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.     

System size effects on probing nuclear dissipation with neutrons

Using a dynamical Langevin equation coupled with a statistical decay model, we calculate the excess of the pre-scission neutron multiplicities over its standard statistical-model values as a function of the nuclear dissipation strength for the three nuclei 190Os, 200Hg, and 210Po which have the same neutron-to-proton ratio N/Z. We find that by decreasing the size of the fissioning nuclei, the effects of nuclear dissipation on the excess of the pre-scission neutron multiplicity are substantially amplified, and that the sensitivity of this excess to the nuclear friction strength is considerably increased as well. We suggest that for those fissioning systems with the same N/Z that are populated in fusion reactions, to obtain a more accurate information of the nuclear dissipation strength by measuring the pre-scission neutron multiplicity, it is best to choose a system with a small size.     

Study of pre-scission particle emissions and fission probability of the ~(178)W produced in fusion reactions

A dynamical model based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles, and the fission probability for compound nucleus178 W produced in fusion reactions. The pre-scission multiplicities of particles and fission probability are calculated and compared with the experimental data over a wide range of excitation energy. A modified wall and window dissipation with a reduction coefficient, ks, has been used in the Langevin equations for reproducing experimental data. It was shown that the results of the calculations are in good agreement with the experimental data by using values of ks in the range 0.24 ks 0.47.     

System size effects on probing nuclear dissipation with neutrons

Using a dynamical Langevin equation coupled with a statistical decay model, we calculate the excess of the pre-scission neutron multiplicities over its standard statistical-model values as a function of the nuclear dissipation strength for the three nuclei 19~Os, 2~~Hg, and 21~po which have the same neutron-to-proton ratio N/Z. We find that by decreasing the size of the fissioning nuclei, the effects of nuclear dissipation on the excess of the pre-scission neutron multiplicity are substantially amplified, and that the sensitivity of this excess to the nuclear friction strength is considerably increased as well. We suggest that for those fissioning systems with the same N/Z that are populated in fusion reactions, to obtain a more accurate information of the nuclear dissipation strength by measuring the pre-scission neutron multiplicity, it is best to choose a system with a small size.     

Role of N/Z in Pre-scission Neutrons as an Observable of Nuclear Friction

A dynamical Langevin model is employed to evaluate the excess of the neutron emission in the fission of heavy nuclei ^240Cf, ^246 Cf, ^254Cf, ^240U relative to the standard statistical-model prediction at various saddle-to-scission friction strengths. It is shown that when the neutron-to-proton ratio N/Z of the system increases, the sensitivity of the excess to the friction decreases substantially, and it almost disappears for ^240U. We suggest that using those compound systems with low N/Z favors an accurate determination for the saddle-to-scission friction strength based on the measurement of the pre-scission neutron multiplicity.     

Influence of nuclear dissipation on fission dynamics of the excited nucleus <Superscript>248</Superscript>Cf 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.     

Role of N/Z in Pre-scission Neutrons as an Observable of Nuclear Friction

A dynamical Langevin model is employed to evaluate the excess of the neutron emission in the fission of heavy nuclei ²⁴⁰Cf, ²⁴⁶Cf, ²⁵⁴Cf, ²⁴⁰U relative to the standard statistical-model prediction at various saddle-to-scission friction strengths. It is shown that when the neutron-to-proton ratio N/Z of the system increases, the sensitivity of the excess to the friction decreases substantially, and it almostdisappears for ²⁴⁰U. We suggest that using those compound systems with low N/Z favors an accurate determination for the saddle-to-scission friction strength based on the measurement of the pre-scission neutron multiplicity.     

A Detailed Study of Pre-scission γ Emission as a Probe of Nuclear Dissipation

Using a Langevin equation coupled with a statistical model, we calculate pre-scission giant dipole resonance （GDR） γ-ray multiplicity of nuclei 194 pb, 200Pb, 206Pb, and 200 Os. It is demonstrated that with increasing the isospin asymmetry of these fissioning nuclei the sensitivity of the emitted γ multiplicity to the nuclear viscosity coefficient is decreased significantly. For 200Os nuc/eus, this γ-ray emission is no longer sensitive to the magnitude of the viscosity coefficient. In addition, the effect of the isospin asymmetry on the γ rays as a probe of nuclear dissipation is reduced with increasing angular momentum. These results suggest that to obtain a more accurate information of the viscosity coemfficient by the measurement of pre-scission GDR γ-ray multiplicity it is better to choose those compound systems with small isospin asymmetry and low spin.     

Fission dynamics of the compound nucleus 213Fr formed in heavy-ion-induced reactions

A stochastic approach based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles and the fission probabilities for the compound nucleus ²¹³Fr and the results are compared with the experimental data. In these calculations, a modified wall and window dissipation with a reduction coefficient, k _s , has been used in the Langevin equations. It was shown that the results of the calculations are in good agreement with the experimental data by using values of k _s in the range 0.3?≤?k _s ?≤?0.5.     

Particle multiplicities in the fission-like reactions of 340 MeV Si on Th

Pre-scission and post-scission multiplicities of neutrons and alpha particles have been simultaneously measured for the fission-like reactions of 340 MeV ²⁸Si on ²³²Th. Dynamical model calculations using HICOL code predict that about 90% of the observed events are of quasi-fission type while the remaining 10% are from compound nucleus fission decay. Moving source fits were carried out to the observed neutron and alpha particle spectra, measured at different angles with respect to the fragment directions. The pre-scission and post-scission neutron multiplicities are deduced to be 8.7±2.0 and 9.4±2.0, respectively. The corresponding multiplicity values for alpha particles are found to be 0.22±0.08 and 0.1±0.03. From the measured post-scission neutron multiplicity, it is inferred that about 65±20 MeV of the initial excitation energy remains at scission. This may be compared to the value of 85±30 MeV estimated from PACE2 statistical model calculations, adjusted to reproduce the measured pre-scission neutron multiplicity. From a comparison of the Statistical Model predictions with the measured pre-scission neutron multiplicity, the fission delay is estimated to be of 5⁺⁷₋₃×10⁻²⁰ s which overlaps with the average duration of fission-like process from the contact to the scission point (2×10⁻²⁰ s) as determined from HICOL-based dynamical calculations. For the delay time deduced as above, the pre-scission alpha particle multiplicity calculated by the PACE2 code is about a factor two larger than the experimental one, demonstrating the difficulties in modelling the alpha particle emission from highly elongated shapes that characterize the fissioning system from the contact point to scission.     

Effect of viscosity on the fission dynamics of the excited compound nucleus 251Es produced in fusion reaction

A stochastic approach based on two-dimensional dynamical model has been used to simulate the fission dynamics of the excited compound nucleus ²⁵¹Es produced in ¹⁹F+²³²Th reaction. In the dynamical calculations the elongation parameter has been 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. The value of post-saddle friction was inferred by reproducing experimental data on the mean pre-scission neutron multiplicity for ²⁵¹Es. It was shown that the results of calculations are in good agreement with the experimental data by applying values of the post-saddle friction equal to 13−15×10²¹s⁻¹.     

Measurement of fission anisotropy for 16O+181Ta

Anisotropies in fission fragment angular distributions measured for the system ¹⁶O + ¹⁸¹Ta over a range of bombarding energies from 83 MeV to 120 MeV have been analysed. It is shown that statistical transition state model (TSM) with pre-scission neutron correction described adequately the measured anisotropy data. Strong friction parameter is found to be necessary to estimate the pre-saddle to pre-scission neutron ratio.     

The dependence of fission time-scales on fragment mass asymmetry in the 20Ne+165Ho reaction at 50A MeV

The pre-scission and post-scission multiplicities of alpha particles were determined in coincidence with fission fragments for four windows of exit channel mass asymmetry in the reaction ²⁰Ne+¹⁶⁵Ho at 50A MeV. The technique used employed a kinematic analysis of the energy spectra of alpha particles as a function of the emission angle with respect to the fission axis. Using a procedure of fitting the experimental energy spectra with those resulting from a Monte Carlo simulation program, the total multiplicity of alpha particles was separated into pre-scission and post-scission components. Using the pre-scission and post-scission multiplicities, neutron multiplicity measurements and other empirical observations, both the initial excitation energy and the excitation energy at scission of the compound nucleus were determined. The pre-scission times in the de-excitation of a highly excited ¹⁷⁸W compound nucleus with initial excition energy of 570 MeV were evaluated using statistical model calculations. Only a small decrease in scission time was derived for the most asymmetric events studied. The possible contribution of very damped deep inelastic processes is discussed.     

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, ??} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k _s = 0.25 and k _s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k _s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z ²/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k _s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, ??n _pre(M)??, and between, this multiplicity and the kinetic energy of fission fragments, ??n _pre(E _k )??, are also presented.     

Fission times of excited nuclei: An experimental overview

An overview of selected recent experimental results on fission times is presented. Evidences for over-damped motion up to saddle point during the fission process of highly excited nuclei have been obtained independently through fission probability, pre-scission multiplicity and direct time measurements. In addition, strong clues have been found for a temperature dependency of friction. Experiments probing transient effects through fission probabilities are presented and the counterbalanced effects of friction and level density parameters are discussed. Promising perspectives for super-heavy stability studies, based on fission time measurements, are presented.     

Surveying post-saddle nuclear dissipation with protons and a particles as probes

Using a Langevin model, we calculate post-saddle proton and a-particle multiplicities as a function of the post-saddle dissipation strength (β) for the heavy systems ~(234)Cf, ~(240)Cf, ~(246)Cf and ~(240)U. We find that, with increasing isospin of the system, the sensitivity of post-saddle light charged-particle multiplicities to β decreases considerably and, moreover, for 240U the charged-particle multiplicities are no longer sensitive to β. These results suggest that in order to determine the post-saddle friction strength more accurately by measuring the multiplicities of pre-scission protons and a particles, it is best to populate those heavy compound systems with low isospin.     

Analysis of fusion-fission process with neutron evaporation in superheavy mass region

The fusion-fission process for the synthesis of superheavy elements is discussed on the basis of the fluctuation-dissipation dynamics. We analyze the experimental data using a three-dimensional Langevin calculation. We take the neutron emission into account in the Langevin calculation and compare the results with experimental data. Also we discuss the evaporation residue cross section for superheavy elements.     

Mass-split dependence of the pre- and post-scission neutron multiplicities for fission of 251Es

Pre- and post-scission neutron multiplicities have been measured as a function of fission mass-split for the reactions of 105 and 120 MeV ¹⁹F with ²³²Th. The post-scission multiplicities show no evidence for persistence of the sawtooth yield observed for spontaneous fission of ²⁵²Cf; the dependence on mass-split is not consistent with the random neck rupture model. The pre-scission multiplicities show no evidence of quasi-fission for asymmetric mass-splits. It is proposed that pre-scission neutron multiplicity measurements should be a useful tool in studying quasi-fission produced by reactions with heavier projectiles.     

角动量对断前粒子发射壳效应的影响

用Smoluchowski方程研究了角动量对一个轻的闭壳核¹³²Sn裂变前粒子蒸发壳效应的影响,发现壳对断前粒子发射的影响敏感地依赖于这个裂变系统的角动量.对可能的原因进行了讨论