Pre-scission Neutron Multiplicity Research Articles

Systematic study of prescission neutron multiplicity: Revealing the role of entrance channel magicity

The prescission neutron multiplicities (νpre) are studied for a systematic understanding of the influence of entrance-channel shell closure in fusion-fission dynamics. The existing νpre data are analyzed for reactions with a wide variety of target and projectile combinations. For completeness, the measured νpre data for the fusion-fission reactions with the doubly closed shell 16O projectile on the targets having either proton (204,206Pb) or both proton and neutron (208Pb) shell closure is reanalyzed. Although the measured νpre for 224Th disagree with the available data reported by Rossner et al. (1992) [1], our results are found to be more consistent and follow a systematic trend as described in this letter. Theoretical analysis is performed within the standard statistical model framework, where dissipation strength is used as a tunable parameter. It is observed that irrespective of the compound nuclear excitation energy, the entrance channel magicity imparts an intriguing impact on the dissipation strength. A similar entrance channel effect in the evaporation residue cross-section is also demonstrated. In conclusion, the present analysis establishes an entanglement of the exit channel observables with the entrance channel shell closure. It contradicts the hypothesis of complete equilibrium in compound nuclear reactions.

Neutron multiplicity measurement and investigation of nuclear dissipation and shell effects in Si30+W182,184,186 reactions

Background: Enhanced prescission neutron multiplicity (${\ensuremath{\nu}}_{\mathrm{pre}}$) over statistical model calculations assuming Bohr-Wheeler fission width is explained using Kramers' fission width incorporating dissipative effects. The dissipation strength obtained from such studies reported significant effect of the neutron shell closure of $N=126$ of the fissioning system as well as nuclear temperature. The dependence of dissipation strength on shell effect and temperature is also attributed to the choice of input parameters in the statistical model calculations.Purpose: We investigate the role of $N/Z$, shell effect, collective enhancement of level density (CELD), and excitation energy on ${\ensuremath{\nu}}_{\mathrm{pre}}$ in reactions forming isotopes of the Ra nucleus.Methods: The neutron multiplicity excitation function is measured for the $^{30}\mathrm{Si}+^{182,184,186}\mathrm{W}$ reactions populating $^{212,214,216}\mathrm{Ra}$ nuclei using the National Array of Neutron Detectors (NAND) at the Inter-University Accelerator Centre, New Delhi. Among these compound nuclei, $^{214}\mathrm{Ra}$ has a major neutron shell closure of $N=126$. Measured ${\ensuremath{\nu}}_{\mathrm{pre}}$ are analyzed within the framework of a statistical model incorporating dynamical hindrance in nuclear fission due to dissipation, shell corrections in the fission barrier and level density, and CELD.Results: Experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ show a marginal isotopic dependence at all excitation energies. ${\ensuremath{\nu}}_{\mathrm{pre}}$ values do not show any noticeable effect of neutron magic number $N=126$. Dissipation strength of $\ensuremath{\beta}=8\phantom{\rule{4pt}{0ex}}{\mathrm{zs}}^{\ensuremath{-}1}$ ($5.27\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$) reasonably reproduces the experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ excitation functions for all three nuclei in the measured energy range. Appreciable variations in presaddle neutron emissions are observed when shell effect or CELD is excluded in the calculations. Even though both the shell and CELD are found to impact primarily in the presaddle sector, they alter the excitation energy and multiplicity in the saddle-to-scission sector as well in a complementary manner.Conclusions: A temperature independent dissipation coefficient is observed to reproduce the experimental results in this study throughout the excitation energy range measured. Shell corrections in fission barrier and level density parameters and CELD in fission and particle evaporation widths also influence the neutron multiplicities. The observed effect of CELD in the presaddle phase is attributed to the large enhancement of level density at the saddle due to its large deformation and consequent enhancement of fission width.

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.

Investigating the fission dynamics of the following neutron shell closed nuclei within a stochastic dynamical approach: 210Po, 212Rn, and 213Fr* *D.A. acknowledges the financial support from the University Grants Commission (UGC), Government of India, received in the form of a research fellowship (Ref. No. 19/06/2016/(i) EU-V, Sr. No. 2061651303)

The dissipative dynamics of nuclear fission is a well confirmed phenomenon that can be either described by a Kramers-modified statistical model or by a dynamical model employing the Langevin equation. Although dynamical models as well as statistical models incorporating fission delays have been found to explain the measured fission observables in several studies, they present conflicting results for shell closed nuclei in the mass region of 200. Notably, an analysis of the recent data on neutron shell closed nuclei in the excitation energy range of 4080 MeV failed to provide a satisfactory description of the data, which was attributed to a mismatch with shell effects and/or entrance channel effects, without reaching a definite conclusion. In the present study, we demonstrate that a well established stochastic dynamical code can simultaneously reproduce the available data for pre-scission neutron multiplicities and fission and evaporation residue excitation functions for the following neutron shell closed nuclei Po and Rn and their isotopes Po and Rn without the need for including any extra shell or entrance channel effects. The relevant calculations are performed by using a phenomenological universal friction form factor with no ad-hoc adjustment of the model parameters. However, we note a significant deviation, beyond experimental errors, for some Fr isotopes.

Simulation of the fission process of the excited compound nuclei Rn210 and Fr215 produced in fusion reactions within the framework of the modified statistical model

In the framework of the modified statistical model there have been simulated fission process of the excited compound nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$ produced in $^{16}\mathrm{O}+^{194}\mathrm{Pt}$ and $^{19}\mathrm{F}+^{196}\mathrm{Pt}$ reactions and calculated the evaporation residue cross section, the fission cross section, the fission probability, the average prescission neutron multiplicity, the mean fission time, and the anisotropy of fission fragments angular distribution as a function of excitation energy. The classical collective motion of the excited compound nuclei about the ground state, the temperature dependence of the location, the height of fission transition points, and the projection of the total spin of the compound nucleus onto the symmetry axis $K$ have been considered in the statistical calculations. A constant nuclear dissipation was applied in the statistical calculations. In the statistical calculations, the temperature coefficient of the effective potential $k$ and the scaling factor of the fission-barrier height ${r}_{s}$ were considered as a free parameter and their magnitudes inferred by fitting measured data on the evaporation residue cross section and the fission cross section for the excited compound nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$. It was shown that the results of calculations are in good agreement with the experimental data by using appropriate values for these parameters equal to $k=0.0160\ifmmode\pm\else\textpm\fi{}0.0050\phantom{\rule{0.28em}{0ex}}\mathrm{Me}{\mathrm{V}}^{\ensuremath{-}2}$ and ${r}_{s}=1.0030\ifmmode\pm\else\textpm\fi{}0.0020$ for $^{210}\mathrm{Rn}$ and $k=0.0065\ifmmode\pm\else\textpm\fi{}0.0040\phantom{\rule{0.16em}{0ex}}\mathrm{Me}{\mathrm{V}}^{\ensuremath{-}2}$ and ${r}_{s}=1.0040\ifmmode\pm\else\textpm\fi{}0.0015$ for $^{215}\mathrm{Fr}$. Furthermore, by using appropriate values of parameters $k$ and ${r}_{s}$ have been calculated the average prescission neutron multiplicity, the fission probability, the mean fission time, and the anisotropy of fission fragments angular distribution for the nuclei $^{210}\mathrm{Rn}$ and $^{215}\mathrm{Fr}$. Comparison of the theoretical data with the experimental data were shown that the modified statistical model is well able to reproduce different experimental data. Although, at high excitation energies the results of calculations for the anisotropy of fission fragments angular distribution and fission probability are slightly lower than the experimental data.

Inference on fission timescale from neutron multiplicity measurement in 18O + 184W

The pre-scission and post-scission neutron multiplicities are measured for the 18O + 184W reaction in the excitation energy range of 67.23–76.37 MeV. Langevin dynamical calculations are performed to infer the energy dependence of fission decay time in compliance with the measured neutron multiplicities. Different models for nuclear dissipation are employed for this purpose. Fission process is usually expected to be faster at a higher beam energy. However, we found an enhancement in the average fission time as the incident beam energy increases. It happens because a higher excitation energy helps more neutrons to evaporate that eventually stabilizes the system against fission. The competition between fission and neutron evaporation delicately depends on the available excitation energy and it is explained here with the help of the partial fission yields contributed by the different isotopes of the primary compound nucleus.

Measurement of fission excitation function for 19F + 194, 196, 198Pt reactions

Experimental fission cross-sections are reported for the 19F + 194,196,198Pt reactions populating an isotopic chain of compound nuclei comprising both closed and non-closed shell nuclei. The fission cross-sections are obtained at near and above Coulomb barrier energies by measuring fission fragment angular distributions. The present work aims to estimate nuclear dissipation and find its isotopic and shell closure dependence from statistical model (SM) analysis of experimental data. Pre-scission neutron multiplicity data for the same systems is also included in the SM analysis. An updated version of SM is used in the present analysis, which includes shell corrections in level density and fission barrier as well as the effect of collective enhancement of level density and orientation effect of the compound nucleus along the symmetry axis. An isotopic dependence of the dissipation strength fitting the fission excitation functions is observed. The pre-scission neutron multiplicity, however, is underestimated by the SM.

Probing entrance channel effects in fusion-fission dynamics through neutron multiplicity measurement of 208Rn

The pre- and post-scission neutron multiplicities are measured for the fission of 208Rn, populated with the reactions 30Si+178Hf and 48Ti+160Gd in the excitation energy range of 54.5 - 80.8 MeV. We found significant differences in the pre-scission neutron multiplicities of these two systems. Also, both the reactions exhibit an enhancement in the pre-scission multiplicity with respect to the existing data for the 16O+194Pt reaction populating 210Rn. The measured multiplicities are compared with the theoretical predictions obtained from the Langevin dynamical model for fission. Dynamical simulations are also performed to estimate the capture cross-sections. Contribution of the neutrons, emitted during the fusion process, is shown to be crucial in determining the neutron multiplicities for the present systems. Moreover, in case of the 48Ti+160Gd reaction, rapid quasi-fission dynamics prevents neutron emission from the thermalized target-projectile composite. The present measurement helps us to understand the relative importance of fusion and quasi-fission processes and their timescales depending on the entrance channel mass asymmetry.

Pre-scission neutron multiplicity in the S32+W184 reaction

The neutron energy spectra in coincidence with both the correlated fission fragments in $^{32}\mathrm{S}+^{184}\mathrm{W}$ reaction forming the compound nucleus $^{216}\mathrm{Th}$ at an excitation energy of 71.31 MeV have been measured at various angles with respect to one of the fission fragments. Pre- and post-scission neutron multiplicities of $2.68\ifmmode\pm\else\textpm\fi{}0.48$ and $3.3\ifmmode\pm\else\textpm\fi{}0.20,$ respectively, have been extracted by analyzing angular correlation of the neutron energy spectra using moving source fitting procedure. The excess pre-scission neutron multiplicity in comparison to statistical model joanne2 code predictions have been converted into total fission delay. A comparative study of fission delay has been carried out for the $^{16}\mathrm{O}+^{208}\mathrm{Pb}$ reaction forming the compound nucleus $^{224}\mathrm{Th}$ at similar excitation energy as in $^{32}\mathrm{S}+^{184}\mathrm{W}$ reaction. Both the reactions have been analyzed within the frame work of joanne2 code including fission delay, deformation dependent level densities, particle binding energies, and transmission coefficients. The observed fission delay for both the reactions can be quantitatively understood if different formation time predicted by dynamical model hicol code are considered.

Evaporation and fission decay of Er158 composite nuclei within the statistical model

Light charged particles emitted by the compound nucleus $^{158}\mathrm{Er}$ produced in the reaction $^{32}\mathrm{S}$ $(180 \mathrm{MeV})+^{126}\mathrm{Te}$, at the excitation energy ${E}_{x}=92$ MeV, have been measured at Laboratori Nazionali di Legnaro in coincidence with fission fragments and evaporation residues. The $4\ensuremath{\pi}$ detector array $8\ensuremath{\pi}\mathrm{LP}$ coupled to a system of parallel-plate avalanche counters to detect evaporation residues has been used. Data have been analyzed in the framework of the statistical model of evaporation with the code pace2_n11. This enlarged version of the code pace2 has been used to reproduce the large set of observables measured in the fusion-evaporation and fusion-fission channels along with experimental prescission neutron multiplicity and fission cross section taken from literature. It is found that the simultaneous reproduction of the prescission neutron, proton, and $\ensuremath{\alpha}$-particle multiplicities can be obtained with zero fission delay without dynamical effects. However, the same set of model input parameters does not allow us to reproduce proton and $\ensuremath{\alpha}$-particle multiplicities in the evaporation channel. Extensive calculations, with different sets of parameters, show the limits of the statistical model in reproducing the whole set of data. This work evidences the importance of measuring a large set of observables in order to obtain a reliable description of the decay of the compound nucleus, and in particular of the fission process.

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.

Effects of isospin and dissipation coefficient of the K coordinate in simulation of fission dynamics of excited compound nuclei

A stochastic approach based on four-dimensional (4D) dynamical model has been used to simulate the fission process of the excited compound nuclei [Formula: see text]Fr, [Formula: see text]Fr and [Formula: see text]Fr produced in fusion reactions. Effects of isospin and dissipation coefficient of the [Formula: see text] coordinate, [Formula: see text], on estimation of the evaporation residue (ER) cross-section, the prescission neutron multiplicity, the variance of the mass and energy distributions of fission fragments and the anisotropy of fission fragments angular distribution have been investigated for the excited compound nuclei [Formula: see text]Fr, [Formula: see text]Fr and [Formula: see text]Fr. Three collective shape coordinates [Formula: see text] plus the projection of total spin of the compound nucleus to the symmetry axis, [Formula: see text], were considered in the 4D dynamical model. In the 4D dynamical model, the magnitude of the dissipation coefficient of [Formula: see text], [Formula: see text], was considered as a free parameter and its magnitude inferred by fitting measured data on the ER cross-section. Results of the extracted dissipation coefficients of [Formula: see text] for different isotopes of Fr were shown that the magnitude of the dissipation coefficient of [Formula: see text] increases with decreasing isospin of fissioning compound nucleus. It was also shown that the prescission neutron multiplicity and the anisotropy of fission fragments angular distribution increase with increasing isospin whereas the variance of the mass and energy distributions of fission fragments decrease with increasing isospin of fissioning compound nucleus. Furthermore, it was shown that the calculated values of prescission neutron multiplicity and the variance of the mass distribution of fission fragments for the excited compound nuclei [Formula: see text]Fr, [Formula: see text]Fr and [Formula: see text]Fr decrease with the dissipation strength of [Formula: see text], whereas the variance of the energy distribution of fission fragments and the anisotropy of fission fragments angular distribution increase with the dissipation strength of [Formula: see text].

Mass-split dependence of pre-scission neutron multiplicity by four-dimensional Langevin dynamics in 16,18O, 40Ar and 64Ni-induced fusion–fission reactions

By using the multidimensional Langevin model, including elongation, neck thickness, asymmetry parameter and orientation degree of freedom, the fission dynamics of some [Formula: see text]O-, [Formula: see text]Ar- and [Formula: see text]Ni-induced fusion–fission reactions were investigated. We calculated mean pre-scission neutron kinetic energy, pre-scission neutron multiplicity and fission time. Mass-split dependence of pre-scission neutron multiplicity and sensitivity of multiplicity on different value of the level density parameter for fission and neutron emission of highly excited compound nuclei were studied. One can conclude reasonable agreement between theory and tentative results for different reactions.

Nuclear dissipation at high excitation energy and angular momenta in reaction forming Np227

Neutron multiplicity excitation function has been measured for the $^{30}\mathrm{Si}+^{197}\mathrm{Au}$ reaction populating the $^{227}\mathrm{Np}$ compound nucleus at excitation energies in the range 44.1--78.8 MeV using the National Array of Neutron Detector facility of Inter University Accelerator Centre, New Delhi. Measured pre-scission neutron multiplicity values are analyzed using a statistical model incorporating Krammer's fission width due to the dissipative drag in nuclear fission, shell corrections in fission barrier and level density, collective enhancement of level density, and $K$-orientation effect. The present work demonstrates that a strong fission hindrance is essential to reproduce the experimental pre-scission neutrons, whereas the temperature dependent dissipation coefficient as observed in a few recent measurements is not required to reproduce the experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ data. No substantial effect of collective enhancement of nuclear level density and tilting away effect of compound nucleus spin on neutron emission prior to the scission configuration was observed unlike fission of preactinides.

Detailed statistical model analysis of observables from fusion-fission reactions

This work attempts to overcome the existing inconsistencies in modelling decay of fissile nucleus by inclusion of important physical effects in the model and through a systematic analysis of a large set of data over a wide range of CN mass (ACN). The model includes shell effect in the level density (LD) parameter, shell correction in the fission barrier, effect of the orientation degree of freedom of the CN spin (Kor), collective enhancement of level density (CELD) and dissipation in fission. Input parameters are not tuned to reproduce observables from specific reaction(s) and the reduced dissipation coefficient is treated as the only adjustable parameter. Calculated evaporation residue (ER) cross sections, fission cross sections and particle, i.e. neutron, proton and alpha-particle, multiplicities are compared with data covering ACN = 156-248. The model produces reasonable fits to ER and fission excitation functions for all the reactions considered in this work. Pre-scission neutron multiplicities are underestimated by the calculation beyond ACN~200. An increasingly higher value of pre-saddle dissipation strength is required to reproduce the data with increasing ACN. Proton and alpha-particle multiplicities, measured in coincidence with both ERs and fission fragments, are in qualitative agreement with model predictions. The present work mitigates the existing inconsistencies in modelling statistical decay of the fissile CN to a large extent.

Study of mass yield and kinetic energy distribution of fission fragments from fission of the excited compound nucleus 254Fm produced in fusion reaction

A stochastic approach based on four-dimensional Langevin fission dynamics has been used to calculate the anisotropy of fission fragment angular distribution, the mass and energy distribution of fission fragments, the yield and variance of the mass distribution of fission fragments, the fission cross section and the pre-scission neutron multiplicity for the compound nucleus 254Fm produced in the reaction 16O + 238U. In the dynamical calculations dissipation coefficient of K , \( \gamma_k\) , was considered as a free parameter and its magnitude inferred by fitting measured data on the anisotropy of fission fragments angular distribution. It was shown that the results of the anisotropy of fission fragments angular distribution for the compound nucleus 254Fm are in good agreement with the experimental data by using values of dissipation coefficient of K, equal to \(\gamma_{k}=(0.076-0.088)\) (MeV zs)-1/2. We also calculated the above-mentioned experimental data for the compound nucleus 254Fm by using \(\gamma_{k}=(0.076-0.088)\) (MeV zs)-1/2 and results of the calculations compared with the experimental data. A comparison of the theoretical results with the experimental data showed that the results of calculations are in good agreement with the experimental data, although at high energy the difference between the results of calculations with the experimental data for the variance of the mass distribution of fission fragments and the pre-scission neutron multiplicity is slightly high. It was also shown that at high energy the variance of the mass distribution of fission fragments and the pre-scission neutron multiplicity can be reproduced for the compound nucleus 254Fm by using values of dissipation coefficient of K equal to \(\gamma_{k}=0.098\) (MeV zs)-1/2 and \(\gamma_{k}=0.065\) (MeV zs)-1/2, respectively.

Measurement of mass-gated neutron multiplicity for the Ti48+Pb208 reaction at 57.4 MeV excitation energy

The neutron emission in coincidence with the fragments have been investigated for the $^{48}\mathrm{Ti}+^{208}\mathrm{Pb}$ reaction populating the near superheavy compound nucleus $^{256}\mathrm{Rf}$ at an excitation energy of 57.4 MeV. The National Array of Neutron Detectors facility is used for a precise determination of the prescission (${M}_{n}^{\mathrm{pre}}$) and postscission (${M}_{n}^{\mathrm{post}}$) neutron multiplicities as a function of fission observables. A moving source fitting procedure has been adopted to deduce ${M}_{n}^{\mathrm{pre}}$ and ${M}_{n}^{\mathrm{post}}$. The variation of ${M}_{n}^{\mathrm{pre}}$ with the mass-split and total kinetic energy (TKE) of the fission fragments have been studied to understand the fission dynamics of $^{256}\mathrm{Rf}$. It is observed that ${M}_{n}^{\mathrm{pre}}$ increases from the value of 1.66 $\ifmmode\pm\else\textpm\fi{}$ 0.07 to 2.23 $\ifmmode\pm\else\textpm\fi{}$ 0.07 with transition from the asymmetric to the symmetric mass region. ${M}_{n}^{\mathrm{pre}}$ is also found to increase with the decrease in TKE, which is probably due to the neutron emission during the acceleration time of the fission fragments in this heavy system. The experimental results for neutron multiplicity have also been compared with the theoretical predictions from the statistical model calculations. From this comparison, the value of reduced dissipation strength for the $^{256}\mathrm{Rf}$ nucleus is found to be (13.0 $\ifmmode\pm\else\textpm\fi{}$ 1.0) $\ifmmode\times\else\texttimes\fi{} {10}^{21} {\mathrm{s}}^{\ensuremath{-}1}$ and a fission delay time of (${67.3}_{\ensuremath{-}3.9}^{+5.3}$) $\ifmmode\times\else\texttimes\fi{} {10}^{\ensuremath{-}21}$ s has also been estimated. For the spontaneous fission of $^{256}\mathrm{Rf}$, the extracted average neutron multiplicity ${M}_{n}^{sf}$ is found to be 4.4 $\ifmmode\pm\else\textpm\fi{}$ 1.0 which is in good agreement with the recently reported value for the $^{258,260}\mathrm{Rf}$ isotopes.

Dynamical study of fission process at low excitation energies in the framework of the four-dimensional Langevin equations

A stochastic approach based on four-dimensional Langevin equations has been used to estimate the fission probability, the mean kinetic energy of fission fragments, the mean prompt neutron multiplicity, the average pre-scission neutron multiplicity and the mass distribution of fission fragments for the compound nucleus 238Np produced in neutron induced reaction at low excitation energy. 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, dissipation was generated through the chaos weighted wall and window friction formula and dissipation coefficient of K, γK, considered as a non-constant parameter. Comparison of the theoretical results with the above mentioned experimental data showed that different features of fission of the excited compound uncles 238Np at low excitation energy can be satisfactorily reproduced by the four dimensional Langevin equations.

Influence of the asymmetry parameter and dissipation coefficient of the K coordinate on different aspects of fission of excited compound nuclei

The dynamics of fission of the excited compound nuclei $^{256}\mathrm{Fm}, ^{215}\mathrm{Fr}, ^{187}\mathrm{Ir}, ^{172}\mathrm{Yb}, ^{162}\mathrm{Yb}$, and $^{142}\mathrm{Ce}$ produced in fusion reactions with 158.8 MeV $^{18}\mathrm{O}$ has been studied by solving three- and four-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The constant dissipation coefficients of $K, {\ensuremath{\gamma}}_{K}=0.077\phantom{\rule{0.28em}{0ex}}{(\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}\mathrm{zs})}^{\ensuremath{-}1/2}, {\ensuremath{\gamma}}_{K}=0.2\phantom{\rule{0.16em}{0ex}}{(\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}\mathrm{zs})}^{\ensuremath{-}1/2}$ and a nonconstant dissipation coefficient of $K$ have been used to reproduce the experimental data for both symmetric and asymmetric splitting of the fissioning systems. The average kinetic energies of fission fragments, the pre-scission neutron multiplicities, the fission time, and the variances of the mass and kinetic energy of fission fragments are calculated for the excited compound nuclei $^{256}\mathrm{Fm}, ^{215}\mathrm{Fr}, ^{187}\mathrm{Ir}, ^{172}\mathrm{Yb}, ^{162}\mathrm{Yb}, ^{142}\mathrm{Ce}$, and results of the calculations are compared with each other and with the experimental data. Comparison of the theoretical results with the experimental data calculated by using different values of ${\ensuremath{\gamma}}_{K}$ shows that the difference is small between the results of calculations for symmetric and asymmetric simulations of the fission process of excited intermediate nuclei, whereas for heavy compound nuclei the difference is slightly high. In other words, the effect of the asymmetry parameter on the fission process of intermediate nuclei is smaller than the effect on heavy nuclei. Furthermore, we show that the pre-scission neutron multiplicity decreases rapidly with increasing fragment asymmetry.

Statistical and dynamical modeling of heavy-ion fusion–fission reactions

A modified statistical model and a four dimensional dynamical model based on Langevin equations have been used to simulate the fission process of the excited compound nuclei 207At and 216Ra produced in the fusion 19F + 188Os and 19F + 197Au reactions. The evaporation residue cross section, the fission cross section, the pre-scission neutron, proton and alpha multiplicities and the anisotropy of fission fragments angular distribution have been calculated for the excited compound nuclei 207At and 216Ra. In the modified statistical model the effects of spin K about the symmetry axis and temperature have been considered in calculations of the fission widths and the potential energy surfaces. It was shown that the modified statistical model can reproduce the above mentioned experimental data by using appropriate values of the temperature coefficient of the effective potential equal to λ=0.0180±0.0055, 0.0080±0.0030 MeV−2 and the scaling factor of the fission barrier height equal to rs=1.0015±0.0025, 1.0040±0.0020 for the compound nuclei 207At and 216Ra, respectively. Three collective shape coordinates plus the projection of total spin of the compound nucleus on the symmetry axis, K, were considered in the four dimensional dynamical model. In the dynamical calculations, dissipation was generated through the chaos weighted wall and window friction formula. Comparison of the theoretical results with the experimental data showed that two models make it possible to reproduce satisfactorily the above mentioned experimental data for the excited compound nuclei 207At and 216Ra.