Dynamic picture of the formation of spins of induced fission fragments

A way of calculating the average spins of induced fission fragments is developed, based on the dynamic model of their angular distributions. The range of relaxation times for the degree of freedom associated with the orientation of the axis of symmetry of a fissioning nucleus relative to its total angular momentum is determined by analyzing experimental data on the energy dependences of average spins and the anisotropy of the angular distributions of fission fragments for the ¹²C, ¹⁶O + ²³²Th reactions at E _сm = 55–150 MeV.     

Dynamical model of fission fragment angular distributions

A dynamical model of fission fragment angular distributions is developed. The experimental data on the angular anisotropy of fission fragments is analyzed for the ¹⁶O + ²⁰⁸Pb, ²³²Th, ²³⁸U, and ²⁴⁸Cm reactions at energies of the incident ¹⁶O ions ranging from 90 to 160 MeV. This analysis allows us to extract the relaxation time for the tilting mode. It was also demonstrated that the angular distributions are sensitive to the deformation dependence of the nuclear friction.

     

Investigation of the reaction <Superscript>208</Superscript>Pb(<Superscript>18</Superscript>O, <Emphasis Type="Italic">f</Emphasis>): Folding angular distributions of fission fragments and gamma-ray multiplicity

Correlations between folding angular distributions of fission fragments and the gamma-ray multiplicity are studied for ¹⁸O + ²⁰⁸Pb interactions at energies of the beam of ¹⁸O ions in the range E _lab = 78–198.5 MeV. The probabilities are determined for complete-and incomplete-fusion processes inevitably followed by the fission of nuclei formed in these processes. It is found that the probability of incomplete fusion followed by fission increases with increasing energy of bombarding ions. It is shown that, for the incomplete-fusion process, folding angular distributions of fission fragments have a two-component structure. The width of folding angular distributions (FWHM) for complete fusion grows linearly with increasing energy of ¹⁸O ions. The multiplicity of gamma rays from fission fragments as a function of the linear-momentum transfer behaves differently for different energies of projectile ions. This circumstance is explained here by the distinction between the average angular momenta of participant nuclei in the fusion and fission channels, which is due to the difference in the probabilities of fission in the cases where different numbers of nucleons are captured by the target nucleus.     

Influence of nuclear dissipation on fission dynamics of the excited nucleus <Superscript>248</Superscript>Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus ²⁴⁸Cf formed in the ¹⁶O+²³²Th reactions. Postsaddle nuclear dissipation strength of (12–14) × 10²¹ s^?1 was extracted for Cf nucleus by fitting the results of calculations with the experimental data. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nuclear dissipation.     

Angular momentum dependence of 200Pb fission studied by comparison of 19F on 181Ta with 16O on 184W

The time development of fission in highly excited Pb nuclei has been studied by the crystal blocking technique. Thin Ta crystals were bombarded with ¹⁹F ions in the energy range 90–120 MeV and the yield of fission fragments was measured for emission directions close to a strong axis. The experimental blocking dips are compared with calculated dips containing a superposition of two components, corresponding to short- and long-lived compound nuclei. The information extracted is the energy dependence of the relative amount of fission which comes from compound nuclei with lifetimes of τ≳3 × 10⁻¹⁷s. The total fission cross section and angular distribution of fission fragments were also measured for ¹⁹F bombardment of ¹⁸¹Ta in the energy range 84.3–114.7 MeV and for ¹⁶O bombardment of ¹⁸⁴W in the energy range 83.4–107.9 MeV. The results of the three types of measurements have been interpreted through comparison with statistical model calculations that follow the spin and energy distribution of compound nuclei through the neutron evaporation cascade. The ¹⁹F + ¹⁸¹Ta measurements, when compared with the present ¹⁶O + ¹⁸⁴W cross section and angular distribution measurements and earlier lifetime measurements for ¹⁶O + W, yield information on the spin distribution for the compound nucleus and its influence on the fission process.     

Dynamic approach to the analysis of angular distributions of fission and quasi-fission fragments

A dynamic approach to the calculation of angular distributions of fission and quasi-fission fragments is proposed. The approach is tested in the analysis of the experimental data for the ²⁸Si, ³²S + ²⁰⁸Pb reactions at E _lab = 160–280 MeV. Dependence of the relaxation time for the degree of freedom related to the projection of the angular momentum onto the symmetry axis of the decaying system on the deformation and the angular momentum is discussed.     

Angular distribution of fission fragments in reactions of complete fusion of deformed nuclei

Formation of angular distributions of fission fragments for the ¹⁶O + ²³²Th and ¹²C + ^235,236U reactions has been analyzed within a dynamic approach. In this approach, the component of the total angular momentum along the fission axis K is considered as a fluctuating quantity and the corresponding relaxation time is assumed to be the main parameter controlling the evolution of this mode. Particular attention is paid to the analysis of the effect of initial distributions over K (formed during fusion) on the angular distribution of fission fragments of nuclei having fission barriers comparable with the nuclear temperatures.     

Influence of shell effects on the angular distributions of fission fragments

A dynamical-statistical model is used to analyze the experimental angular distributions of fission fragments in the reactions α + ²³⁸U, ²³⁷Np at E _α = 20–100 MeV, as well as to determine the Am isotope fission probabilities and the shape isomer yields in the reactions d + ^242,240Pu at E _d = 20–30 MeV. Manifestations of shell effects are found in the fission barrier structure up to the excitation energies of 50–60 MeV.     

Stochastic model of angular distributions of fragments originating from the fission of excited compound nuclei

The anisotropy of angular distributions of fission fragments and the average multiplicity of prescission neutrons were calculated within a stochastic approach to fission dynamics on the basis of three-dimensional Langevin equations. This approach was combined with a Monte Carlo algorithm for the degree of freedom K (projection of the total angular momentum I onto the fission axis). The relaxation time τ _K in the coordinate K was considered as a free parameter of the model; it was estimated on the basis of a fit to experimental data on the anisotropy of angular distributions. Specifically, the relaxation time τ _K was estimated at 2 × 10^?21 s for the compound nuclei ²²⁴Th and ²²⁵Pa and at 4 × 10^?21 s for the heavier nuclei ²⁴⁸Cf, ²⁵⁴Fm, and ²⁶⁴Rf. The potential energy was calculated on the basis of the liquid-drop model with allowance for finiteness of the range of nuclear forces and for the diffuseness of the nuclear surface. A modified one-body viscosity mechanism featuring a coefficient k _s that takes into account the reduction of the contribution from the wall formula was used to describe collective-energy dissipation. The coefficient k _s was also treated as a free parameter and was estimated at 0.5 on the basis of a fit to experimental data on the average prescission multiplicity of neutrons.     

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, M_γ(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 M_γ(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 M_γ as a function of the total kinetic energy (TKE) of fragments, M_γ(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.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atE _cm ^inc =750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.     

Angular Distributions and Anisotropy of the Fragments from Neutron-Induced Fission of <Superscript>239</Superscript>Pu and <Superscript>nat</Superscript>Pb in the Energy Range of 1–200 MeV

The angular distributions of fragments from the neutron-induced fission of ^natPb and ²³⁹Pu nuclei have been measured in the energy of range 1–200 MeV using the neutron time-of-flight spectrometer GNEIS. Fission fragments have been detected by position sensitive multiwire proportional counters. The results for the anisotropy of fission fragments deduced from the measured angular distributions have been presented. The results have been compared with the experimental data of other authors.     

Asymmetric mass distribution from the fusion-fission reaction40Ar+243Am

The mass distributions and total c.m. kinetic energies of fission fragments formed in the reaction⁴⁰Ar+²⁴³Am at bombarding energies of 214, 222, 240 and 300 MeV have been measured using the angular correlation method. Angular distributions and anisotropy for 222 and 300 MeV have also been obtained. A symmetric mass distribution corresponding to the decay of a highly excited compound nucleus was obtained at 300 MeV bombarding energy. However, with decreasing bombarding energy the fission fragment mass distribution becomes asymmetric, the most probable heavy fragment mass being about 200–210 amu.     

The reaction238U +238U at 7.42MeV/u

One-particle-inclusive measurements have been performed for the charge, kinetic energy and angular distributions of reaction products from²³⁸U +²³⁸U at 1 766MeV (7.42MeV/u) incident energy. The deep inelastic products exhibit features similar to those seen in reactions induced by medium heavy nuclei: increasing particle transfer is observed with increasing energy damping, the angular distributions are peaked near the grazing angle, they broaden significantly with increasing energy loss and/or charge transfer. The dominant reaction mechanism, however, is found to be sequential fission of one or both primary reaction products. The reconstructed primaryZ- andQ-value distributions show more particle transfer at a given energy loss than in other systems, i.e. the diffusion process seems to proceed colder in this system. This is confirmed by relatively large cross sections for surviving deep inelastic reaction products belowZ=92. A direct search forα-decay or fission of superheavy nuclei being produced in a deep inelastic reaction and being implanted in a surface barrier detector resulted in an upper cross section limit of 2 ×10^?32cm².     

Evaporation residue formation competing with the fission process in the197Au+16O,12C reactions and fission barriers at a specifiedJ window

Evaporation-residue excitation functions for¹⁶O and¹²C+¹⁹⁷Au reactions were measured by means of the activation technique. The competition between evaporation and fission of the compound nuclei was studied by comparing the observed evaporation-residue data with the published fission excitation functions. A newly devised analysis was applied in order to deduce a fission barrier height at a specified angular momentum and determine the relevant fissioning nucleus as well. We found the fission barriers to be 8.2 MeV for the²¹¹Fr nucleus at 16? and 8.2 MeV for the²⁰⁷At nucleus at 27?.     

Spectroscopy of A = 16 from 13C(6Li,t)16O

The ¹³C(⁶Li, t)¹⁶O reaction has been studied at 34 MeV. Selective population of narrow states is observed up to 21 MeV excitation in ¹⁶O. This reaction populates strongly both unnatural-and natural-parity states that have little or no ¹²C + α₀ width. The measured angular distributions are compared with Hauser-Feshbach and finite-range DWBA calculations. Reasonable agreement with the DWBA calculations is found for most of the states strongly populated. The widths of the narrow states populated in the 16–20 MeV excitation region are presented. Comparison of the present data with that from medium-energy inelastic scattering and other multiparticle transfer reactions is made.     

Effect of the Input Channel of Heavy-Ion Reactions on Fission-Fragment Spins

Within a dynamical approach, the average spins of fission fragments originating from the ¹²C + ^235,236U and ¹³C + ²³⁵U complete fusion reactions at c.m. energies in the range of E_c.m. = (55–75) MeV are analyzed as a function of energy. Particular attention is given to the process of formation of initial distributions for the components of the total angular momentum of compound nuclei. It is shown that substantial distinctions in the behavior of average spins of fission fragments for different fusion reaction channels are expected to be observed in the range of subbarrier energies.