Fission Fragment Mass Energy Distributions Research Articles

Fission of Hg*180,182,183 and Pt*178 nuclei at intermediate excitation energies

Background: The nature of asymmetric fission of preactinides is not yet understood in detail, despite intense experimental and theoretical studies carried out at present.Purpose: The study of asymmetric and symmetric fission of $^{180,182,183}\mathrm{Hg}$ and $^{178}\mathrm{Pt}$ nuclei as a function of their excitation energy and isospin.Methods: Mass-energy distributions of fission fragments of $^{180}\mathrm{Hg}, ^{178}\mathrm{Pt}$ (two protons less than $^{180}\mathrm{Hg}$), and $^{182}\mathrm{Hg}$ (two neutrons more than $^{180}\mathrm{Hg}$) formed in the $^{36}\mathrm{Ar}+^{144}\mathrm{Sm}, ^{142}\mathrm{Nd}$, and $^{40}\mathrm{Ca}+^{142}\mathrm{Nd}$ reactions were measured at energies near and above the Coulomb barrier. Fission of $^{183}\mathrm{Hg}$ obtained in the reaction of $^{40}\mathrm{Ca}$ with $^{143}\mathrm{Nd}$ was also investigated to see if one extra neutron could lead to dramatic changes in the fission process due to the shape-staggering effect in radii, known in $^{183}\mathrm{Hg}$.The measurements were performed with the double-arm time-of-flight spectrometer CORSET.Results: The observed peculiarities in the fission fragment mass-energy distributions for all studied nuclei may be explained by the presence of a symmetric fission mode and three asymmetric fission modes, manifested by the different total kinetic energies and fragment mass splits. The yield of symmetric mode grows with increasing excitation energy of compound nucleus.Conclusions: The investigated properties of asymmetric fission of $^{180,182,183}\mathrm{Hg}$ and $^{178}\mathrm{Pt}$ nuclei point out the existence of well-deformed proton shell at $Z\ensuremath{\approx}36$ and a less deformed proton shell at $Z$ \ensuremath{\approx} 46.

Description of the mass-asymmetric fission of the Pt isotopes, obtained in the reaction Ar36+Nd142 within the two-stage fusion-fission model

The two stages dynamical stochastic model developed earlier for description of fusion-fission reactions is applied to the calculation of mass- and energy-distributions of fission fragments of platinum isotopes in reaction ${\rm ^{36}Ar + ^{142}Nd \to ^{178-x}Pt + xn}$. The first stage of this model is the calculation of the approaching of projectile nucleus to the target nucleus. On the second stage of the model, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by three-dimensional Langevin equations for the shape parameters of the system. The mutual orientation of the colliding ions and tunneling through the Coulomb barrier in the entrance channel are also taken into account. The potential energy of the system is calculated within the macroscopic-microscopic approach. The calculated mass-energy distributions of fission fragments are compared with the available experimental data. The impact of shell effects, rotation of the system and neutron evaporation on the calculated results is discussed.

Analysis of the total kinetic energy of fission fragments with the Langevin equation

We analyzed the total kinetic energy (TKE) of fission fragments with three-dimensional Langevin calculations for a series of actinides and Fm isotopes at various excitation energies. This allowed us to establish systematic trends of TKE with $Z^2/A^{1/3}$ of the fissioning system and as a function of excitation energy. In the mass-energy distributions of fission fragments we see the contributions from the standard, super-long, and super-short (in the case of $^{258}$Fm) fission modes. For the fission fragments mass distribution of $^{258}$Fm we obtained a single peak mass distribution. The decomposition of TKE into the prescission kinetic energy and Coulomb repulsion showed that decrease of TKE with growing excitation energy is accompanied by a decrease of prescission kinetic energy. It was also found that transport coefficients (friction and inertia tensors) calculated by a microscopic model and by macroscopic models give drastically different behavior of TKE as a function of excitation energy. The results obtained with microscopic transport coefficients are much closer to experimental data than those calculated with macroscopic ones.

Fission dynamics of intermediate-fissility systems: A study within a stochastic three-dimensional approach

The system of intermediate fissility $^{132}\mathrm{Ce}$ has been studied experimentally and theoretically to investigate the dissipation properties of nuclear matter. Cross sections of fusion-fission and evaporation-residue channels together with light charged particle multiplicities in both channels, their spectra, light charged particle-evaporation residue angular correlations, and mass-energy distribution of fission fragments have been measured. Theoretical analysis has been performed using a multidimensional stochastic approach coupled with a Hauser-Feshbach treatment of particle evaporation. The main conclusions are that the full one-body shape-dependent dissipation mechanism allows the reproduction of the full set of experimental data and that after a time ${\ensuremath{\tau}}_{d}=5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ s from the equilibrium configuration of the compound nucleus, fission decay can occur in a time that can span several orders of magnitude.

Investigation of dissipation in the tilting degree of freedom from four-dimensional Langevin dynamics of heavy-ion-induced fission

A four-dimensional dynamical model based on Langevin equations was applied to calculate a wide set of experimental observables for heavy fissioning compound nuclei. Three collective shape coordinates plus the tilting coordinate were considered dynamically from the ground state deformation to the scission into fission fragments. A modified one-body mechanism for nuclear dissipation with a reduction coefficient ks of the contribution from a ‘wall’ formula was used for shapes parameters. Different possibilities of deformation-dependent dissipation coefficient for the tilting coordinate () were investigated. Presented results demonstrate that the influence of the ks and γK parameters on the calculated quantities can be selectively probed. The nuclear viscosity with respect to the nuclear shape parameters influences the , the fission fragment mass–energy distribution parameters, and the angular distribution of fission fragments. At the same time the viscosity coefficient γK affects the angular distribution of fission fragments only. The independence of anisotropy on the fission fragment mass is found at both Langevin calculations performed with deformation-dependent and constant γK coefficients.

Bimodal fission of Hs*

Mass and energy distributions of fission fragments obtained in the reactions 22Ne + 249Cf, 26Mg + 248Cm, and 22Ne + 238U have been measured. A special attention will be paid on the properties of mass-energy distribution of fission fragments obtained in the reaction 26Mg + 248Cm at an excitation energy of 35 MeV. At this energy shell effects should become more effective in fission, the TKE distribution of symmetric fragments obtained in the reaction 26Mg + 248Cm differs strongly from a Gaussian shape. Besides a low-energy component, a high-energy component, not foreseen in the LDM, arises. This is attributed to the fact that both fission fragments are close to the spherical neutron shell N = 82. It means that for the compound nucleus 274Hs*, formed in the reaction 26Mg + 248Cm, the phenomenon of bimodal fission was observed for the first time. For the compound nucleus 260No* formed in the reaction 22Ne + 238U at the initial excitation energy of 41 MeV the bimodal fission as well as superasymmetric fission were observed.

Influence of orientation degree of freedom on fission dynamics of higly excited nuclei

Four-dimensional dynamical model was developed and employed for study fission characteristics in a wide range of fissility parameter. The three collective shape coordinates plus the K coordinate, which is the spin of the nucleus with respect to the symmetry (fission) axis, were considered dynamically from the ground state deformation till the scission into fission fragments. A modified one-body mechanism for nuclear dissipation with a reduction coefficient ks of the contribution from a wall formula have been used in the study. The four-dimensional calculations for heavy nuclei could describe the fission fragment mass-energy distribution (MED) parameters and prescission neutron multiplicity with almost single ks value, in contrast with 3D dynamical calculations, where a consistent description of all observables with the same ks is not possible for heavy nuclei. The estimation of a dissipation coefficient for the orientation degree of freedom K = 0.077 (MeVzs) −1/2 is good for heavy nuclei and lower value of K = 0.05 (MeVzs) −1/2 is needed for nuclei with mass A � 200. The results of 4D and 3D Langevin dynamical calculations for light nuclei near the Businaro-Gallone point predict close results for the fission fragment MED parameters and prescission particles multiplicities.

Four-dimensional Langevin dynamics of heavy-ion-induced fission

A four-dimensional dynamical model based on Langevin equations was developed and applied to calculate a wide set of experimental observables for the reactions ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}\ensuremath{\rightarrow}{}^{224}\mathrm{Th}$ and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\ensuremath{\rightarrow}{}^{248}\mathrm{Cf}$ over a wide range of excitation energy. The fusion-fission and evaporation residue cross sections, fission fragment mass-energy distribution parameters, prescission neutron multiplicities, and anisotropy of angular distribution of fission fragments could be reasonably reproduced using a modified one-body mechanism for nuclear friction with a reduction coefficient of the contribution from a wall formula ${k}_{s}\ensuremath{\simeq}0.25$ and a dissipation coefficient for the orientation degree of freedom ($K$ coordinate) ${\ensuremath{\gamma}}_{K}\ensuremath{\simeq}$ 0.077 ${(\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}\mathrm{zs})}^{\ensuremath{-}1/2}$. Inclusion of the $K$ coordinate into calculation of potential energy changes the stiffness of the nucleus with respect to mass asymmetry coordinate for the values of $K\ensuremath{\ne}0$ and results in a shift of the Businaro-Gallone point towards larger ${Z}^{2}/A$ values. The experimental data on the fission fragment mass-energy distribution parameters together with mean prescission neutron multiplicity for heavy fissioning nuclei are reproduced through the four-dimensional Langevin calculations more accurately than through three-dimensional calculations.

Examination of isospin effects in multi-dimensional Langevin fission dynamics

One-dimensional and three-dimensional dynamical fission calculations based on Langevin equations are performed for the compound nuclei 194Pb, 200Pb, 206Pb, 182Hg, and 204Hg to investigate the influence of the compound nucleus isospin on the prescission particle multiplicities and on the fission fragment mass–energy distribution. It is found that the prescission neutron, proton, and alpha particle multiplicities have approximately the same sensitivity to the dissipation strength for a given nucleus. This is at variance with conclusions of recent papers. The sensitivity of the calculated prescission particle multiplicities to the dissipation strength becomes higher with decreasing isospin of fissioning compound nucleus, and the increase of prescission particle multiplicities could reach 200%, when the reduction coefficient of one-body viscosity ks increases from 0.1 to 1, for the most neutron deficient nuclei considered. The variances of fission fragment mass and kinetic energy distributions are less sensitive to the change of dissipation strength than the prescission light particle multiplicities. A comparison to experimental data concerning 200Pb nucleus is also presented.

Nuclear dissipation effects on fission and evaporation in systems of intermediate fissility

The systems of intermediate fissility 132 Ce and 158 Er have been studied experimentally and theo- retically in order to investigate the dissipation properti es of nuclear matter. Cross sections of fusion-fission and evaporation residues channels together with charged particles multiplicities in both channels, their spectra, an- gular correlations and mass-energy distribution of fission fragments have been measured. Theoretical analysis has been performed using multi-dimensional stochastic approach with realistic treatment of particle evaporation. The results of analysis show that full one-body or unusually strong two-body dissipation allows to reproduce experimental data. No temperature dependent dissipation was needed.

Investigation of the 208Pb(18O, f) fission reaction: Mass-energy distributions of fission fragments and their correlation with the gamma-ray multiplicity

The mass-energy distributions of fragments originating from the fission of the compound nucleus 226Th and their correlations with the multiplicity of gamma rays emitted from these fragments are measured and analyzed in 18O + 208Pb interaction induced by projectile oxygen ions of energy in the range E lab = 78–198.5 MeV. Manifestations of an asymmetric fission mode, which is damped exponentially with increasing E lab, are demonstrated. Theoretical calculations of fission valleys reveal that only two independent valleys, symmetric and asymmetric, exist in the vicinity of the scission point. The dependence of the multiplicity of gamma rays emitted from both fission fragments on their mass, Mγ(M), has a complicated structure and is highly sensitive to shell effects in both primary and final fragments. A two-component analysis of the dependence Mγ(M) shows that the asymmetric mode survives in fission only at low partial-wave orbital angular momenta of compound nuclei. It is found that, for all E lab, the gamma-ray multiplicity Mγ as a function of the total kinetic energy (TKE) of fragments, Mγ(TKE), decreases linearly with increasing TKE. An analysis of the energy balance in the fission process at the laboratory energy of E lab = 78 MeV revealed the region of cold fission of fragments whose total kinetic energy is TKE ∼Q max.

Analysis of angular momentum dependence of fission fragment mass-energy distribution within Langevin dynamics

Dependence of fission fragment mass-energy distribution on the angular momentum is studied within Langevin dynamics. The calculations are performed in the framework of the generalized temperature- dependent finite-range liquid drop model. The analysis is done for five compound nuclear systems representing heavy fissioning nuclei, medium fissioning nuclei, and a light fissioning one with the angular momentum varied in a wide range from l = 0 to 70 � . The coefficients d 〈 E K 〉 / dl 2 and are extracted. Previous analysis of the coefficient is generalized. Excitation energy dependence of the fission fragment mass-energy dis- tribution is also found. The qualitative comparison of the extracted values with the experimental data reveals good agreement for all the cases. The calculated values of the coefficients and are functions of the angular momentum, in contrast to the experimental estimations.

Fine Structures by Deformation in the Mass-Energy Distribution of Fission Fragments

It is shown within a seission point model that for a fixed mass and charge fragmentation the potential energy of the scission configuration has several minima as a function of the deformation parameters of the fragments. The scission at these minima leads to a relatively enhanced yield of the fragments with a certain TKE and creates fine structures in the TKE-mass distribution which are different from those produced by the odd-even effect.

Possible explanation of fine structures in mass-energy distribution of fission fragments

Within an improved scission point model, experimental data on the relative yield, mean value and variance of the total kinetic-energy distribution of fission fragments are described. It is shown that for a fixed mass and charge fragmentation, the potential energy of the scission configuration has several minima as a function of the deformation parameters of the fragments. The scission at these minima leads to a relatively enhanced yield of the fragments with a certain TKE and creates fine structures in the TKE-mass distribution which are different from those produced by the odd-even effect.

Fusion ofCa+Sm near the Coulomb barrier: enhancement vs. suppression

Fusion-evaporation and fusion-fission cross sections have been measured in the reaction 48 Ca+ 154 Sm from well below to well above the Coulomb barrier. The comparison of fusion cross sections for this reaction with previous data corresponding to 16 O+ 186 W, leading to the same compound nucleus 202 Pb * , puts in evidence an interesting competition between sub-barrier enhancement, due to the strong couplings related to the 154 Sm deformation, and above barrier suppression for the 48 Ca induced reaction. The fusion hindrance mechanism has been attributed to the strong quasi-fission component observed in the mass-energy distributions of fission fragments.

Fusion ofCa+Sm near the Coulomb barrier: enhancement vs. suppression

Fusion-evaporation and fusion-fission cross sections have been measured in the reaction 48 Ca+ 154 Sm from well below to well above the Coulomb barrier. The comparison of fusion cross sections for this reaction with previous data corresponding to 16 O+ 186 W, leading to the same compound nucleus 202 Pb * , puts in evidence an interesting competition between sub-barrier enhancement, due to the strong couplings related to the 154 Sm deformation, and above barrier suppression for the 48 Ca induced reaction. The fusion hindrance mechanism has been attributed to the strong quasi-fission component observed in the mass-energy distributions of fission fragments.

Fusion of 48Ca+ 154Sm near the Coulomb barrier: enhancement vs. suppression

Fusion-evaporation and fusion-fission cross sections have been measured in the reaction 48Ca+ 154Sm from well below to well above the Coulomb barrier. The comparison of fusion cross sections for this reaction with previous data corresponding to 16O+ 186W, leading to the same compound nucleus 202Pb *, puts in evidence an interesting competition between sub-barrier enhancement, due to the strong couplings related to the 154Sm deformation, and above barrier suppression for the 48Ca induced reaction. The fusion hindrance mechanism has been attributed to the strong quasi-fission component observed in the mass-energy distributions of fission fragments.

Fusion Hindrance and Quasi-Fission in48Ca Induced Reactions

Fusion-fission and fusion-evaporation cross sections have been measured in a large energy range for the 4 8 Ca+ 1 6 8 Er, 1 5 4 Sm reactions. The comparison of the reduced evaporation data for such reactions and for collisions induced by light projectiles leading to the same compound nuclei 2 1 6 Ra* and 2 0 2 Pb* puts in evidence a fusion hindrance, which is particularly large for the first composite system. This fusion suppression is consistent with a noticeable contribution coming from quasi-fission events observed in the mass-energy distribution of fission fragments. The asymmetric shape of the quasi-fission component has been explained in terms of shell effects in the exit channel, favouring the population of closed shell fission fragments. The comparison of 4 8 Ca+ 1 5 4 Sm with preliminary data on 4 8 Ca+ 1 4 4 Sm seems to suggest that the target deformation plays a role in the onset of the quasi-fission mechanism.

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".

Probabilistic scission of a fissile nucleus into fragments

A probabilistic criterion is proposed for the scission of a fissile nucleus into fragments. The probability of the rupture of the neck between would-be fragments is estimated by considering scission as a fluctuation. The energy of the prescission configuration and the energy of the separated-fragment configuration are computed on the basis of a macroscopic model that takes into account a finite range of nuclear forces and the diffuseness of the nuclear surface. The effect of the probabilistic criterion of nuclear scission on fission-process observables, such as the moments of the mass-energy distribution of fission fragments, the mean multiplicity of prescission neutrons, and mean fission times, is demonstrated. It is shown that the Strutinsky criterion, according to which nuclear scission occurs at a finite neck radius of 0.3R0, is a rather good approximation to the probabilistic scission criterion in Langevin dynamical calculations employing the one-body nuclear-viscosity mechanism modified in such a way that the wall-formula contribution is reduced, the reduction factor satisfying the condition ks<05.