Average Neutron Multiplicity Research Articles

Simulation of the fission dynamics of the excited compound nuclei 206Po and 168Yb produced in the reactions 12C+194Pt and 18O+150Sm

A two-dimensional dynamical model based on the Langevin equation was used to study the fission dynamics of the compound nuclei 206Po and 168Yb produced in the reactions 12C+194Pt and 18O+150Sm, respectively. The fission cross section and average pre-scission neutron multiplicity were calculated for the compound nuclei206Po and 168Yb, and results of the calculations compared with the experimental data. The elongation coordinate was used as the first dimension and the projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in the Langevin dynamical calculations. In the two-dimensional calculations, a constant dissipation coefficient of K and a non-constant dissipation coefficient have been used to reproduce the above-mentioned experimental data. It is shown that the two-dimensional Langevin equation can satisfactorily reproduce the fission cross section and average pre-scission neutron multiplicity for the compound nuclei 206Po and 168Yb by using constant values of the dissipation coefficient of K equal to γK = 0.18(MeV zs)−1/2 and γK = 0.20(MeV zs)−1/2 for the compound nuclei 206Po and 168Yb, respectively.

Mass, total kinetic energy, and neutron multiplicity correlations in the binary fragmentation of Ti50+Pb208 at 294 MeV bombarding energy

The correlations between mass distributions of the binary fragments, total kinetic energy (TKE), and neutron multiplicity have been investigated for the reaction $^{50}\text{Ti}+\phantom{\rule{0.16em}{0ex}}^{208}\text{Pb}$ at 294 MeV bombarding energy. Although this reaction has been used to synthesize the Rf ($Z=104$) superheavy element, a complete study of its fragmentation dynamics is still not available in the literature. In this work, average neutron multiplicities were extracted as a function of different fragment mass splits and TKE windows. A weak increase of the prescission neutron multiplicity is observed going from asymmetric to symmetric mass splits. A fission delay time of $4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s has been extracted for the symmetric fission. The neutron multiplicity extracted for the symmetric mass split was used to derive the average number of neutrons emitted in the spontaneous fission of $^{258}\text{Rf}$. The extrapolated value of $4.7\ifmmode\pm\else\textpm\fi{}1.4$ is found to be consistent with systematics of spontaneous and neutron-induced fission in heavy nuclei and with the results of previous works for superheavy nuclei with $Z=116$ and $Z=124$.

Dynamical simulation of the fission process and anisotropy of the fission fragment angular distributions of excited nuclei produced in fusion reactions

Abstract. A stochastic approach based on four-dimensional Langevin equations was applied to calculate the anisotropy of fission fragment angular distributions, average prescission neutron multiplicity, and the fission probability in a wide range of fissile parameters for the compound nuclei $^{197}\mathrm{Tl},^{225}\mathrm{Pa},^{248}\mathrm{Cf}$, and $^{264}\mathrm{Rf}$ produced in fusion reactions. 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. In the dynamical calculations, nuclear dissipation was generated through the chaos-weighted wall and window friction formula. Furthermore, in the dynamical calculations the dissipation coefficient of $K,{\ensuremath{\gamma}}_{k}$ was considered as a free parameter, and its magnitude inferred by fitting measured data on the anisotropy of fission fragment angular distributions for the compound nuclei $^{197}\mathrm{Tl},^{225}\mathrm{Pa},^{248}\mathrm{Cf}$, and $^{264}\mathrm{Rf}$. Comparison of the calculated results for the anisotropy of fission fragment angular distributions with the experimental data showed that the results of the calculations are in good agreement with the experimental data by using values of the dissipation coefficient of $K$ equal to (0.185--0.205), (0.175--0.192), (0.077--0.090), and (0.075--0.085) ${(\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}\mathrm{zs})}^{\ensuremath{-}1/2}$ for the compound nuclei $^{197}\mathrm{Tl},^{225}\mathrm{Pa},^{248}\mathrm{Cf}$, and $^{264}\mathrm{Rf}$, respectively. It was also shown that the influence of the dissipation coefficient of $K$ on the results of the calculations of the prescission neutron multiplicity and fission probability is small.

Point-by-Point model calculation of the prompt neutron multiplicity distributionν(A)forU238(n,f)at incident neutron energies ranging from 1 MeV to 80 MeV

Prompt neutron multiplicity distributions \ensuremath{\nu}($A$) are generally required for prompt emission correction of double energy ($2E$) measurements of fission fragments in order to determine pre-neutron fragment properties. The lack of experimental \ensuremath{\nu}($A$) data especially at higher incident neutron energy imposes the use of prompt emission models to predict \ensuremath{\nu}($A$). At incident neutron energies ($\mathit{En}$) where multiple fission chances are involved, the Point-by-Point (PbP) model of prompt emission is able to provide the individual \ensuremath{\nu}($A$) of the compound nuclei of the main and secondary nucleus chains that are undergoing fission at a given $\mathit{En}$. The total \ensuremath{\nu}($A$) are obtained by averaging these individual \ensuremath{\nu}($A$) over the fission chance probabilities (expressed as total and partial fission cross-section ratios). An indirect validation of the total \ensuremath{\nu}($A$) results is proposed. At high $\mathit{En}$ (above 70 MeV) the PbP results of individual \ensuremath{\nu}($A$) of the first few nuclei of the main and secondary nucleus chains exhibit an almost linear increase. This shape is explained by the damping of shell effects entering the superfluid expression of the level-density parameters. They tend to approach the asymptotic values for a great part of the fragments. This fact leads to a smooth and almost linear increase of fragment excitation energy with the fragment mass number that is reflected in a smooth and almost linear behavior of individual \ensuremath{\nu}($A$). The comparison of the present results with those of the GEF code reveals different shapes of \ensuremath{\nu}($A$) as well as different total average neutron multiplicity as a function of the $\mathit{En}$. At high $\mathit{En}$ the PbP calculations definitely reflect the influence of the almost linear shape of individual \ensuremath{\nu}($A$) of the first few nuclei of the U and Pa chains. The differences between the total \ensuremath{\nu}($A$) obtained by averaging the PbP results of individual \ensuremath{\nu}($A$) over fission cross-section ratios of different evaluations are insignificant.

Influence of nuclear dissipation on fission dynamics of the excited nucleus 248Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus 248Cf formed in the 16O+232Th reactions. Postsaddle nuclear dissipation strength of (12–14) × 1021 s−1 was extracted for Cf nucleus by fitting the results of calculations with the experimental data. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nuclear dissipation.

Neutron-fragment and Neutron-neutron Correlations in Low-energy Fission

A computational method has been developed to simulate neutron emission from thermal-neutron induced fission of 235U and from spontaneous fission of 252Cf. Measured pre-emission mass-yield curves, average total kinetic energies and their variances, both as functions of mass split, are used to obtain a representation of the distribution of fragment velocities. Measured average neutron multiplicities as a function of mass split and their dependence on total kinetic energy are used. Simulations can be made to reproduce measured factorial moments of neutron-multiplicity distributions with only minor empirical adjustments to some experimental inputs. The neutron-emission spectra in the rest-frame of the fragments are highly constrained by ENDF/B-VII.1 prompt-fission neutron-spectra evaluations. The n-f correlation measurements of Vorobyev et al. (2010) are consistent with predictions where all neutrons are assumed to be evaporated isotropically from the rest frame of fully accelerated fragments. Measured n-f and n-n correlations of others are a little weaker than the predictions presented here. These weaker correlations could be used to infer a weak scission-neutron source. However, the effect of neutron scattering on the experimental results must be studied in detail before moving away from a null hypothesis that all neutrons are evaporated from the fragments.

γ-ray spectroscopy of fission fragments produced inPb208(O18,f)

Prompt gamma-ray spectroscopy of fission fragments produced in the heavy-ion induced fusion-fission reaction $^{208}\mathrm{Pb}(^{18}\mathrm{O},f)$ at $E=90$ MeV has been performed. The relative isotopic yields of the fission fragments and the fragment mass distribution have been studied. Structures in the mass distribution have been discussed in the light of earlier results. Relative yields of several odd-$A$ isotopes of Mo, Ru, Pd, and Cd and the odd-$A$ isotones with $N=62$ and 64 have been studied along with the yields of the neighboring even-$Z$, even-$N$ fragments and correlated to nuclear structural effects. The average total neutron multiplicity during fission has been measured to be $5.48\ifmmode\pm\else\textpm\fi{}0.59$. The level schemes of the two neutron-rich nuclei $^{110}\mathrm{Pd}$ and $^{116}\mathrm{Cd}$ have been studied from $\ensuremath{\gamma}$-ray triple coincidence data. A large number of transitions, previously reported only from $\ensuremath{\beta}$-decay studies, have been observed in $^{110}\mathrm{Pd}$ for the first time. The yrast band in $^{116}\mathrm{Cd}$ has been extended up to spin $({16}^{+})$. In addition, a rotational sequence built upon an excited ${5}^{\ensuremath{-}}$ state in $^{116}\mathrm{Cd}$ has been observed up to $({13}^{\ensuremath{-}})$. The level schemes have been discussed in the context of existing results, both experimental and theoretical, in the literature.

Study of viscosity on the fission dynamics of the excited nuclei 228U produced in 19F + 209Bi reactions

A two-dimensional (2D) dynamical model based on Langevin equations was applied to study the fission dynamics of the compound nuclei 228 U produced in 19 F + 209 Bi reactions at intermediate excitation energies. The distance between the centers of masses of the future fission fragments was used as the first dimension and the projection of the total spin of the compound nucleus onto the symmetry axis, K, was considered as the second dimension in Langevin dynamical calculations. The magnitude of post-saddle friction strength was inferred by fitting measured data on the average pre-scission neutron multiplicity for 228 U . It was shown that the results of calculations are in good agreement with the experimental data by using values of the post-saddle friction equal to 6–8 × 1021 s -1.

Similarities between calculated scission-neutron properties and experimental data on prompt fission neutrons

The main properties of the neutrons released during the neck rupture are calculated for U236 in the frame of a dynamical scission model: the angular distribution with respect to the fission axis (on spheres of radii R=30 and 40 fm and at time T=4×10−21 s), the distribution of the average neutron energies (for durations of the neck rupture ΔT=1 and 2×10−22 s) and the total neutron multiplicity (for two values of the minimum neck-radius rmin=1.6 and 1.9 fm). They are compared with measurements of prompt fission neutrons during U235(nth,f). The experimental trends are qualitatively reproduced, i.e., the focusing of the neutrons along the fission axis, the preference of emission from the light fragment, the range, slope and average value of the neutron energy-spectrum and the average total neutron multiplicity.

Why not: Prompt Fission Neutrons are Released at Scission

The main properties of the neutrons released during the neck rupture and emitted immediately thereafter are calculated for 236U in the frame of a dynamical scission model. These properties are: the angular distribution with respect to the fission axis (calculated on spheres of radii R=30 and 40fm and at time T = 4 × 10−21sec), the distribution of the average energies of neutrons emitted from each state (calculated for durations of the neck rupture ΔT = 1 and 2 × 10−22sec) and the total neutron multiplicity (calculated for two values of the minimum neck-radius rmin=1.6 and 1.9fm). They are compared with measurements of prompt fission neutrons during 235U(nth, f). The experimental trends are well reproduced, i.e., the focussing of the neutrons along the fission axis, the preference of emission from the light fragment, the range, slope and average value of the neutron energy-spectrum and the average total neutron multiplicity. The neutron emission during a non-adiabatic scission process is therefore a viable alternative to the evaporation (from fully accelerated fragments) hypothesis.

Prompt neutron multiplicity in correlation with fragments from spontaneous fission ofCf252

The spontaneous fission of $^{252}\mathrm{Cf}$ serves as an excellent benchmark of prompt emission in fission since experimental data can be obtained without the need of an incident beam. With the purpose of providing experimental data on the prompt fission neutron properties in correlation with fission-fragment characteristics, an experiment on $^{252}\mathrm{Cf}$(SF) has been performed. In addition, the experiment serves as a benchmark of setup and analysis procedures for measurements of fluctuations in the prompt-neutron properties as a function of incident neutron energy in fission of the major actinides $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$. The experiment employs a twin Frisch grid ionization chamber as fission-fragment detector while neutrons were counted by using a liquid scintillator placed along the symmetry axis of the ionization chamber. Average neutron multiplicity has been obtained as a function of fission-fragment mass and total kinetic energy (TKE). The average multiplicity as a function of mass agrees well with available data in the literature in the mass range from 80 to 170 u. The existence of additional sawtooth structures in the far asymmetric mass region could not be confirmed, although the statistical accuracy of the present experiment is as good as the previous study where such structures have been reported [Nucl. Phys. A 490, 307 (1988).]. The available data in the literature on the TKE dependence of the multiplicity show strong deviations. Therefore, effort was focused on investigating experimental factors in low-efficiency neutron-counting experiments that may lead to faulty determination of this dependence. Taking these factors into account, a result that agrees well with data from high-efficiency neutron-counting experiments is obtained. The experimental arrangement allows determination of the angle between the detected neutron and the fission axis, which permits the neutron properties to be transformed into the fission-fragment rest frame. Fission neutron emission spectra in the fragment center-of-mass frame have thereby been obtained as a function of the fission-fragment mass and TKE.

Study of fission dynamics of the excited nuclei produced in fusion reactions in the framework of the four-dimensional Langevin equations

The dynamics of fission of excited nuclei has been studied by solving four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. The projection of the total spin of the compound nucleus to the symmetry axis, K, was considered as the fourth dimension in Langevin dynamical calculations. The average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy have been calculated in a wide range of fissile parameter for compound nuclei 162Yb, 172Yb, 215Fr, 224Th, 248Cf, 260Rf and results compared with the experimental data. Calculations were performed with a constant dissipation coefficient of K, γK (MeV zs)-1/2, and with a non-constant dissipation coefficient. Comparison of the theoretical results for the average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy with the experimental data showed that the results of four-dimensional Langevin equations with a non-constant dissipation coefficient are in better agreement with the experimental data. Furthermore, the difference between the results of two models for compound nuclei with low fissile parameter is low whereas, for heavy compound nuclei, is high.

Study of Fission and Evaporation Residue Cross Sections and Pre-Scission Neutron Multiplicities for ^(168)Yb

A Kramers-modified statistical model was applied to the study of the fission properties of the compound nucleus ^(168)Yb formed in heavy ion-induced fusion reactions in an intermediate range of excitation energies. The evaporation residue cross section, fission cross section, and the average pre-fission neutron multiplicities were calculated for ^(168)Yb formed in ^(18)O + ^(150)Sm reactions and the results compared with the experimental data. To calculate these quantities, the effects of temperature and the spin K about the symmetry axis have been considered in the calculations of the potential energy surfaces and the fission widths. It was shown that the results of the calculations are in good agreement with the experimental data by using values of the temperature coefficient of the effective potential and scaling factor of the fission-barrier height equal to k = 0.007 ± 0.002 MeV^(-2) and r_s = 0.994 ± 0.002, respectively.

Study of fission dynamics of 215Fr and 213Fr produced in fusion reactions with three-dimensional Langevin equations

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations was used to calculate the average pre-scission neutron multiplicities, fission probabilities, mass and energy distribution of fission fragments, and the dependences of the multiplicities of pre-scission neutrons on the masses of fission fragments and their kinetic energies for compound nuclei 213Fr and 215Fr. In these calculations, dissipation was generated through the chaos weighted wall and window friction formula. Comparison of the theoretical results with the experimental data showed that three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula make it possible to satisfactorily reproduce the experimental data.

Study of different features of fission dynamics in heavy-ion-induced reactions

A stochastic approach based on three-dimensional Langevin equations was used to calculate the average pre-scission neutron multiplicities, fission probabilities and the mean kinetic energy of fission fragments. The chaos-weighted wall and window friction formula was applied to determine the dissipative forces in Langevin equations. The analysis of the results shows that the above-mentioned experimental data can be reproduced using the chaos-weighted wall and window friction formula. However, for heavy nuclei the results of calculations for the average pre-scission neutron multiplicities and the variances of the mass and kinetic energy distributions are lower than the experimental data.

Event-by-event evaluation of the prompt fission neutron spectrum from239Pu(n,f)

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 ENDF-B/VII.0 evaluation. We present our results, discuss relevant tests of this new evaluation, and describe possible further improvements.

Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei 210Po and 224Th formed in the fusion-fission reactions 4He + 206Pb , 16O + 208Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.

Advanced Monte Carlo modeling of prompt fission neutrons for thermal and fast neutron-induced fission reactions onPu239

Prompt fission neutrons following the thermal and 0.5 MeV neutron-induced fission reaction of $^{239}\mathrm{Pu}$ are calculated using a Monte Carlo approach to the evaporation of the excited fission fragments. Exclusive data such as the multiplicity distribution $P(\ensuremath{\nu})$, the average multiplicity as a function of fragment mass $\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}(A)$, and many others are inferred in addition to the most used average prompt fission neutron spectrum $\ensuremath{\chi}({E}_{\text{in}},{E}_{\text{out}})$, as well as average neutron multiplicity $\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}$. Experimental information on these more exclusive data help constrain the Monte Carlo model parameters. The calculated average total neutron multiplicity is ${\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}}_{c}=2.871$ in very close agreement with the evaluated value ${\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}}_{e}=2.8725$ present in the ENDF/B-VII.0 library. The neutron multiplicity distribution $P(\ensuremath{\nu})$ is in very good agreement with the evaluation by Holden and Zucker. The calculated average spectrum differs in shape from the ENDF/B-VII.0 spectrum, evaluated with the Madland-Nix model. In particular, we predict more neutrons in the low-energy tail of the spectrum (below about 300 keV) than the Madland-Nix calculations, casting some doubts on how much scission neutrons contribute to the shape of the low-energy tail of the spectrum. The spectrum high-energy tail is very sensitive to the total kinetic energy distribution of the fragments as well as to the total excitation energy sharing at scission. Present experimental uncertainties on measured spectra above 6 MeV are too large to distinguish between various theoretical hypotheses. Finally, comparisons of the Monte Carlo results with experimental data on $\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}(A)$ indicate that more neutrons are emitted from the light fragments than the heavy ones, in agreement with previous works.

Fission fragment properties obtained in the γ - γ - γ coincidence method in the reaction 208Pb(18O, f )

Independent fission fragment yields have been obtained for the six fragment pairs ( Z L/Z H = 44/46 , 42/48, 40/50, 38/52, 36/54 and 34/56) in 208Pb(18O, f ) at the beam energy E = 85 MeV. γ -ray spectroscopy technique was applied to analyze the experimental data. With use of these data the mass distribution of fission fragments was restored. Data on average fragment spin distribution and total neutron multiplicity are presented. The agreement of the obtained results with other experimental data proves the validity of the applied method to solve this kind of problems.

Partition of total excitation energy between fragment pairs in asymmetric and symmetric fission modes

Primary and secondary fragment mass and fragment total kinetic energy were measured by the time-of-flight technique in the $12\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ proton induced fission of $^{232}\mathrm{Th}$. The average neutron multiplicity was obtained from the difference of the primary fragment mass and the secondary one as a function of mass and total kinetic energy of fission fragments. Simulation calculations were applied for correction of observed fission data affected by instrumental fluctuations in measurements of flight time and kinetic energies of fragments. Anomalous behaviors of the average neutron multiplicity as a function of total kinetic energy in the mass region of $98--107$ for the lighter fragment and $126--135$ for the heavier were observed and they were found to correlate with two fission modes, symmetric and asymmetric fission. The overall trend of the average neutron multiplicity was discussed in terms of the two fission modes. Partition of the total excitation energy between fragment pairs deduced from the neutron multiplicity data was evaluated for each fission mode for the first time.