Fusion-fission Reactions Research Articles

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.

Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions

Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time-scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. In the regime $T>1$ MeV, Kramers' theory should be replaced by a new theory based on the Ornstein-Uhlenbeck first-passage time method that is proposed here. The theory is applied to fission time data from fusion-fission experiments on $^{16}$O+$^{208}$Pb $\rightarrow$ $^{224}$Th. The proposed model provides an internally consistent one-parameter fitting of fission data with a constant nuclear friction as the fitting parameter, whereas Kramers' fitting requires a value of friction which falls out of the allowed range. The theory provides also an analytical formula that in future work can be easily implemented in numerical codes such as CASCADE or JOANNE4.

Quest for consistent modelling of statistical decay of the compound nucleus

A statistical model description of heavy ion induced fusion–fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhancement for evaporation residue cross-sections.

Prompt-delayed $\gamma$ γ -ray spectroscopy with AGATA, EXOGAM and VAMOS++

A new experimental setup to measure prompt-delayed $\gamma$ -ray coincidences from isotopically identified fission fragments, over a wide time range of 100ns-200μ s, is presented. The fission fragments were isotopically identified, on an event-by-event basis, using the VAMOS++ large acceptance spectrometer. The prompt $\gamma$ rays emitted at the target position and corresponding delayed $ \gamma$ rays emitted at the focal plane of the spectrometer were detected using, respectively, thirty two crystals of the AGATA $\gamma$ -ray tracking array and seven EXOGAM HPGe Clover detectors. Fission fragments produced in fusion and transfer-induced fission reactions, using a 238U beam at an energy of 6.2 MeV/u impinging on a 9Be target, were used to characterize and qualify the performance of the detection system.

Fission-fragment mass yields of highly excited nuclei with 119 ≤ A ≤ 218 produced in various reactions

The characteristics of fission fragments of various highly-excited nuclei with 119≤A≤218, which are formed by γ- and α-captures, and by fusion–fission reactions, are discussed in details. The yields of fission fragments of these nuclei are related to the number of states of the two-fragment systems at the two-body saddle points. The various experimental distributions of fission fragments are well described in the model.

Dissipative effects in fission investigated in complete kinematics measurements

The study of dissipative effects in fission has been carried out with fusion-fission reactions by using a limited number of observables, such as the fission probabilities, the mass distribution of the fission fragments, or the neutron multiplicities. However, the large angular momenta gained by the compound nucleus in this kind of reaction could affect the conclusions drawn from such experiments. In this work, we propose to investigate the fission dynamics by the use of spallation reactions on 208Pb because the fissioning systems are produced with low angular momentum, small deformations, and high excitation energies, enhancing the dissipative effects. The complete kinematics measurements of the fission fragments and light-charged particles were performed by the use of the SOFIA setup combined with the inverse kinematics technique, allowing us for the first time a full indentification in atomic and mass number of the two fission fragments. These measurements permit us to define new fission observables for the investigation of the temperature and deformation dependencies of the dissipation parameter.

Allowance for the tunnel effect in the entrance channel of fusion–fission reactions

A two-stage model is developed in order to describe fusion–fission reactions. The process in the course of which colliding ions approach each other is simulated at the first stage, the deformations and relative orientations of the ions being taken into account. The first stage of the calculation is completed as soon as colliding nuclei touch each other. A continuous nuclear system (monosystem) is formed at this instant. The emerging distributions of the angular momenta of this system and of its potential and internal energies at the point of touching are used as input data that are necessary for triggering the second stage of the calculation. The evolution of collective coordinates that describe the shape of the monosystem is calculated at the second stage. The description of this evolution is terminated either at the instant of its fission or upon the release of a major part of its excess energy via particle and photon emission. In the latter case, the probability for the fission of the monosystem or a further decrease in its excitation energy becomes extremely small. The ion-collision process and the evolution of the monosystem formed after primary nuclei come into contact are simulated on the basis of stochastic Langevin equations. The quantities appearing in them (which include the potential energy and inertial and friction parameters) are determined with allowance for the shell structure of nuclei. The tunneling of colliding nuclei through the Coulomb barrier is taken into account, and the effect of this phenomenon on model predictions is studied.

Dissipation strength of the tilting degree of freedom in fusion-fission reactions

The four-dimensional Langevin model was applied to calculate a wide set of experimental observables for compound nuclei, formed in heavy-ion fusion-fission reactions. 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 K coordinate (γK) were investigated. Presented results demonstrate that the influence of the ks and γK parameters on the calculated quantities can be selectively probed. It was found that it is possible to describe experimental data with the deformation-dependent γK coefficient. One of the possibility is to use large values of γK � 0.2 (MeV zs) −1/2 for compact shapes featuring no neck and small values of γK � 0.0077 (MeV zs) −1/2 for elongated shapes. Fission still is one of the most interesting and challenging topics in nuclear physics providing a perfect opportunity to investigate the large scale evolution of initial compound nucleus into fission products. During the past two decades stochastic approach based on multidimensional Langevin equations has been extensively and rather successfully used to elucidate many problems of collective nuclear dynamics in fusion-fission reactions at high excitation energies [1, 2]. A reasonable choice of collective degrees of freedom for modeling shape evolution and considering particle evaporation allow modeling the complex interplay between static and dynamical effects in fission and succeeding in explaining a wide range of experimental data [3, 4].

Description of the Fusion-Fission Reactions in the Framework of Dinuclear System Conception

Within the dinuclear system model fusion-fission reactions 78Kr+40Ca and 86Kr+48Ca is investigated. The charge distributions of the decay products are predicted at bombarding energy 10 MeV/nucleon. The competition is treated between complete fusion followed by the decay of compound nucleus and quasifission channels. The possible explanation of the odd-even staggering in the yield of the final reaction products at high excitation energies is discussed.

Dissipative effects in fission investigated with proton-on-lead reactions

The complete kinematic measurement of the two fission fragments permitted us to investigate dissipative effects at large deformations, between the saddle-point and the corresponding scission configurations. Up to now, this kind of study has only been performed with fusionfission reactions using a limited number of observables, such as the mass distribution of the fission fragments or the neutron multiplicities. However, the large angular momenta gained by the compound nucleus could affect the conclusions drawn from such experiments. In this work, the use of spallation reactions, where the fissioning systems are produced with low angular momentum, small deformations and high excitation energies, favors the study of dissipation, and allowed us to define new observables, such as postscission neutron multiplicities and the neutron excess of the final fission fragments as a function of the atomic number of the fissioning system. These new observables are used to investigate the dissipation at large deformations.

Lifetime Measurments of Excited States in Neutron-rich Fission Fragments

Lifetimes of short-lived excited states in a wide range of neutron-rich fission fragments were measured using the recoil distance Doppler shift (RDDS) technique, which was applied to fusion-fission reactions in inverse kinematics for the first time. The fission fragments were identified eventby- event in mass, charge, and atomic number using the VAMOS magnetic spectrometer at GANIL. Gamma rays originating from the fission fragments were measured with the EXOGAM array of Ge Clover detectors around the target position. Using a degrader, the change in the Doppler shift of the $\gamma$ ray allows the application of the RDDS method. Details of the experimental technique will be discussed and the status for the ongoing analysis for odd-mass yttrium isotopes will be presented.

Detector instrumentation for nuclear fission studies

The study of heavy-ion-induced fusion–fission reactions require nuclear instrumentation that include particle detectors such as proportional counters, ionization chambers, silicon detectors, scintillation detectors, etc., and the front-end electronics for these detectors. Using the detectors mentioned above, experimental facilities have been developed for carrying out fusion–fission experiments. This paper reviews the development of detector instrumentation at IUAC.

Dynamics of neutron-induced fission ofU235using four-dimensional Langevin equations

Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and $\ensuremath{\gamma}$-ray emission.Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and $\ensuremath{\gamma}$-ray multiplicity for $^{236}\mathrm{U}$ as compound nuclei that are constructed after fusion of a neutron and $^{235}\mathrm{U}$.Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to ``funny hills'' parametrization.Results: Fission fragment mass distribution, neutron and $\ensuremath{\gamma}$-ray multiplicity, and the average kinetic energy of emitted neutrons and $\ensuremath{\gamma}$ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations.Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

The transport coefficient of collective motion within the two-center shell model shape parameterization

The transport coefficients of large-scale nuclear collective motion (potential energy, tensors of friction and mass) used in the description of fission process or fusion–fission reactions with the help of Langevin equations are calculated within the two-center shell-model shape parameterization. The transport coefficients are defined both in the macroscopic (wall formula for friction and Werner–Wheeler approximation for the mass tensor) and microscopic (linear response theory and local harmonic approximation) approaches. It is shown that at low excitation energy, the macroscopic and microscopic quantities differ substantially in dependence both on deformation and temperature. Thus, the microscopic effect in transport coefficients should be taken in account by the description of low-energy nuclear collisions and fission process.

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

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

Dynamical features of nuclear fission

It is now established that the transition-state theory of nuclear fission due to Bohr and Wheeler underestimates several observables in heavy-ion-induced fusion–fission reactions. Dissipative dynamical models employing either the Langevin equation or equivalently the Fokker–Planck equation have been developed for fission of heavy nuclei at high excitations (T∼1 MeV or higher). Here, we first present the physical picture underlying the dissipative fission dynamics. We mainly concentrate upon the Kramers’ prescription for including dissipation in fission dynamics. We discuss, in some detail, the results of a statistical model analysis of the pre-scission neutron multiplicity data from the reactions 19F+194,196,198Pt using Kramers’ fission width. We also discuss the multidimensional Langevin equation in the context of kinetic energy and mass distribution of the fission fragments.

GALS – setup for production and study of heavy neutron rich nuclei

The present limits of the upper part of the nuclear map are very close to stability while the unexplored area of heavy neutron-rich nuclides along the neutron closed shell N = 126 below 208 Pb is extremely important for nuclear astrophysics investigations and, in particular, for the understanding of the r-process of astrophysical nucleosynthesis. This area of the nuclear map can be reached neither in fusion–fission reactions nor in fragmentation processes widely used nowadays for the production of exotic nuclei. A new way was recently proposed for the production of these nuclei via low-energy multi-nucleon transfer reactions. The estimated yields of neutron-rich nuclei are found to be significantly high in such reactions and several tens of new nuclides can be produced, for example, in the near-barrier collision of 136 Xe with 208 Pb. A new setup is proposed to produce and study heavy neutron-rich nuclei located along the neutron closed shell N =126.

Analysis of Experimental Data from Fusion-fission Reactions Within Four-dimensional Langevin Dynamics

Analysis of Experimental Data from Fusion-fission Reactions Within Four-dimensional Langevin Dynamics

Effect of shell structure on neutron multiplicity of fissioning systems220,222,224Th nuclei

The pre- and post-scission neutron multiplicities have been extracted for the 220,222,224Th nuclei for the excitation energy range of 40 MeV to 64 MeV using the National Array of Neutron Detectors (NAND). The Th isotopes are populated from the fusion reaction of 16O+204,206,208Pb systems in order to investigate the dynamics of fusion-fission reactions using the neutron multiplicity as a probe. The theoretical calculations were performed using the Bohr-Wheeler fission width as well as the dissipative dynamical fission width from Kramers prescription. It is observed that the Bohr-Wheeler fission width underestimates the pre-scission yields to a large extent. A large amount of dissipation is required in the Kramers width to fit the observed pre-scission neutron multiplicities.

Statistical model calculations of pre-scission neutron multiplicity for the heavy ion induced fusion-fission reactions with actinide target232Th

The reaction mechanism of 19F + 232Th and 28Si + 232Th systems populating the near-super-heavy compound nuclei 251Es and 260Rf respectively are investigated using neutron multiplicity as a probe. The prescission neutron multiplicities of these compound nuclei are calculated at different excitation energies using a statistical model code. These calculations are performed using the Bohr-Wheeler transition state fission width as well as the dissipative dynamical fission width based on the Kramers’ prescription. For 19F + 232Th system, the measured yield of pre-scission is compared with the statistical model calculations for the decay of a compound nucleus in the excitation energy range of 54-90 MeV. The comparison between the measured and the calculated values indicates that the Bohr-Wheeler fission width underestimates the pre-scission neutron yield and a large amount of dissipation strength is required to reproduce the experimental pre-scission neutron multiplicities. The excitation energy dependence of the fitted values of the dissipation coefficient is also discussed. In addition, exploratory statistical model calculations of pre-scission neutron multiplicity for the 28Si + 232Th system are presented in the above range of excitation energy.