Average Total Kinetic Energy 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.

Calculation of the fission products for neutron-induced fission of 235U

The fission model, G4ParaFissionModel, was enhanced in this study, mainly focusing on refining the energy dependence of the peak-to-valley ratio in the mass distribution and the energy dependence of the average total kinetic energy (TKE). The enhanced model was employed to investigate the characteristics of fission products from 235U(n, f) reaction. The calculated results, including fission yield, TKE distribution, prompt fission neutron and gamma spectra, were compared with both evaluated and experimental data. The comparison shows that these physical observables related nuclear data, which are of importance for developments of the nuclear power and physics, can be reasonably well reproduced.

TALYS calculations of prompt fission observables and independent fission product yields for the neutron-induced fission of ^{235}U

The TALYS nuclear reaction code’s Hauser-Feshbach statistical decay model has been adapted in order to calculate prompt fission neutron and gamma -ray observables by iterating over deexciting fission fragments. Several fission fragment generators such as GEF, HF^{3}D, and SPY were employed to provide TALYS with databases. These databases contain standardized tables with fission fragment yields, mean excitation energies and their widths, and average total kinetic energy, as a function of charge and mass number of primary fission fragments. The resulting calculations, including prompt particle multiplicities, spectra, average energies, and independent fission product yields, were compared with experimental and evaluated data. This work first outlines the new methodology implemented in TALYS and examines the effects of three important parameters on the final evaporation data. Furthermore, the neutron-induced fission of ^{235}U is investigated in detail as a function of incident energy. The results from TALYS, with input from GEF and HF^{3}D, were compared with available experimental data and the results of the stand-alone GEF code. The proposed methodology contributes to an improved capability to model the fission process.

Influence of the transition from symmetric to asymmetric fission mode on the average total kinetic energy and neutron multiplicity

Influence of the transition from symmetric to asymmetric fission mode on the average total kinetic energy and neutron multiplicity

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.

Producing Evaluation-quality 239Pu Average Prompt Fission Neutron Multiplicities using a Correlated Fission Model

An evaluation of the average prompt fission neutron multiplicity, ν¯ p, of 239Pu(n,f) is shown. This evaluation includes (a) the correlated fission model CGMF, and (b) a detailed analysis of past and recently published experimental data. Using CGMF-calculated ν¯ pas prior enables to link, through the use of evaluated model input parameters, ν¯ p to other fission observables such as the prompt fission neutron spectrum (PFNS), pre-neutron emission fission yields as a function of mass, and the average total kinetic energy of the fragments. These evaluated parameters produce realistic predictions of many fission observables, while the evaluated ν¯ p agrees well (χ2 ≈ 1) with data. Moreover, with the new evaluated ν¯ p, the effective neutron multiplication factor of fast Pu ICSBEP critical assemblies are predicted with a mean bias of 58 pcm compared to 18 pcm with ENDF/B-VIII.0, when paired with a new 239Pu PFNS and fission cross section. Due to these encouraging validation results, the evaluated ν¯ p is currently part of a release candidate for the 239Pu ENDF/B-VIII.1 file. Hence, a correlated fission model was used for the first time for evaluating ν¯ p that is of evaluation quality. This is an important step towards consistent evaluations of prompt fission observables.

An accurate empirical formula for the average total kinetic energy released in fission

An accurate empirical formula for the average total kinetic energy released in fission

Announcement of the winner of the Longuet-Higgins Early Career Researcher Prize 2021

ABSTRACT The reactions between ground state and forming and were investigated in the range of collision energies between and 10 K using a merged-beam approach. The reaction rates measured experimentally are compared to those obtained for the reaction between and forming under similar experimental conditions. Below 1 K, a clear enhancement of the reaction rate coefficient compared to the Langevin rate measured at higher collision energies was observed in both reaction systems. This enhancement is interpreted as originating from the interaction between the charge of and the quadrupole of para and ortho molecules in the J = 1 rotational level. The enhancement of the reaction with was found to be significantly less than that of the reaction with , reflecting the relative population of the J = 1 rotational level of (75%) and (33%) in natural samples at low temperatures. Simulations of the experimental results based on the theoretical predictions of the reaction cross sections by Dashevskaya et al. [J. Chem. Phys. 145, 244315 (2016)] reveal agreement within the experimental uncertainties. The branching ratio η of the reaction involving and and forming and near E coll = 0 was determined to be 0.341(15). Time-of-flight measurements of the velocity distributions of the reaction products are compatible with an isotropic product emission with an average total kinetic energy of 0.45(5) eV for both channels, representing about 30% of the total energy released by the reaction.

Influence of pre-scission neutron emission on high-energy U238 fission studied by the Langevin approach

Background: The information about the pre-scission emitted neutrons is crucial for the fission dynamics study such as fission time scale and dissipation mechanism. Purpose: The aim is to investigate the influence of the pre-scission neutron emission on the fragments mass, total kinetic energy, and the deformation distribution at the scission point in $^{238}\mathrm{U}(n,f)$ fissions at 110, 325, and 500 MeV. Method: A three-dimensional Langevin approach considering nucleus elongation, deformation, and mass asymmetry is applied to simulate fission dynamics. The Hauser-Feshbach statistical decay model is coupled to simulate the pre-scission neutron emission. Results: The properties of the pre-scission emitted neutron are first investigated. It is found that the multiplicity and the average kinetic energy increase with increasing excitation energy. The energy carried away by neutron emission is not negligible and it leads to the multichance fission, especially for the 110 MeV case. The fragments mass, total kinetic energy, and the deformation distribution at the scission point are then calculated with and without coupling the Hauser-Feshbach statistical decay model. It is found that the calculations partially reproduce the leftward shift of the experimental fragment mass distribution at high excitation energy. The pre-scission neutron emission also causes a reduction of the average total kinetic energy by about 2 MeV and a leftward shift of the distribution. The deformation distribution shows that about 75% of the fragments are produced in spherical and prolate ellipsoid shapes. No significant influence on deformation at the scission point was found. Conclusions: For high-energy fission, the energy reduction by pre-scission neutron emission should be considered, which will lead to the multichance fission. The pre-scission neutron emission is one of the reasons for the decrease of the average mass and the leftward shift of the fission fragments mass and total kinetic energy distribution.

Measurement of mass and total kinetic energy distributions for the C12+Lu175 system

Fission fragment mass and total kinetic energy (TKE) distributions were measured for $^{12}\mathrm{C}+^{175}\mathrm{Lu}$ system at excitation energies down to 16.7 MeV above the saddle point. The overall mass and TKE distributions could be fitted with single Gaussian functions. The observed width of the mass and TKE distributions agree well with the systematics based on liquid drop (LD) behavior. The average TKE also shows parabolic dependence on fragment mass, as expected from LD behavior. Small contributions due to microscopic corrections from $Z\ensuremath{\approx}38$ and 45 shells can be extracted, if the widths of the LD component are fixed from systematics. Contrary to the theoretical predictions of substantial contributions from microscopic corrections, dominance of liquid drop behavior was observed.

Fragmentation analysis of Z=112 –116 nuclei using a Skyrme energy density formalism within the collective clusterization approach

The Skyrme energy density formalism is applied to address the capture cross sections of $_{112}^{286}\mathrm{Cn}^{*}$, $_{114}^{292}\mathrm{Fl}^{*}$, and $_{116}^{296}\mathrm{Lv}^{*}$ superheavy nuclei formed in $^{48}\mathrm{Ca}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U},^{244}\mathrm{Pu},^{248}\mathrm{Cm}$ reactions. The dynamics of $^{48}\mathrm{Ca}$-induced reactions is investigated by including GSkI and SSk forces for the hot-optimum configurations of decay fragments. The neutron evaporation $(3n \mathrm{and} 4n)$, compound nucleus fission (CN fission) and quasifission (QF) cross sections are calculated with the application of both forces, but the GSkI force seems to be appropriate only for the neutron evaporation channels. However, by including SSk force various decay processes can be handled by including the only parameter of the model, called the neck length parameter $(\mathrm{\ensuremath{\Delta}}R)$. The fragment mass distribution of $Z=112$--116 nuclei shows considerable modifications in the fission, symmetric quasifission $({\mathrm{QF}}_{\mathrm{sym}.})$ and asymmetric quasifission $({\mathrm{QF}}_{\mathrm{asym}.})$ regions with the inclusion of the SSk force as compared to analysis based on the density independent potentials. In addition to this, the role of ${\ensuremath{\beta}}_{2}$ deformations and magic shell effects (around the Pb isotope) is scrutinized through the fragmentation behavior and preformation probability of $_{112}^{286}\mathrm{Cn}^{*}$, $_{114}^{292}\mathrm{Fl}^{*}$, and $_{116}^{296}\mathrm{Lv}^{*}$ nuclei. Finally, the distribution of the average total kinetic energy of fragments is calculated with the density dependent SSk force and compared with experimental data and earlier work based on the proximity potential.

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.

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.

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.

Deviation of the rate of the reaction from Langevin behaviour below 1 K, branching ratios for the and product channels, and product-kinetic-energy distributions

The reactions between ground-state (X ) and forming and were investigated in the range of collision energies between and 10 K using a merged-beam approach. The reaction rates measured experimentally are compared to those obtained for the reaction between and forming under similar experimental conditions. Below 1 K, a clear enhancement of the reaction rate coefficient compared to the Langevin rate measured at higher collision energies was observed in both reaction systems. This enhancement is interpreted as originating from the interaction between the charge of and the quadrupole of para and ortho molecules in the J = 1 rotational level. The enhancement of the reaction with was found to be significantly less than that of the reaction with , reflecting the relative population of the J = 1 rotational level of (75%) and (33%) in natural samples at low temperatures. Simulations of the experimental results based on the theoretical predictions of the reaction cross sections by Dashevskaya et al. [J. Chem. Phys. 145, 244315 (2016)] reveal agreement within the experimental uncertainties. The branching ratio η of the reaction involving and and forming and D () near was determined to be 0.341(15). Time-of-flight measurements of the velocity distributions of the reaction products are compatible with an isotropic product emission with an average total kinetic energy of 0.45(5) eV for both channels, representing about 30% of the total energy released by the reaction.

Oversize of the average prompt neutron multiplicity measured by the 1V1E method in the symmetric region of thermal neutron-induced fission of 239Pu

Using a Monte Carlo method, the measurement by the 1V1E technique of the average prompt neutron multiplicity as a function of the mass of fragments from the thermal neutron-induced fission of 239Pu is simulated. The input data, associated with the masses of complementary primary fragments (A1, A2), consist of the yield (Y), the average total kinetic energy (TKE-) and its standard deviation (σTKE), the average prompt neutron multiplicity (ν-s, a sawtooth approach of an experimental curve ν-), and the slope of neutron multiplicity against total kinetic energy, -dν/d<TKE>, plotted as a function of fragment mass. The output data, associated with the provisional masses of complementary fragments (m1∗, m2∗) calculated with the 1V1E method, consist of the simulated quantities Y, TKE-, σTKE, N-, comparable to the measured ones. In comparison with ν-s, N- and ν-are oversized in the region of light fragment masses near the symmetric fission. To interpret the results, the neighboring masses ratio RA =YA+1/Y(A) and the term FA=A-m∗, where m∗ is the average of provisional mass as a function of A, are defined. It is shown that N--ν-s and ν--ν-s are correlated with -F(R-1). It is concluded that the oversize of ν- relative to ν-s is due to the interplay of the prompt neutron emission and the slope of the mass yield curve.

Calculated fission-fragment mass yields and average total kinetic energies of heavy and superheavy nuclei

Fission-fragment mass and total-kinetic-energy (TKE) distributions following fission of even-even nuclides in the region 74 le Z le 126 and 92 le N le 230, comprising 896 nuclides have been calculated using the Brownian shape-motion method. The emphasis is the region of superheavy nuclei. To show compatibility with earlier results the calculations are extended to include earlier studied regions. An island of asymmetric fission is obtained in the superheavy region, 106le Zle 114 and 162le Nle 176, where the heavy fragment is found to be close to ^{208}Pb and the light fragment adjusts accordingly. Most experimentally observed alpha -decay chains of superheavy nuclei with Z > 113 terminate by spontaneous fission in our predicted region of asymmetric fission. In these cases, the pronounced large asymmetry is accompanied by a low TKE value compatible with measurements.

Fission fragment mass yields and total kinetic energy release in neutron-induced fission of U233 from thermal energies to 40 MeV

Properties of fission in $^{233}\mathrm{U}$ were measured at the Los Alamos Neutron Science Center at incident neutron energies from thermal to 40 MeV. Fragments were observed in coincidence by using a twin ionization chamber with Frisch grids. The average total kinetic energy released and fragment mass yields were determined by using the double energy analysis method based on conservation of mass and momentum. The experimental method was validated by using $^{232}\mathrm{Th}$ and absolute energy was calibrated by using thermal-neutron--induced fission of $^{235}\mathrm{U}$. This work incorporates novel applications of multi-chance fission channel cross sections and fission models to account for the complexities introduced by prompt neutron emission at high energy and extends results up to higher incident neutron energies than previously measured. Accurate experimental measurements of these parameters are necessary to better understand the fission process in isotopes central to the thorium fuel cycle.