Étude de la dissipation d'énergie dans la fission de 234u à l'aide de la réaction 233U(d,pf)

The energy balance in the fission of ²³⁴U has been investigated on the basis of experimental results from the ²³³U(d, pf) reaction. Taking into account the neutron evaporation we have deduced the total kinetic energy and excitation energy distributions of the primary fragments as functions of the excitation energy of the fissioning nucleus. The neutron evaporation temperatures have been adjusted so as to reproduce the average value and width of the measured kinetic energy distributions for each fragmentation. Excitation energy distributions of the fragments have been deduced. The data are discussed in the framework of the liquid-drop model with shell corrections. Evidence for energy dissipation in the fission of ²³⁴U, involving drastic changes in the scission configuration, is shown for some fragmentation modes.     

The dependence of fission time-scales on fragment mass asymmetry in the 20Ne+165Ho reaction at 50A MeV

The pre-scission and post-scission multiplicities of alpha particles were determined in coincidence with fission fragments for four windows of exit channel mass asymmetry in the reaction ²⁰Ne+¹⁶⁵Ho at 50A MeV. The technique used employed a kinematic analysis of the energy spectra of alpha particles as a function of the emission angle with respect to the fission axis. Using a procedure of fitting the experimental energy spectra with those resulting from a Monte Carlo simulation program, the total multiplicity of alpha particles was separated into pre-scission and post-scission components. Using the pre-scission and post-scission multiplicities, neutron multiplicity measurements and other empirical observations, both the initial excitation energy and the excitation energy at scission of the compound nucleus were determined. The pre-scission times in the de-excitation of a highly excited ¹⁷⁸W compound nucleus with initial excition energy of 570 MeV were evaluated using statistical model calculations. Only a small decrease in scission time was derived for the most asymmetric events studied. The possible contribution of very damped deep inelastic processes is discussed.     

Nuclear-charge polarization at scission in the 12 MeV proton-induced fission of <Superscript>232</Superscript>Th

The most probable charges of secondary fragments, produced after neutron evaporation from primary fragments, have been evaluated using fractional cumulative and mass yields in the 12MeV proton-induced fission of ²³²Th . The nuclear-charge polarization of primary fragments at scission has been obtained by correcting the most probable charge of secondary fragments for neutron evaporation. The fragment mass dependence of the nuclear-charge polarization at scission shows good agreement with that for thermal neutron-induced fission of ²³⁵U , indicating that the nuclear-charge polarization is nearly insensitive to mass and excitation energy of the fissioning nucleus for asymmetric fission in the actinide region.     

Fragments' mass and energy characteristics in the spontaneous fission of 236Pu, 238Pu, 240Pu, 242Pu,and 244Pu

The results of a systematic study of the mass and energy of fission fragments emitted in the spontaneous fission of ^{236,238,240,242,244}Pu are reported. A comparison of the fragments' mass and energy distributions demonstrates the occurrence of different fission modes with varying relative probability. These results are discussed in terms of the random neck rupture model as well as in terms of the scission point model, showing the influence of the neutron number of the fissioning system. Finally an improved method of analysis allows the investigation of the cold fission region.     

Particle multiplicities in the fission-like reactions of 340 MeV Si on Th

Pre-scission and post-scission multiplicities of neutrons and alpha particles have been simultaneously measured for the fission-like reactions of 340 MeV ²⁸Si on ²³²Th. Dynamical model calculations using HICOL code predict that about 90% of the observed events are of quasi-fission type while the remaining 10% are from compound nucleus fission decay. Moving source fits were carried out to the observed neutron and alpha particle spectra, measured at different angles with respect to the fragment directions. The pre-scission and post-scission neutron multiplicities are deduced to be 8.7±2.0 and 9.4±2.0, respectively. The corresponding multiplicity values for alpha particles are found to be 0.22±0.08 and 0.1±0.03. From the measured post-scission neutron multiplicity, it is inferred that about 65±20 MeV of the initial excitation energy remains at scission. This may be compared to the value of 85±30 MeV estimated from PACE2 statistical model calculations, adjusted to reproduce the measured pre-scission neutron multiplicity. From a comparison of the Statistical Model predictions with the measured pre-scission neutron multiplicity, the fission delay is estimated to be of 5⁺⁷₋₃×10⁻²⁰ s which overlaps with the average duration of fission-like process from the contact to the scission point (2×10⁻²⁰ s) as determined from HICOL-based dynamical calculations. For the delay time deduced as above, the pre-scission alpha particle multiplicity calculated by the PACE2 code is about a factor two larger than the experimental one, demonstrating the difficulties in modelling the alpha particle emission from highly elongated shapes that characterize the fissioning system from the contact point to scission.     

Nuclear-charge polarization at scission in proton-induced fission of <Superscript>233</Superscript>U

The primary and the secondary fragment mass yields and neutron multiplicity in the 11.5MeV proton-induced fission of ²³³U were determined by a double time-of-flight method. The most probable charges of the secondary fragments in the isobaric chains with A = 126 , 127, 129, 132, and 136 have been derived from the secondary mass yields together with the literature values of the fractional cumulative and independent yields measured radiochemically. The nuclear-charge polarization of primary fragments at scission was obtained by correcting the secondary fragment mass for neutron evaporation. The results show that the nuclear-charge polarization is mostly determined by the minimum potential energy of nuclei at scission and that this behavior is nearly independent not only of mass and excitation energy but also of neutron-to-proton ratios of the fissioning nuclei.     

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.     

THE MICROSCOPIC CALCULATION OF THE STATISTICAL THEORY OF NUCLEAR FISSION

Based on the statistical fission theory, we have calculated the mass and kinetic energy distributions as well as other physical quantities of ²³⁵U fission induced by thermal neutron using microscopical method. That is, the quantum state densities of the fragments at scission point are calculated by means of BCS hamiltonian. The contribution of the collective deformation of fragments to the quantum state density has been taken into consideration. The potential energy of fragment is calculated by means of Strutinski procedure, and the shelling effect, pairing correlation as well as collective deformation have been taken into consideration in calculating the excitation energy at scission point. The scission point distance is treated as an adjustable parameter.Comparing with other statistical fission theories, our results give better agreement with existing experiments.     

Cold deformed fission in232U(n,f) and239Pu(n,f)

Masses, charges and kinetic energies of light fission fragments from the reactions²³²U(n, f) and²³⁹Pu(n, f) induced by thermal neutrons have been measured on the Cosi fan tutte spectrometer of the Institut Laue-Langevin in Grenoble. Both at very high and very low kinetic energies marked fine structures in the mass yields and odd-even staggerings in the charge yields are observed. In the framework of a scission point model the results are shown to point to compact and deformed scission configurations, respectively, where at scission the fragments carry no intrinsic excitation energy. The two limiting processes may, therefore, be called cold compact fission (usually known as cold fission) and cold deformed fission. The latter process as a general phenomenon of low energy fission has come into focus only recently.     

Gamma-ray multiplicities and fission modes in (208)Pb((18)O,f)

Two components in the M(gamma)(M) distribution were established in detailed measurements of mean gamma-ray multiplicities from fission fragments of (226)Th. For the first time in the M(gamma)(M) dependencies we were able to distinguish two components associated with primary and the final (after the neutron evaporation) fission fragments, and show that at the scission point M(gamma) is extremely sensitive to symmetric and asymmetric modes of fission. Theoretical calculations of the pre-scission shapes of the fissioning nuclei confirm our conclusions.     

Semi-microscopical description of the scission configuration in the neutronless fission of 252Cf

The neutronless fission of ²⁵²Cf is studied in the frame of a molecular model in which the scission configuration is described by two aligned fragments interacting by means of Coulomb (+ nuclear) forces. The study is carried out for different distances between the fragments tips and excitation energies. For a given deformation, the fragment's total energy is computed via the constrained Hartree-Fock + BCS formalism. The total excitation energy present in the fragments is supposed to contribute only to the fragments deformation and the asymptotic value of the kinetic energy is equated to the inter-fragment potential at scission. These two constraints are yielding a few fission channels for a fixed tip distance and excitation energy. Discarding those fission channels corresponding to a disequilibrium in the sharing of the excitation energy between the two fragments, we establish the most likely scission configurations for a specified excitation energy. Received: 24 September 1999     

<Emphasis Type="Italic">T</Emphasis>-odd asymmetries for evaporation γ-rays in nuclear fission

T-odd asymmetries in angular distributions of evaporation γ-rays emitted by thermalized fragments resulting from the fission of axially symmetric deformed nuclei induced by cold polarized neutrons are investigated within the quantum theory of fission. The asymmetries in question are due to the anisotropy of the angular distributions of evaporation γ-rays, caused by zero wriggling vibrations of the fissioning nucleus and associated with the orientation of large fission fragment spins in the direction perpendicular to the direction n ₀ of the symmetry axis of the fissioning nucleus at the time of its separation into fragments. The angle of rotation of the vector n ₀ with respect to the asymptotic direction of the light fission fragment emission is calculated with allowance for the interference of fission amplitudes of neutron resonances excited in the fissioning nucleus as it captures the incident neutron. It is shown that the angular and energy characteristics of the T-odd asymmetry calculated for evaporation γ-rays agree with the characteristics of the experimentally investigated T-odd asymmetry in angular distributions of all γ-rays emitted by a fissioning ²³⁶U nucleus.     

T-odd asymmetries for evaporation neutrons in nuclear fission

T-odd asymmetries in the angular distributions of evaporation neutrons emitted by thermalized fission fragments in the fission of axially symmetric deformed nuclei by cold polarized neutrons are investigated within the quantum theory of fission. The asymmetries in question are due to the anisotropy of angular distributions of evaporation neutrons in the center-of-mass systems of the fission fragments, and this anisotropy arises from the orientation of large-value fission fragment spins in the direction perpendicular to the direction K ₀ of the symmetry axis of the fissioning nucleus at the time of its scission, caused by zero wriggling vibrations of the fissioning nucleus. The angle of rotation of the vector k ₀ with respect to the asymptotic direction k ₀ of the fissioning nucleus symmetry axis is calculated with allowance for the interference of fission amplitudes of neutron resonances excited in a fissioning nucleus as it captures an incident neutron. It is shown that the T-odd asymmetry coefficient for evaporation neutrons is close in structure and value to the analogous coefficient for evaporation γ-rays.     

Momentum transfer in light-ion-induced fission reactions

Angular correlations and angular distributions of the fission fragments produced in the bombardment of a ²³²Th target with protons, deuterons and α-particles in the energy range between 35 and 1000 MeV/nucleon have been measured. From these measurements, the distributions of linear momentum imparted to fissioning nuclei have been deduced in the various energy regimes; dominating reaction mechanisms are classified according to the fraction of the available incident momentum transferred to the target. The experimental results are compared to the predictions of intra-nuclear cascade calculations. An optimum excitation energy supported by the fissioning nuclei could be the dominant limitation to momentum transfer at high incident energies. The angular distributions of the fission fragments were used to extract fission cross sections and upper limits of the angular momentum imparted to the fissioning nuclei.     

Mechanism of the appearance of angular distribution anisotropy for evaporation neutrons in center-of-mass systems emitting their thermalized fission fragments

Anisotropy in the angular distributions of cascade-evaporation neutrons in center-of-mass systems emitting their fission fragments is analyzed in the context of the quantum theory of fission. It is emphasized that such anisotropy is caused not by bending but by wriggling oscillations of the fissioning nucleus in the vicinity of its point of scission; these lead to the appearance of high-value spins of primary fission fragments [(J)\vec]₁\vec J_1 and [(J)\vec]₂\vec J_2 oriented in a plane perpendicular to direction [(n)\vec]₀\vec n_0 of the axis of symmetry of the fissioning nucleus at the instant of scission. This direction coincides with the asymptotic direction of the emission of fission fragments with a high degree of accuracy. The analytical dependences of the anisotropy coefficient on the orbital momentum l and total spin j in angular distributions of cascade-evaporation neutrons are calculated using the methods developed in analyzing angular distributions of cascade-evaporation gamma quanta. The proper spin of a neutron is shown to have almost no effect on the aforesaid anisotropy coefficient due to the weak dependence of the neutron transmission coefficient T _lj ([`(e)]\bar \varepsilon ) on the values of j.     

The study of prompt and delayed muon induced fission

Mass yield and total kinetic energy release (TKE) distributions of fragments from prompt and delayed muon induced fission, separately, have been measured for the isotopes²³⁵U,²³⁸U,²³⁷Np and²⁴²Pu. The distributions from prompt muon induced fission are compared with the corresponding distributions from hadronic reactions and from spontaneous fission (s.f.). The distributions from the delayed muonic fission processes are compared to the distributions for neutron and proton-induced fission. No mass distributions measured in the prompt muonic fission process show any signature, which can be attributed to the presence of the muon. Differences observed between the TKE distributions of prompt muon induced and hadron induced fission can be explained by the screening effect of the negative charge of the muon bound in the orbit of one of the fission fragments. The observed yield of symmetric muon induced fission was found to be defined merely by the value of the excitation energy.     

Kinetic energy distributions around symmetric thermal fission of U234 and U236

The kinetic energy distributions have been measured at LOHENGRIN for symmetric fission of U²³⁴ and U²³⁶. The pre-neutron emission values for the average total kinetic energy and its rms width have been deduced using a Monte Carlo simulation for neutron evaporation. The total kinetic energy dip between symmetric and asymmetric divisions is 24 MeV for U²³⁴ and 29 MeV for U²³⁶. A strong peak in the initial rms width has been observed for masses 111–123 in U²³⁴ and for 111–125 in U²³⁶. A static scission point model is used to understand the origin of these features.     

The dynamical description of the mass distribution of fission fragments

The variances of the mass distribution of fission fragments for nuclei in the fissility parameter range 30 < Z²/A < 40 have been calculated. The Fokker-Planck equation for the distribution function of collective variables is used as a dynamical equation to describe the descent of the fissioning nucleus from the saddle to scission. The calculations reproduce the experimentally observed increase of the mass variances with a growth of the parameter Z²/A. The increase of the calculated variances is due to a considerable decrease in the stiffness coefficients corresponding to the saddle points for heavy fissioning nuclei and to the non-equilibrium character of the descent.     

Measurement of fission anisotropy for 16O+181Ta

Anisotropies in fission fragment angular distributions measured for the system ¹⁶O + ¹⁸¹Ta over a range of bombarding energies from 83 MeV to 120 MeV have been analysed. It is shown that statistical transition state model (TSM) with pre-scission neutron correction described adequately the measured anisotropy data. Strong friction parameter is found to be necessary to estimate the pre-saddle to pre-scission neutron ratio.