Fusion-fission Reactions Research Articles

Impact of nuclear structure of correlated pairs of fission fragments in mass distribution spectra of heavy-ion fusion–fission reactions

Impact of nuclear structure of correlated pairs of fission fragments in mass distribution spectra of heavy-ion fusion–fission reactions

Well-dressed repulsive-core solitons and nonlinear optics of nuclear reactions

We introduce the concept of nonlinear optics of nuclear reactions and reveal a deep analogy between nonlinear dynamics of the so-called “well-dressed repulsive-core” solitons and the nuclear reactions that take place among atomic nuclei. We derive a nonlinear evolution equation for the Fermi nuclear density and the Woods–Saxon potential based on the inverse problem in the diffraction and dispersion scattering. We obtain a simple formula for the self-interaction (binding) energy, which provides the shape and structural stability of “soliton-like nucleus” with the Fermi density distribution. We find the shape squareness parameter (edge steepness) for “soliton-like nucleus” density distribution and demonstrate its specific quantization related to the conservation of the total number of nucleons. The shape squareness parameter plays a decisive role in increasing the binding soliton energy and appearing the oscillatory side-band spectral structures responsible for the fusion and fission reactions with soliton-like nuclei. We hope that nonlinear-optical analogies found in our work will be able to shed additional light on the fundamental problems of stellar nucleosynthesis. We support our findings with concrete examples of fusion and fission reactions with “well-dressed repulsive-core” nucleus-like solitons: the carbon and oxygen-burning processes, the iron-synthesis, and nuclear fusion–fission reactions induced by alpha particles.

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.

Study of dissipation role in fusion–fission reaction dynamics in mass region A>190 via fission time

Study of dissipation role in fusion–fission reaction dynamics in mass region A>190 via fission time

Statistical model calculation of the compound nuclear fission timescale in fusion-fission reactions

In the decay of an excited heavy nucleus, both the fission or evaporation residue (ER) cross sections and the fission time are determined by the competition between the various evaporation channels and fission. Statistical model (SM) calculations for several heavy-ion-induced fusion-fission reactions are presented which reproduce the fission or ER excitation functions. The corresponding calculated fission times are found to depend upon the compound nuclei and their excitation energies. The multichance fission probabilities and the corresponding fission times are also obtained, and they are shown to depend sensitively on the shell correction energies and the neutron separation energies of the compound nuclei involved. The experimental neutron multiplicities are reproduced by adjusting the saddle-to-scission transition time interval. An additional delay time for compound nuclear formation is found necessary to fit the experimental neutron multiplicities for a system with higher entrance channel mass symmetry.

Structure of As83, As85, and As87 : From semimagicity to γ softness

The structure of $^{83}$As, $^{85}$As and $^{87}$As have been studied in fusion-fission reaction $^{238}$U+$^9$Be. Fission fragments were identified in mass and atomic number using the VAMOS++ spectrometer and the coincident $\gamma$-rays were detected in the $\gamma$-ray tracking array AGATA. New transitions in $^{83}$As and $^{85}$As are reported and placed in the level schemes. A level scheme of the excited states in $^{87}$As is proposed for the first time. The data are interpreted in frame of Large-Scale Shell-Model calculations, SU3 symmetries and Beyond Mean-Field frameworks. A spherical regime at magic number $N$=50 is predicted and the location of the proton $g_{9/2}$ orbital is proposed for the first time. Development of collectivity in a prolate deformed, $\gamma$-soft regime in the open shell cases $^{85}$As and $^{87}$As, most neutron-rich isotopes beyond $N$=50, is concluded. Data and theoretical calculations give confidence to a relatively high extrapolated excitation energy about 4 MeV of the $9/2^+$ state in $^{79}$Cu, one proton above $^{78}$Ni.

Influence of uranium dioxide and reflector surface on neutron yields of the nuclear hybrid fusion-fission reaction using MCUNED code

The goal of the present work is to demonstrate the effects of adding uranium dioxide (UO2) to deuterium fuel in the fusion-fission hybrid reactions. The effectiveness of applying a reflector surface on the neutron yield in D-D and D-UO2 reactions has been investigated. The neutrons yielded from the fusion reactions were considered as a neutron source for fission reactions. For this purpose, MCNPX and its extension, the MCUNED code, for D-D fusion processes and UO2 fission reactions were used to calculate the neutron yield and the generated power. Using externally evaluated nuclear data libraries, MCUNED is capable of light ion transport. The D (d), (n) 3He reaction with 0.25 gm of deuterium and the fission reactions with 0.25 and 1.0 gm of UO2 were utilized. The results showed that the calculated neutron flux from the D-D fusion reaction increased by a considerable amount when applying the reflector surface. Adding 1.0 gm of UO2 to deuterium fuel enhanced neutron flux by 4.95 times on average, outside the source with the reflector surface. The calculated power increased by about 3-folds when 1.0 gm of UO2 was added. Despite the narrow cross section of the D-D reactions used in this study, it was found that utilizing the reflector surface and UO2 or depleted uranium with restrictive high masses may be able to multiply the generated neutrons and the resulting power.

Isospin conservation in compound nuclear fusion–fission reactions – empirical evidence

Isospin symmetry has gained importance in nuclear phenomena involving heavy nuclei in recent years. We present empirical evidence of isospin dependence in the compound nuclear fission cross-sections and fission widths, which suggests the idea that the compound nucleus (CN) possibly retains the memory of the isospin when it is formed and affects the CN fission. This idea was first proposed by E.L. Yadrovsky [E.L. Yadrovsky, Phys. Lett. 55B, 157 (1975)]. An observable difference between the fission branching ratios in two different isospin states suggests that the CN seems to remember its isospin at the point of formation. Further, the data also suggest a possible new signature of weakening of the CN process and gradual transition to non-compound processes as the energy rises. This is a very interesting and useful observation which needs to be confirmed by further and more precise experiments.

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.

Role of viscosity in fusion-fission dynamics via simultaneously measured neutron and α -particle multiplicities

The multiplicities of $\ensuremath{\alpha}$ particles and neutrons have been measured simultaneously for the reaction $^{16}\mathrm{O}+^{196}\mathrm{Pt}$ forming $^{212}\mathrm{Rn}$ compound nucleus at excitation energies of 56 MeV, 61 MeV, and 68 MeV. Neutrons and $\ensuremath{\alpha}$ particles were detected at various angles in coincidence with the fission fragments. To extract the contribution of pre- and postmultiplicities using the total $\ensuremath{\alpha}$-particle and neutron spectra, moving source formalism was implemented. In the case of $\ensuremath{\alpha}$ particle, near scission contribution has also been extracted. Study of the fission mechanism using light particle emissions are helpful in understanding the detailed fusion-fission reaction dynamics. The statistical model code joanne2, which includes deformation-dependent particle transmission coefficients, binding energies and level densities, has been used to reproduce the measured multiplicities of neutrons and $\ensuremath{\alpha}$ particles by varying the transient (${\ensuremath{\tau}}_{tr}$) and saddle to scission (${\ensuremath{\tau}}_{ssc}$) times. It is found that the fission time scales of the order of $50--70\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ sec are required to reproduce the neutron and $\ensuremath{\alpha}$-particles multiplicities simultaneously. The fission time scales are the measure of the nuclear viscosity, which is responsible for the dynamic hindrance of the fission process.

Search for stabilizing effects of the Z=82 shell closure against fission

Presence of closed proton and/or neutron shells causes deviation from macroscopic properties of nuclei which are understood in terms of the liquid drop model. It is important to investigate experimentally the stabilizing effects of shell closure, if any, against fission. This work aims to investigate probable effects of proton shell ($Z = 82$) closure in the compound nucleus, in enhancing survival probability of the evaporation residues formed in heavy ion-induced fusion-fission reactions. Evaporation residue cross sections have been measured for the reactions $^{19}$F+$^{180}$Hf, $^{19}$F+$^{181}$Ta and $^{19}$F+$^{182}$W from $\simeq9\%$ below to $\simeq42\%$ above the Coulomb barrier, leading to formation of compound nuclei with same number of neutrons ($N = 118$) but different number of protons across $Z = 82$. Measured excitation functions have been compared with statistical model calculation, in which reduced dissipation coefficient is the only adjustable parameter. Evaporation residue cross section, normalized by capture cross section, is found to decrease gradually with increasing fissility of the compound nucleus. Measured evaporation residue cross sections require inclusion of nuclear viscosity in the model calculations. Reduced dissipation coefficient in the range of 1\textendash3 $\times$ $10^{21}$ s$^{-1}$ reproduces the data quite well. No abrupt enhancement of evaporation residue cross sections has been observed in the reaction forming compound nucleus with $Z = 82$. Thus, this work does not find enhanced stabilizing effects of $Z = 82$ shell closure against fission in the compound nucleus. One may attempt to measure cross sections of individual exit channels for further confirmation of our observation.

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.

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 High-Energy Fission in Inverse Kinematics

Fission at low excitation energy, is a process in which both macroscopic and microscopic aspects are involved. Some features in the total kinetic energy and in the N/Z distributions of the fragments, commonly associated with shell effects, came out in a series of recent experiments with high excitation energy fusionfission reactions in inverse kinematics. In the latest experiment of this campaign, a study of high-energy fission and quasi-fission between a 238U beam and a series of light targets was carried out by using the aforementioned technique, in order to probe the role of the shell structure in these processes.

Role of isospin and its conservation in neutron-rich fission fragments

Following on from our earlier paper Garg and Jain (2017 Phys. Scr. 92 094001) containing some initial results, we present a detailed discussion and complete results in this paper, which provide the first direct evidence for the validity of isospin as a nearly good quantum number in neutron-rich systems. The evidence comes from the reproduction of the general features of the partition-wise relative yields of neutron-rich fission fragments produced in two heavy-ion induced fusion fission reactions, namely 208Pb (18O, f) and 238U (18O, f), by using the concept of isospin conservation. To fix the isospin values and use the isospin algebra, we invoke what we term Kelson’s conjectures. We present a consistent scheme for isospin assignments based on these considerations. Our calculated results confirm that isospin behaves as an approximately good quantum number in neutron-rich systems, in this case, the fission fragments.

Reply to ‘Comment on “Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions” '

In this Reply, we address the issues raised by Gontchar and Chushnyakova in the preceding Comment [Gontchar and Chushnyakova, Phys. Rev. C 98, 029801 (2018)] with respect to the relation between the Eccles-Roy-Gray-Zaccone (ERGZ) analytical model of nuclear fission lifetime and previous models based on the mean-first passage time approach. We clarify that the originality of the ERGZ approach lies in the ability to provide closed-form expressions for the lifetime valid across the entire range of nuclear temperature.

Comment on “Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions”

We discuss several misleading statements made in the article by Eccles et al. [Phys. Rev. C 96, 054611 (2017)]. In particular, contrary to what is claimed in that paper, the analysis of the borders of Kramers formula applicability as a function of temperature using the mean first-passage time formula was performed earlier in the paper by Gontchar et al. [Phys. Rev. C 82, 064606 (2010)].

Erratum: Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions [Phys. Rev. C 96 , 054611 (2017)

Received 25 January 2018DOI:https://doi.org/10.1103/PhysRevC.98.019905©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFissionHydrodynamic modelsLow & intermediate energy heavy-ion reactionsStatistical phenomena & chaosThermal & statistical modelsNuclear Physics

Fission fragment yields from heavy-ion-induced reactions measured with a fragment separator

The systematic study of fission fragment yields under different initial conditions has provided valuable experimental data for benchmarking models of fission product yields. Nuclear reactions using inverse kinematics coupled to the use of a high-resolution spectrometer with good fragment identification are shown here to be a powerful tool to measure the inclusive isotopic yields of fission fragments. In-flight fusion-fission was used in this work to produce secondary beams of neutron-rich isotopes in the collisions of a 238U beam at 24 MeV/u with 9Be and 12C targets at GANIL using the LISE3 fragment separator. Unique identification of the A, Z, and atomic charge state, q, of fission products was attained with the $\Delta E$ -TKE-B $\rho$ -ToF measurement technique. Mass, and atomic number distributions are reported for the two reactions. The results show the importance of different reaction mechanisms in the two cases. The optimal target material for higher yields of neutron-rich high-Z isotopes produced in fusion-fission reactions as a function of projectile energy is discussed.

Isospin Conservation in Neutron Rich Systems of Heavy Nuclei

It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems [1]. Lane and Soper [2] also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations [3, 4] for the fission fragment distributions obtained from heavy-ion fusion fission reactions. We discuss in detail the procedure adopted to assign the isospin values and the role of neutron multiplicity data in obtaining the total fission fragment distributions. We show that the observed fragment distributions can be reproduced rather reasonably well by the calculations based on the idea of conservation of isospin. This is a direct experimental evidence of the validity of isospin in heavy nuclei, which arises largely due to the neutron-rich nature of heavy nuclei and their fragments. This result may eventually become useful for the theories of nuclear fission and also in other practical applications.