Pre-scission Neutron Multiplicity Research Articles

Consistent application of the finite-range liquid-drop model to Langevin fission dynamics of hot rotating nuclei

A generalized finite-range liquid-drop model based on the Yukawa-plus-exponential potential was applied to describe fission dynamics of hot rotating nuclei. The potential energy, level-density parameter and Helmholtz free energy are calculated in a consistent way by using the generalized finite-range liquid-drop model. The level-density parameter was approximated by a leptodermous-type expression. The coefficients of this expansion are in surprisingly good agreement with those obtained earlier by Ignatyuk and co-workers. The results of Langevin dynamical calculations of the mean prescission neutron multiplicity and fission probability are practically the same both for the level-density parameter calculated with Ignatyuk's coefficients and the one calculated using the generalized finite-range liquid-drop model. This fact lets us assume that all previous results of dynamical Langevin calculations performed with Ignatyuk's level-density parameter stay reliable.

Shell effects on pre-scission particle emission

The shell effects on the emission of light particles in fission processes are explored in the framework of the Smoluchowski equation. Two doubly magic nuclei, 132Sn and 208Pb, are chosen as representatives to demonstrate the shell effects. Calculations show that the shell has a significant effect on the neutron emission for the two nuclei and that this shell effect on pre-scission neutron multiplicity gradually fades out with increasing excitation energy. In addition, a dependence of shell effects in neutron emission on angular momentum has been found.

Reduction coefficient in surface-plus-window dissipation: Analysis of experimental data from fusion-fission reactions within a stochastic approach

A stochastic approach based on three-dimensional Langevin equations was applied to detailed study of fission dynamics in fusion-fission reactions. The reduction coefficient in surface-plus-window dissipation is deduced by analyzing the available experimental data on various observable quantities in fusion-fission reactions. Analysis of the results shows that not only characteristics of the mass-energy distribution of fission fragments but also the mass and kinetic-energy dependence of the prescission and postscission neutron multiplicities, the angular anisotropy, and fission probability can be reproduced using surface-plus-window dissipation with the reduction coefficient from a wall formula ks =0 .25-0.5 for com- pound nuclei lighter than 224 Th. The analysis performed reveals that the coordinate-independent reduction coefficient ks is not compatible with the simultaneous description of the main fission characteristics for fissioning systems heavier than 224 Th. c � 2003 MAIK "Nauka/Interperiodica".

Pre- and post-scission neutron multiplicities in $19F$ + $209Bi$ reaction at 108 MeV

The pre- and post-scission neutron multiplicities have been determined from the fragment-neutron angular-correlation measurements in 19F + 209Bi reaction at bombarding energy of 108 MeV. The average pre-scission neutron multiplicity ( νpre) is significantly larger than that calculated on the basis of the statistical model. The excess in νpre value is used to estimate the dynamical delay in the fusion-fission time scale for the 228U compound system. For a level density parameter a n = A/10 MeV-1 and a n = a f, the fusion-fission dynamical time was established to be 120 ± 10 × 10-21 s. We also observe that νpre is higher for asymmetric mass splits as compared to symmetric mass splits. The enhancement in the νpre for the asymmetric region could be due to strong variations in the fragment mass distribution at different stages in multiple chance fission at medium excitation energies.

More detailed study of fission dynamics in fusion-fission reactions within a stochastic approach

A stochastic approach based on three-dimensional Langevin equations was applied to a more detailed study of fission dynamics in fusion-fission reactions. The dynamical model has been developed and extended to investigate fission characteristics of light fissioning nuclei at low excitation energies. The energy dependences of an anisotropy of the fission fragment angular distribution, an evaporation residue cross section, a fission cross section, mean prescission neutron, and giant dipole $\ensuremath{\gamma}$ multiplicities have been analyzed for the ${}^{16}\mathrm{O}{+}^{208}\mathrm{Pb}$-induced fission of ${}^{224}\mathrm{Th}.$ Also, dependence of the prescission neutron multiplicity on the fragment mass asymmetry and total kinetic energy have been calculated. Analysis of the results shows that not only characteristics of the mass-energy distribution of fission fragments, but also the mass and kinetic-energy dependence of the prescission neutron multiplicity, the angular anisotropy, and fission probability can be reproduced using a modified one-body mechanism for nuclear dissipation with a reduction coefficient of the contribution from a wall formula ${k}_{s}=0.25--0.5$ for compound nuclei ${}^{172}\mathrm{Yb},$ ${}^{205}\mathrm{Fr},$ ${}^{215}\mathrm{Fr},$ and ${}^{224}\mathrm{Th}.$ Decrease of the prescission neutron multiplicities with fragment mass asymmetry is due to a decrease of the fission time. The results obtained show that prescission neutrons are evaporated predominantly from the nearly spherical compound nucleus at an early stage of fission process before the saddle point is reached. From performed analysis one can conclude that coordinate-independent reduction coefficient ${k}_{s}$ is not compatible with simultaneous description of the main fission characteristics for heavy fissioning systems ${}^{256}\mathrm{Fm}$ and ${}^{252}\mathrm{Fm}.$

Prescission neutron multiplicity and fission probability from Langevin dynamics of nuclear fission

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 contributions of the presaddle and postsaddle neutrons to the total prescission multiplicity. A detailed analysis of our results leads us to conclude that the chaos-weighted wall formula friction can adequately describe the fission dynamics in the presaddle region. This friction, however, turns out to be too weak to describe the postsaddle dynamics properly. This points to the need for a suitable explanation for the enhanced neutron emission in the postsaddle stage of nuclear fission.

Neutron and fragment yields in proton-induced fission of 238U at intermediate energies

The primary fission fragment mass and kinetic energy distributions, and neutron multiplicities as function of fragment mass have been measured in the proton-induced fission of 238U at energies E p=20, 35, 50 and 60 MeV using time-of-flight technique. Pre-scission and post-scission neutron multiplicities have been extracted from double differential distributions. The fragment mass dependence of the post-scission neutron multiplicities reveals the gross nuclear shell structure effect even at the higher proton energies we measured. The yields of neutron-rich fission products in the fission of 238U by 25 MeV protons were measured using an ion guide-based isotope separator technique. The results indicate enhancement for superasymmetric mass division at intermediate excitation energy of the fissioning nucleus. The experimental results have been analysed in the framework of a time-dependent statistical model with inclusion of nuclear friction effects in the fission process.

Three-dimensional Langevin calculations of fission fragment mass-energy distribution from excited compound nuclei

A stochastic approach to fission dynamics based on three-dimensional Langevin equations was applied to calculate fission fragment mass-energy distribution from a number of excited compound nuclei formed in reactions induced by heavy ions. Evaporation of prescission light particles along Langevin fission trajectories from the ground state of the compound nucleus to its scission has been taken into account using a Monte Carlo simulation technique. Inclusion of the third collective coordinate in Langevin dynamics leads to a considerable increase of the variance of the mass and the kinetic-energy distributions of fission fragments as compared with two-dimensional Langevin calculations. A liquid-drop model with finite range of nuclear forces and a modified one-body mechanism for nuclear dissipation have been used in the calculations. The results of the calculations are compared with the available experimental data. The calculations performed using the three-dimensional Langevin dynamics reproduce sufficiently well all the parameters of the two-dimensional fission fragment mass-energy distribution and their dependence on various parameters of the compound nucleus. The mean prescission neutron multiplicities are also reproduced with good accuracy. In order to reproduce simultaneously the measured prescission neutron multiplicities and the variance of the fission fragment mass-energy distribution, the reduction coefficient of the contribution from a wall formula has to be decreased at least by half of the one-body dissipation strength $(0.25<~{k}_{s}<~0.5).$

Dissipative dynamics of fission in the framework of asymptotic expansion of Fokker-Planck equation

The dynamics of fission has been formulated by generalising the asymptotic expansion of the Fokker-Planck equation in terms of the strength of the fluctuations where the diffusion coefficients depend on the stochastic variables explicitly. The prescission neutron multiplicities and the mean kinetic energies of the evaporated neutrons have been calculated and compared with the respective experimental data over a wide range of excitation energy and compound nuclear mass. The mean and variance of the total kinetic energies of the fission fragments have been calculated and compared with the experimental values.

Quasifission reactions as a probe of nuclear viscosity

Fission fragment mass and angular distributions were measured from the ${}^{64}\mathrm{Ni}{+}^{197}\mathrm{Au}$ reaction at 418 MeV and 383 MeV incident energy. A detailed data analysis was performed, using the one-body dissipation theory implemented in the code HICOL. The effect of the window and the wall friction on the experimental observables was investigated. Friction stronger than one body was also considered. The mass and angular distributions were consistent with one-body dissipation. An evaporation code DIFHEAT coupled to HICOL was developed in order to predict reaction time scales required to describe available data on prescission neutron multiplicities. The multiplicity data were again consistent with one-body dissipation. The cross sections for touch, capture and quasifission were also obtained.

Calculating fission rates at high spin: Incorporation of rotational degrees of freedom in thermodynamically fluctuating axially symmetric systems

The methods presently used to calculate fission rates fail to correctly take into account the rotational degrees of freedom of compound nuclei rotating in three dimensions. The statistical model code JOANNE has been modified to correctly calculate the fission rates of classical thermodynamically fluctuating axially symmetric systems rotating in three dimensions. With this new code it is possible to reproduce evaporation residue cross sections, fission cross sections, and prescission neutron multiplicities from O-induced reactions, without the use of large fission delay times or large values of the viscosity of heated nuclear matter.

Dynamical study of fission process and estimation of prescission neutron multiplicity

The dynamics of fission has been studied by solving Euler-Lagrange equations 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 observed that a stronger friction is required in the saddle to scission region as compared to that in the ground state to saddle region.

A C-code for combining a Langevin fission dynamics of hot nuclei with a statistical model including evaporation of light particles and giant dipole γ-quanta

We present a C-code calculating the decay of highly excited and rotating atomic nuclei by fission and light particle (neutrons, protons, α-particles, giant dipole γ-quanta) evaporation. The program calculates the distributions of the relevant observables, their averages, variances and correlations. The most important output parameters are: fission (respectively survival) probabilities, pre-scission neutron and charged-particle multiplicities and spectra, pre-scission gamma-multiplicities and spectra, average energies of these particles, scission lifetime distributions, and excitation energies at scission. For this purpose a dynamical Langevin equation for an overdamped fission process is combined with a statistical model description. In the dynamical part of the model the evaporation of light particles and giant dipole γ-quanta is accounted for by coupling a Monte Carlo algorithm to the fission dynamics. In the statistical part of the model a fission width consistent with the dynamical description is used besides the standard way of calculating the light particle emission. The code provides also the possibility to investigate the influence of different nuclear friction form factors on the observable quantities.

Neutrons in coincidence with fission of238U induced by stopped antiprotons

Neutron multiplicities after antiproton-induced fission have been determined as a function of the total mass of the fission fragments. Pre- and postscission neutron multiplicities of the reaction $\mathrm{p\ifmmode\bar\else\textasciimacron\fi{}}$+${}^{238}$U have been deduced using the moving-source parametrization of the neutron energy spectra by Maxwellian distributions. A postscission multiplicity of 6.3(6) neutrons out of 20.0(10) in total emitted neutrons in fission indicates that fission is a rather slow process. The increase of the evaporative prescission neutron multiplicity is about 80% of the total increase of evaporative neutrons as a measure of excitation energy. The postscission multiplicity gets only 20% of the total increase, thus indicating that the nucleus has only a moderate excitation energy at the moment of scission. The results are compared with standard cascade-evaporation calculations predicting a much lower number of evaporated prescission neutrons as the experiment shows. This is a strong indication of the importance of dissipative effects in the fission process. Application of dissipative effects like a saddle-to-scission delay time and nuclear viscosity in the model calculation describes the experimental results much better.

Determination of nuclear friction in strongly damped reactions from prescission neutron multiplicities.

Nonfusion, fissionlike reactions in collisions of four heavy systems (well below the fusion extra-push energy threshold), for which Hinde and co-workers had measured the prescission neutron multiplicities, have been analyzed in terms of the deterministic dynamic model of Feldmeier coupled to a time-dependent statistical cascade calculation. In order to reproduce the measured prescission multiplicities and the observed (nearly symmetric) mass divisions, the energy dissipation must be dramatically changed with regard to the standard one-body dissipation: In the entrance channel, in the process of forming a composite system, the energy dissipation has to be reduced to at least half of the one-body dissipation strength (${\mathit{k}}_{\mathit{s}}^{\mathrm{in}}$\ensuremath{\le}0.5), and in the exit channel (from a mononucleus shape to scission) it must be increased by a factor ranging for the studied reactions from ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=4 to ${\mathit{k}}_{\mathit{s}}^{\mathrm{out}}$=12. These results are compared with the temperature dependence of the friction coefficient, recently deduced by Hofman, Back, and Paul from data on the prescission giant dipole resonance emission in fusion-fission reactions. The combined picture of the temperature dependence of the friction coefficient, for both fusion-fission and nonfusion reactions, may indicate the onset of strong two-body dissipation already at a nuclear temperature of about 2 MeV. \textcopyright{} 1996 The American Physical Society.

Prescission neutron multiplicities and nuclear viscosity: A systematic study.

Prescission neutron multiplicities have been calculated in the framework of a simple, dynamical model of fission. The fission trajectories have been calculated by solving Euler-Lagrange equations with dissipation generated through two-body nuclear viscosity. Systematic study of the relationship between the prescission neutron multiplicities and nuclear viscosity has been made in the range of mass 150--200 and incident energy 4--13 MeV/nucleon. The values of the viscosity coefficients which are used to predict the observed prescission neutron multiplicities follow a global relation in the region of mass and energy studied.

Prescission neutron emission in 235U(nth,f) through fragment-neutron angular correlation studies.

Measurements of prompt neutron energy spectra and angular distributions from mass and kinetic energy selected fission fragments were carried out in the thermal neutron fission of $^{235}\mathrm{U}$. Neutron energy was determined by the time-of-flight technique and fission fragment energy and angle were measured using a back-to-back gridded ionization chamber. The measured angular distributions of neutrons emitted from fragment pairs of various mass and kinetic energy were compared with results of Monte Carlo calculations assuming neutron emission from fully accelerated fragments to determine the component of neutrons which may be emitted in the prescission stage. The calculations were carried out using as inputs the measured center-of-mass neutron energy spectra and multiplicites and assuming isotropic emission of neutrons in the center-of-mass frame of both the fission fragments, and a three source fitting of the angular distributions was done to deduce the component of prescission neutrons. The value of the prescission neutron multiplicity averaged over all fragment masses is found to be 0.25\ifmmode\pm\else\textpm\fi{}0.05 (about 10% of the total neutron multiplicity). The present results have been discussed on the basis of the energy damping and time scale of the saddle to scission transition in the thermal neutron induced fission process.

Role of nuclear dynamics in deducing the fusion-fission time scales from prescission neutron multiplicities.

Existing data on the prescission neutron multiplicities have been analyzed with a new method combining time-dependent statistical cascade calculations with Feldmeier's model of the dynamics of nucleus-nucleus collisions. The analysis resulted in the determination of the time scale ${\mathrm{\ensuremath{\tau}}}_{\mathit{f}}$ of fusion-fission reactions for different composite systems with excitation energies ranging from 80 to 240 MeV. The deduced values of ${\mathrm{\ensuremath{\tau}}}_{\mathit{f}}$ range from 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}20}$ to ${10}^{\mathrm{\ensuremath{-}}18}$ s. These time scales are approximately 10 times longer than those deduced for the same set of data with the ``static'' model used by Hinde and collaborators.

Time scales of fusion-fission reactions calculated from prescission neutron multiplicities

The time scale of fusion-fission reactions was found to be in the range from τ f = 5 · 10 −20 to 5 · 10 −19 s. This result was obtained from the analysis of the prescission neutron multiplicities with a new method combining the time-dependent statistical cascade calculations with the nuclear dynamics model of Feldmeier.

Influence of pre-saddle neutrons on the fission fragment angular distribution

In the present note it is shown that distinguishing between pre-saddle and saddle-to-scission neutrons removes a discrepancy previously found [2–4] between data for the fission fragment anisotropy and an analysis in the framework of the transition state theory in which it has been assumed that all pre-scission neutrons influence the temperature at the saddle point. The analysis of the present paper requires a fairly weak (β=2 * 1021s−1) friction at compact shapes, in agreement with a previous [9,10] analysis of prescission neutron multiplicities and fission probabilities.