the 728 experimental values of the TKE. These 728 values of TKE for 115 fissioning nuclei with the numbers of proton and nucleons in the ranges 48≤Z≤120 and 78≤A≤302 are measured by various experimental groups in different reactions at various excitation energies of the fissioning nuclei. The dependence of the TKE on the excitation energy of the fissioning nuclei is clearly shown for many nuclei. The account of the excitation energy dependence of the TKE leads to the smallest value of the root-mean-square deviation between the experimental and theoretical TKE values.

Total kinetic energy of fission fragments in heavy actinide fission

Total kinetic energy of fission fragments in heavy actinide fission

Microscopic study of neutron-induced fission process of 239Pu via zero- and finite-temperature density functional theory* *Supported by the National Natural Science Foundation of China (11790325, 12275081, 11790320, 11790321, 11961131010, 11605054, 12105369, 12147219, 12047568) and the Continuous Basic Scientific Research Project (WDJC-2019-09)

To study the neutron-induced fission of Pu, potential energy surface (PES) calculations were performed using zero and finite-temperature density functional theory (FT-DFT) with the Skyrme force. The energy of the incident neutron was simulated by the temperature of the FT-DFT. The variations of the least-energy fission path, fission barrier, total kinetic energy, scission line, and mass distribution of fission fragments with the incident neutron energy were analyzed. It was learned that an increase in the temperature lowers the barrier height, the isomeric-state energy, and the ridge between symmetric and asymmetric fission valleys. Additionally, the gaps of the single particle levels become smaller with an increase in the temperature. As the temperature increases, the pre-fission region shrinks, and the scission occurs at smaller deformation around the symmetric fission channel. At low temperatures, the pairing correlations in the collective space are similar to those in zero-temperature DFT, and when the temperature is 0.3 MeV, the pairing gaps decrease rapidly. Two different methods were used to calculate the fission yields of the neutron-induced fission Pu (n, f) with different incident neutron energies, in the framework of time-dependent generator coordinate method (TDGCM). One way to calculate the fission yield of Pu (n, f) is to solve the collective equation of the TDGCM by using the PES from the FT-DFT with the corresponding temperature. The other involves using the PES from the zero-temperature DFT and adjusting the initial collective energy of the wave packet in the TDGCM according to the incident neutron energy. For the cases of the lower incident neutron energies, these two methods gave similar results and reproduced the experimental peak and width of fission fragment distribution. However, for the highest incident neutron energy considered in this study, the results from the TDGCM using the PES from zero-temperature DFT deviated explicitly from the experimental data, whereas those obtained by using the PES from FT-DFT remained close to the experimental data. This indicated that, with the increase in the incident neutron energy, the shell structure of the compound nuclei changed explicitly; thus, it may not be effective to use the PES from zero-temperature to perform the fission dynamic calculation.

New developments in fission studies within the time-dependent density functional theory framework

We have extended significantly the microscopic description of the fission process by examining a larger set of observables. We extract neutron and proton numbers of fission fragments, their spins and fission fragment relative orbital angular momentum and their correlations, investigate neutrons emitted at or shortly after scission, excitation energy sharing mechanism, total kinetic energy of fission fragments, and the entanglement entropy. I will present a short overview of our simulations obtained with two independent nuclear energy density functionals.

Microscopic investigations into fission dynamics beyond the saddle point

The real-space density-constrained time-dependent Hartree-Fock-Bogoliubov method is exploited to obtain the dynamic potential energy and several experimental variables of fission fragments. The resultant predictions of collective variables, especially the total kinetic energy and total excitation energy of the fission fragments, finely match the experimental data. It is demonstrated that scission dynamics including the shell effects and pairing correlations should be the focus of further studies.

The FFIS spectrometer for determination of fission fragment mass distribution with the energy–velocity method

The FFIS spectrometer (Fission Fragment Identification Spectrometer) for determining independent fission yields has been developed based on the E–v method. By directly measuring the time-of-flight (TOF) and kinetic energy of fission fragments on their flight path, the post-neutron-emission mass yield distributions can be obtained. With the aim of getting the highest possible mass resolution, an axial grid ionization chamber and a TOF measurement system based on microchannel plate (MCP) detectors were designed. The ionization chamber with a silicon nitride entrance window of 100 nm thickness was tested and calibrated with a 252Cf spontaneous fission source. The intrinsic energy resolution for 1.27 MeV/u 63Cu particles is measured to be 450 keV (FWHM). The time resolution was determined with two MCP timing detectors to be 157 ps (FWHM) for 241Am radiation source, implying that the intrinsic time resolution is about 110 ps (FWHM) for a single timing detector. Thermal-neutron-induced fission of 235U was studied at the In-hospital Neutron Irradiator (IHNI). An event-by-event energy loss addback technique was developed based on Geant4 calculation to minimize the correction error. The first results of mass yield distributions from 235U(nth,f) are reported.

Fusion cross section and total kinetic energy of fission fragments by the dynamical dissipative surface-friction model

The capture cross section, the fusion cross section, and the quasi-fission yield producing symmetric fragments ( ACN/2 ± 20u ) in the 48 Ca+ 238 U reaction are analyzed by the multidimensional Langevin equation taking account of the surface friction effect. From the experimental data, the strength of the tangential friction has been determined. It is presented that tangential friction increases in proportional to the power of the relative velocity of the projectile and the target.

Dependence of average total kinetic energy of fission fragments on the excitation energy of the compound nucleus

The expression of dependence of average total kinetic energy release of fission fragments on the excitation energy of the compound nucleus is obtained in the framework of a simple statistical model. The experimental data for the neutron-induced fission of $^{233,235,238}\mathrm{U}$ and $^{239}\mathrm{Pu}$ measured in wide ranges of the excitation energy of the compound nuclei are well described using the obtained expression. The origin of the energy dependence of the average total kinetic energy is discussed in detail.

Evolution of the shape of fission fragment energy spectrum with absorber thickness in two different media and effective charge correction

The energy loss behavior of fission fragments (FFs) from [Formula: see text]Cf(sf) in thin Mylar [Formula: see text] and Aluminium absorber foils has been revisited. The aim is to investigate the observed change in the well-known asymmetric energy of spontaneous fission of [Formula: see text]Cf as the fragments pass through increasingly thick absorber foils. Two different types of absorbers have been used: one elemental and the other an organic compound. The stopping powers have been determined as a function of energy for three fragment mass groups with average masses having [Formula: see text], 141.8, 125.8 corresponding to light, heavy and symmetric fragments of [Formula: see text]Cf. The energy loss data have been compared with the predictions of SRIM 2013 code. The best representations of the data have been achieved using the effective Z correction term in the stopping power relation from the classical Bohr theory. Using the effective charge (Z[Formula: see text]) in the stopping power relation in the classical Bohr theory best describes the stopping power data. Spectrum shape parameters, subsequently, have been extracted from the energy spectra of FFs for different foil thicknesses. The effective charge (Z[Formula: see text]) correction term determined from the stopping power data is then used in the simulation for the absorber thickness dependence of the shape parameters of the energy spectrum. The present simulation results are compared with the TRIM prediction. The trends of the absorber thickness dependence of the spectrum shape parameters, for both Mylar and Aluminium, are well reproduced with the present simulation.

Dependence of average total kinetic energy of fission fragments on excitation energy of fissioning nucleus

The expression of dependence of the average total kinetic energy of fission fragments on the excitation energy of the fissioning system is obtained in a simple model, which takes into account the statistical and quantum properties. The experimental data of the average total kinetic energy of fragments formed in the fission of nuclei 234,236,239U and 240Pu are well described using the obtained expression in the wide range of the excitation energy of these nuclei. The origin of the energy dependence of the average total kinetic energy is discussed in details.

Dependence of total kinetic energy of fission fragments on the excitation energy of fissioning systems

We elucidated the reason why the average total kinetic energy (TKE) of fission fragments decreases when the excitation energy of the fissioning systems increase as indicated by experimental data for the neutron-induced fission events. To explore this problem, we used a method based on the four-dimensional Langevin equations we have developed. We have calculated the TKE of fission fragments for fissioning systems $^{236}\mathrm{U}^{*}$ and $^{240}\mathrm{Pu}^{*}$ excited above respective fission barriers, and compared the results with experimental data for n $+$ $^{235}\mathrm{U}$ and n $+$ $^{239}\mathrm{Pu}$ reactions, respectively. From the Langevin-model analysis, we have found that the shape of the abundant heavy fragments changes from almost spherical for low excitation domain to highly prolate shape for high excitation energy, while that of the light fragments does not change noticeably. The change of the ``shape'' of the heavy fragments causes an increase of a distance between the charge centers of the nascent fragments just after scission as excitation energy increases. Accordingly, the Coulomb repulsion between the two fragments decreases with an increase of the excitation energy, which causes the decrease of the average TKE. In this manner, we found that the change of the shape of the heavy fragment as a function of the excitation energy is the key issue for the TKE of fission fragments to decrease as the excitation energy of the fissioning nuclei increases. In other words, washing out of the shell effects, which affect the shape of the heavy fragments is the key reason for the decreasing energy dependence of the average TKE of the fission fragments.

Correlated transitions in fission mode and shell correction energy at zero excitation in actinides fission

In this paper, the transitions between symmetric and asymmetric modes are investigated for the fission of actinides within the scission point model. All effective energies in fission are investigated in detail, separately. This indicates that the interaction energy and the liquid-drop energy do not change much in the symmetric region, so they cannot play a major role in the transition of actinide fission modes. Additionally, the sum of shell correction of complementary fragments at zero excitation energy is plotted over the fission fragment mass numbers. Also, the mass distributions of actinides fission are calculated within the scission point model. There is a good agreement between the calculated mass distribution and the total shell correction distribution. This indicates that the minimum total shell correction energy at the excitation energy corresponds to the maximum mass distribution for actinides fission, especially for the fermium 258 fission. Therefore, the main reason for the formation of fission mode in the actinides fission is the total shell correction energy of the complementary fission fragments at the zero excitation energy.

Examination of different features of fission fragments of the excited compound nucleus Np236 produced in the p+U235 reaction at 10.3≤Ep≤30.0MeV within a stochastic approach

A stochastic approach based on four-dimensional Langevin equations has been used to estimate the mass distributions of fission fragments, the average masses of heavy fragments, the average total kinetic energies of fragments, and the average number of neutrons emitted per fission of $^{236}\mathrm{Np}$ produced in the $p+^{235}\mathrm{U}$ reaction at $10.3\ensuremath{\le}{E}_{p}\ensuremath{\le}30.0\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. Three collective shape coordinates plus the projection of total spin of the compound nucleus to the symmetry axis $K$ were considered in the four-dimensional dynamical model. The effects of shell corrections and dissipation coefficient of $K {\ensuremath{\gamma}}_{K}$ were considered in the dynamical calculations. Comparison of the theoretical results for the mass distributions of fission fragments, the average masses of heavy fragments, and the average number of neutrons emitted per fission with the experimental data showed that the results of calculations were in good agreement with the experimental data, although the results of calculations for the average total kinetic energies of fission fragments were slightly higher than the experimental data. It was also shown that the number of fission events increased with time, and almost all of the fission events occurred dynamically until $t=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ and that the number of fission events became saturated. Furthermore, it was also shown that the average masses of heavy fragments and the average total kinetic energies of fission fragments of $^{236}\mathrm{Np}$ decreased with increasing projectile energy.

The description of the excitation energy sharing in nuclear fission within the Langevin approach

We apply the four-dimensional Langevin approach to the description of fission of 235U by neutrons and calculate the dependence of the excitation energy of fission fragments on their mass number. For this we run the Langevin equations until the compound nucleus splits into two separated fragments. This is possible since the we used in this work two-center shell model shape parametrization that describes well both compact and separated shapes. The excitation energies of each fragment are calculated assuming that the temperatures of both fragments are the same. The deformation energy of the fragment immediately after scission is added to its excitation energy. The saw-tooth structure of the dependence neutron multiplicity on the fragment’s mass number in reaction 235U + n at En = 5 Mev is qualitatively reproduced.

Systematic Approach to Calculate the Total Kinetic Energy Distribution of Actinides for the Photofission Phenomenon

The total kinetic energy as a function of fragment mass (TKE/A) was calculated for photofission of $${}^{232}$$ Th, $${}^{234}$$ U, $${}^{238}$$ U, $${}^{240}$$ Pu, and $${}^{242}$$ Pu using a systematic statistical scission point model. In the proposed systematic method, all the energies involved in fission need to be expressed as a function of mass and atomic numbers of fission fragments. Therefore, the shell correction energy of fission fragments was approximated in terms of fission fragment mass numbers based on Ruben’s idea. The deformability parameter ( $$\alpha$$ ) of fission fragments was also formulated as a function of mass and atomic numbers of fission fragments by fitting the calculations and experimental data according to Terrell’s formulas. The calculated results are in good agreement with the experimental data, except for fragments with magic numbers, which their shell correction energy and deformability parameters change rapidly.

Delayed fission of atomic nuclei

The history of the discovery of delayed nuclear fission is presented, and the retrospective of investigations into this phenomenon that were performed at various research centers worldwide is outlined. The results obtained by measuring basic delayed-fission features, including the fission probability, the total kinetic energy of fission fragments, and their mass distributions, are analyzed. Recommendations concerning further studies in various regions of nuclear map with the aim of search for atomic nuclei undergoing delayed fission are given. Lines of further research into features of delayed fission with the aim of solving current problems of fission physics are discussed