Dynamical approach to calculating angular distributions of fission fragments

A dynamical approach is proposed for calculating the angular distributions of fission fragments. The relaxation time for the degree of freedom associated with the projection of the total angular momentum of the nuclear system onto the symmetry axis and the coefficient of damping of the fission mode are the basic parameters of this approach. Experimental data on the anisotropy of the angular distributions of fission fragments and on the multiplicities of prescission neutrons are analyzed within the proposed model for ¹⁶O+²⁰⁸Pb (E _lab=110–148 MeV), ¹⁶O+²³²Th (120–160 MeV), ¹⁶O+²⁴⁸Cm (110–148 MeV), and ¹⁶O+²³⁸U (96–148 MeV). The relaxation time and the damping coefficient are estimated at τ_K=(5–6)×10^?21 s and β=4×10²¹ s^?1, respectively.     

Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei ²¹⁰Po and ²²⁴Th formed in the fusion-fission reactions ⁴He + ²⁰⁶Pb , ¹⁶O + ²⁰⁸Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.     

Fragment angular momenta in low and medium energy fission of242Pu

Independent isomeric yield ratios of¹²⁸Sb were determined radiochemically in the thermal neutron induced fission of²⁴¹Pu and 34 MeV alpha particle induced fission of²³⁸U, both involving the same compound nucleus (²⁴²Pu). Fragment angular momenta estimated from the measured isomer ratios using the statistical model analysis showed significantly larger fragment angular momenta in the medium energy fissioning system compared to the low energy fissioning system. This has been attributed to the effect of higher excitation energy and angular momentum in the entrance channel leading to increased fragment temperature, moments of inertia and angular velocity. An attempt was made to calculate the fragment angular momentum in the medium energy fission using the Fermi gas model for the fissioning nucleus, taking into account the multichance fission, saddle shapes of the fissioning nuclei and the angular velocity components of the fissioning nuclei both along and orthogonal to the fission axis. The calculated angular momenta agree well with the experimental results.     

Effect of pre-equilibrium emission on probing postsaddle nuclear dissipation with neutrons

Using the stochastic Langevin model coupled with a statistical decay model, we study the influence of pre-equilibrium(PE) emission on probing postsaddle friction(β) with neutrons. A postsaddle friction value of(14-16.5) ×10~(21)s~(-1) and(11-13) ×10~(21)s~(-1) is obtained from comparing calculated and measured prescission neutron multiplicities of heavy fissioning systems248 Fm and256Fm in the absence and presence of the deformation factor.Moreover, it is found that a larger β is required to fit multiplicity data after the PE effect is accounted for, and that the effect becomes stronger when more energy is removed by PE particles. Our findings suggest that, to more accurately determine the postsaddle friction strength through the measurement of prescission neutrons, in addition to incorporating the contribution of PE evaporation source into the experimental multi-source analysis for particle energy spectra in coincidence with fission fragments, on the theoretical side, it is very important to make a precise evaluation of the energy that PE emission carries away from excited compound systems produced in heavy-ion fusion reactions.     

Effect of entrance channel parameters on fission fragment angular momentum in medium energy fission

Independent isomeric yield ratios of¹³²I were radiochemically determined in alpha particle induced fission of²³⁸U in the energy range 25–44 MeV. Fission fragment angular momenta were deduced from the measured isomeric yield ratios using spin dependent statistical model analysis. It was seen that angular momentum of¹³²I increases with increase of excitation energy and angular momentum of the fissioning nucleus. Comparison of the present data on¹³²I in²³⁸U(α,f) with the literature data for the same product in²³⁸U(p, f) and²³⁸U(γ, f) at various excitation energies show that fragment angular momentum strongly depends on the input angular momentum in the range of excitation energy considered. Experimental fragment angular momentum at all excitation energies were seen to be in agreement with the theoretical values calculated based on thermal equilibration of the various collective rotational degrees after considering the occurence of multichance fission. Thus, strong effect of input angular momentum as well as the statistical equilibration among the various collective rotational degrees of freedom in medium energy fission is corroborated.     

Evaporation and fission decay of 132Ce compound nuclei at Ex=122 MeV: some limitations of the statistical model

Light charged particle (LCP) emission in the evaporation residue (ER) and fusion fission (FF) channels have been studied for the 200 MeV ³²S + ¹⁰⁰Mo reaction, leading to ¹³²Ce composite nuclei at E _x =122 MeV. The main goal was to study the decay of ¹³² Ce on the basis of an extended set of observables, to get insights on the fission dynamics. The proton and alpha particle energy spectra, their multiplicities, ER-LCP angular correlations, ER and FF angular distributions, and ER and FF cross-sections were measured. The measured observables were compared with the Statistical Model (SM). Using standard parameters, the model was able to reproduce only the pre-scission multiplicities and the FF and ER cross-sections. The calculation was observed to strongly overestimate the proton and alpha particle multiplicities in the ER channel. Disagreements were also observed for the ER-LCP correlations, the LCP energy spectra and the ER angular distribution. By varying the SM input parameters over a wide range of values, it is shown that it is not possible to reproduce all the observables simultaneously with a unique set of parameters. The inadequacy of the model in reproducing the ER particle multiplicities is also observed analysing data from the literature for other systems in the A ≈ 150 and E _x ≈ 100?200 MeV region. These results indicate serious limitations about the use of the SM in extracting information on fission dynamics.     

Isomeric yield ratios of fission products in the system of 24 MeV proton-induced fission of238U

Isomeric yield ratios of 30 fission products in 24 MeV proton-induced fission of²³⁸U were measured by the use of the ion-guide isotope separator on-line. The obtained isomeric yield ratios were converted to the angular momenta of primary fission fragments based on the statistical model. The deduced angular momenta were examined from various aspects. It is found that in general the angular momentum continuously increases with the fragment mass number including the region of symmetric mass division. However, there are some exceptions. For Sn isotopes the deduced angular momenta are quite small due to the spherical shape of the nuclear shell configuration. It is also concluded from the consideration of the charge distribution that the angular momentum of fission product scatters considerably within the narrow range of mass division. The dependence of the angular momentum on the available energy of fragments at scission point indicates that the individual fragment possesses a characteristic deformation at scission and/or the deduced angular momentum is seriously affected by the particle excitation after scission.     

Nuclear viscosity of hot rotating 240Cf

In a detailed investigation of giant dipole resonance (GDR) γ-ray yield from ²⁴⁰Cf populated in the ³²S + ²⁰⁸Pb reaction, the absolute γ-ray/fission multiplicities are extracted over a wide range of excitation energy and angular momentum. The enhanced yield of GDR decay γ rays has been analyzed within the framework of a modified statistical model containing the nuclear viscosity as a free parameter. The extracted nuclear dissipation coefficient is found to be independent of the temperature. Large constant dissipation during the saddle-to-scission path provides good fits to the γ-ray spectra.     

More Detailed Study of Deformation Effects in Prescission Particle Emission by a Diffusion Model

Deformation effects on particle emission in a fission process of 251Es nucleus as functions of excitationenergy, angular momentum, and viscosity coefficient have been investigated in detail within the framework of Smolu-chowski equation. Our calculations show that high excitation energy, low angular momentum, and large viscosity willenhance the influence of deformation on multiplicity of prescission particles, and that the roles of these three parameterswill become weak with decreasing deformation.     

More Detailed Study of Deformation Effects in Prescission Particle Emission by a Diffusion Model

Deformation effects on particle emission in a fission process of ^251Es nucleus as functions of excitation energy, angular momentum, and viscosity coefficient have been investigated in detail within the framework of Smolu-chowski equation. Our calculations show that high excitation energy, low angular momentum, and large viscosity will enhance the influence of deformation on multiplicity of prescission particles, and that the roles of these three parameters will become weak with decreasing deformation.     

Combining a langevin description of heavy-ion induced fission including neutron evaporation with the statistical model

A model is developed which combines dynamical (Langevin-) calculations with the Kramers modified statistical model in order to describe heavy-ion induced fission including neutron evaporation. In the example of the¹⁹F+¹⁸¹Ta collision, the energy dependence of fission probabilities, neutron multiplicities and (H.I.,xn)-cross sections is calculated and a fair agreement with the data is achieved with a reduced friction parameter ofβ=3^*10²¹sec^?1. We pay particular attention to the angular momentum dependence of the fusion-fission process.     

Prescission neutrons in the fission of 235U and 252Cf nuclei

Experimental data obtained previously for the energy-angular distribution of neutrons originating from the fission of ²⁵²Cf (spontaneous fission) and ²³⁵U (thermal-neutron-induced fission) nuclei are analyzed, the angle being measured with respect to the direction of fission-fragment motion. A regularity common to all independent experiments is revealed: at an angle of about 90°, there exists an excess of neutrons (30% for ²⁵²Cf and 60% for ²³⁵U) that does not admit explanation within the model of neutron emission from fully accelerated fragments. Two possible explanations of this experimental fact—neutron emission during the acceleration process and the existence of an additional source of neutrons (predominantly, prescission neutrons)—are considered. It is shown that the latter conjecture describes the observed features for both nuclei more adequately. The total yield of prescission neutrons and their energy and angular distributions are determined.     

Effect of the initial excitation energy on the average fission lifetime of nuclei

The dependence of the fission time on the initial nuclear excitation energy E _{tot 0} ^* is studied on the basis of a refined combined dynamical and statistical model. It is shown that this dependence may be nonmonotonic, in which case it features a broad maximum. It turns out that the form of the average fission time 〈t _f 〉 as a function of E _{tot 0} ^* depends greatly on the orbital angular momentum L _n carried away by prescission neutrons.     

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.     

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.     

Interference of fission amplitudes of neutron resonances and <Emphasis Type="Italic">T</Emphasis>-odd asymmetry for various prescission third particles in the ternary fission of nuclei

Differential cross sections for reactions of the true ternary fission of nuclei that was induced by cold polarized neutrons were constructed with allowance of the effect that Coriolis interaction and the interference between fission amplitudes of neutron resonances excited in fissile nuclei upon incidentneutron capture by target nuclei exerted on angular distributions of prescission third particles (alpha particles, neutrons, or photons). It is shown that T -odd TRI- and ROT-type asymmetries for prescission alpha particles are associated with, respectively, the odd and even components of the Coriolis interaction-perturbed amplitude of angular distributions of particles belonging to the types indicated above. These asymmetries have angular distributions differing from each other and stemming from a nontrivial dependence of these components on the neutron-resonance spins J _s and their projections K _s onto the symmetry axis of the nucleus involved. It is shown that angular distributions of prescission photons and neutrons from reactions of the ternary fission of nuclei that is induced by cold polarized neutrons are determined by the effect of Coriolis forces exclusively. Therefore, the emerging T-odd asymmetries have a character of a ROT-type asymmetry and are universal for all target nuclei.     

Mechanisms for the appearance of prescission γ-rays and their related T-odd asymmetries

Conditions for the appearance and observation of prescission γ-rays emitted by a fissioning nucleus before its separation into fission fragments were investigated within the quantum theory of fission. It was demonstrated that these conditions can be fulfilled in the γ-decay of giant electric isovector dipole resonances in a fissioning nucleus that become excited due to the nonadiabaticity of the collective deformation motion of the nucleus at the final stages of its prefission evolution. Angular and energy distributions of prescission γ-rays emitted by unpolarized fissioning nuclei were analyzed. Characteristics of T-odd asymmetries in angular distributions of prescission γ-rays were investigated for fission of unpolarized target nuclei induced by polarized cold neutrons, and these correlations were shown to be similar in nature to the T-odd ROT correlations earlier found for α-particles emitted in ternary nuclear fission.     

Mechanisms of formation of P-odd,P-even and T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons

The experimentally measured P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of products of binary and ternary fission induced by cold polarized neutrons are classified, and the mechanisms of their appearance are studied. Basic asymmetries in the angular distributions of binary-fission fragments are found theoretically and are used to construct induced asymmetries in the angular distributions of prescission and evaporated third particles emitted in true and delayed ternary fission. If effects associated with the collective rotation of the polarized fissile system are disregarded, P-odd, T-even; P-even, T-even; and P-even, T-odd asymmetries in the angular distributions of prescission and evaporated photons are proven to be absent, and the coefficients of the analogous asymmetries in the angular distributions of prescission and evaporated neutrons are calculated for this case. The features of the coefficients of induced P-even, T-odd asymmetries are studied for evaporated photons and neutrons associated with taking into account the quantum rotation of the polarized fissile system.     

The role of rotational degrees of freedom in heavy ion collisions

The degrees of freedom affected by the angular momentum are identified. The relevance of the equilibrium fluctuations in a diffusive evolution of the system is discussed. The statistical limit is described and chosen as a reference for comparing with experiment. The rigid rotation regime is shown to be reached in a variety of reactions. The fragment spin alignment is measured from γ-ray multiplicities and anisotropies as well as from sequential fission angular distributions. Good agreement is obtained with the statistical model for the P_zz component of the polarization tensor. The P_xy component seems also to reach the statistical limit at large Q-value. The effect of shells on the angular momentum transferred to the fragments and on its misalignment is discussed theoretically and specific predictions are made.