Studies of mass and energy correlations in thermal neutron fission of U-235 accompanied by long range alpha particles

Several characteristics of fission accompanied by long range alpha particles (LRA) have been studied in the thermal neutron induced fission of²³⁵U. The kinetic energies of fission fragments and the LRA were measured with a back-to-back ionization chamber and semiconductor detectors respectively. The kinetic energies of the two fragments and the LRA in LRA fission, along with the energies of pair fragments in the normal binary fissions, were recorded event by event on a magnetic tape by means of a four-parameter data acquisition system. The data were analysed to study the dependence of different quantities in LRA fission on the fragment mass ratio, LRA energy and the total kinetic energy of the fission fragments. It is seen that the most probable energy of LRA increases significantly for near symmetric mass divisions. The total kinetic energy for all mass ratios in LRA fission is found to be (2.6±0.7) MeV larger than that in binary fission. The difference in the total kinetic energies in LRA and binary fissions is seen to be dependent on mass ratio. This result may suggest that the scission configuration in LRA fission is different for different mass ratios. Correlations between the fission fragment and LRA energies have been studied for several mass ratios. It is seen that the most probable fragment kinetic energyĒ _k varies nearly linearly with the LRA energyE _a for various mass divisions but the variation of the most probable LRA energyĒ _a with fragment kinetic energyE _k is found to deviate from linearity for several mass ratios. From a least square fit to the variation ofĒ _k withE _a it is found that the slope (dĒ _k/dE_a) increases with the increase in mass ratio. The present results are discussed to arrive at a better understanding of the scission configuration in the fission accompanied by LRA emission.     

Recent experimental studies on 252Cf ternary fission

The rare ternary fission (TF) process was hitherto studied mainly by inclusive measurements of the energies and fractional yields of the light charged particles (LCPs) from fission, or by experiments on the angular and energy correlation between LCPs and fission fragments (FF). The present article briefly describes a series of recent correlation measurements on ²⁵²Cf(sf) TF that include either the registration of neutrons and γ rays with LCPs and FFs, or the coincident registration of two LCPs. The population of excited states in LCPs has been identified, as well as the formation of neutron-unstable nuclei as short-lived intermediated LCPs, the sequential decay of particle-unstable LCP species into charged particle pairs, and “quaternary” fission with the emission of two charged particles right at scission.     

Yields and energy spectra of light charged particles emitted in neutron induced fission of235U

The yields and energy spectra of light charged particles emitted in the fission of²³⁵U have been measured in the neutron energy range of 100 keV to 1 MeV. The yield of long range alpha particles is found to increase around 200 keV neutron energy compared to thermal fission. A low energy component observed in the energy spectrum was assigned to the tritons emitted in fission. The yield of this triton component is seen to have a marked increase around 500 keV. These results indicate that LCP yield is influenced by the transition state level characteristics.     

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.     

The 6He emission accompanying the spontaneous fission of 252Cf

The results of a multiparameter investigation of the ⁶He emission accompanying the spontaneous fission of ²⁵²Cf are presented. The energy spectrum and the yield of the ⁶He particles are found to be in accord with previous measurements, but their angular distribution is observed to be narrower at 13° ± 3° (FWHM) than the value of ? 32° deduced in a previous investigation.Comparisons of the experimental with published calculated energy spectra and angular distributions for ³H, ⁴He and ⁶He particles are shown to provide evidence for a compact scission configuration in ternary fission.     

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     

Quantum description of quaternary nuclear fission

The quantum theory of binary and ternary fission is generalized to the case of recently observed quaternary nuclear fission. Formulas for the amplitudes of partial fission widths and angular and energy distributions of quaternary fission products are derived with allowance for strong channel coupling. The nonevaporation mechanism for formation of light particles is used to explain the experimentally observed decrease in the probability for emission of light particles (α, α), (α, t), and (t, t) as compared with the product of emission probabilities for the same particles in ternary fission. It is concluded that in quaternary fission, as in ternary fission, light particles escape from the neck of the fissioning nucleus much earlier than scission of the nucleus into heavy fragments occurs.     

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.     

Ternary fission involving4He emission in the16O (144 MeV)+232Th and12C (108 MeV)+197Au reactions

The results of coincidence measurements of⁴He emission with fission fragments in reactions of¹²C(108 MeV) ions with a¹⁹⁷Au target and of¹⁶O(144 MeV) ions with a²³²Th target are presented. On the basis of a Monte Carlo kinematic simulation of nuclear reactions the experimental energy spectra and velocity distributions of alpha particles have been analyzed. A conclusion has been drawn that the main source of⁴ He emission is evaporation from the fissioning compound nucleus. Substantial part of alpha particles was emitted from fully accelerated fission fragments. Some of⁴He nuclei with an average energy of about 16 MeV (in the CM system) emitted mainly perpendicular to the fission axis were identified as being similar long-range alpha particles produced in ternary fission of heavy nuclei at a low excitation energy. The emission multiplicities of these particles are considerably higher than those observed at a low excitation energy. The experimental results are compared with the statistical model predictions.     

Ternary fission within statistical approach

The ternary system with a light nucleus between two heavy fragments is assumed to appear from the binary configuration near scission. The formation of a third light nucleus in the binary system is considered. The calculated charge distributions in spontaneous ternary fission of ²⁵²Cf and in induced ternary fission of ⁵⁶Ni are compared with the available experimental data. The neutron multiplicity from the fission fragments is described. The fine structures of the TKE-mass distribution are predicted.     

Fission-mode calculations for 239U,a revision of the multi-modal random neck-rupture model

In the course of an experimental study of the fragment characteristics after neutron-induced fission of ²³⁸U with incident neutron energies between 1.2 and 5.8 MeV fission-mode calculations in the frame of the multi-modal random neck-rupture model have been performed. During these calculations some technical parts of the model have been revised. The identification of fission modes is now based on unequivocal and reproducible criteria. The Rayleigh criterion has consequently been applied to determine each possible scission configuration. The most remarkable new results are that all physically relevant fission modes branch off in the second potential minimum exhibiting different outer barriers, and that the total kinetic energy distribution of the fission fragments is a direct consequence of the Rayleigh criterion. The fragment characteristics as the mean mass, the mean total kinetic energy and the corresponding width obtained from the fission-mode calculations compare reasonably well with the experimental findings.For the first time the weighted fission cross sections through each particular fission mode have been analyzed simultaneously using a Hill-Wheeler type expression for the transmission through a double-humped fission barrier. The results support the picture of individual outer barriers with slightly different penetrabilities and a slightly lower inner barrier.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

New experimental studies on the quaternary fission of <Superscript>233, 235</Superscript>U(n<Subscript>th</Subscript>, f ) and <Superscript>252</Superscript>Cf (sf )

Experiments have been performed for studying quaternary fission (QF) in spontaneous fission of ²⁵²Cf, on the one hand, and for the neutron-induced fission reactions ^{233, 235}U(n_th, f ), on the other hand. In this higher-multiplicity fission mode, by definition, four charged products appear in the final state. In other words, as a generalization of the ternary-fission process, not only one but two light charged particles (LCPs) are accompanying the splitting of an actinide nucleus into the customary pair of fission fragments. In the two sets of measurements, which have used quite different approaches, the yields of several QF reactions with α-particles and tritons as the LCPs have been determined and the corresponding kinetic-energy distributions of the α-particles measured. The QF process can appear in two basically different ways: i) the simultaneous creation of two LCPs in the act of fission (“true” QF) and ii) via a fast sequential decay of a single but particle-unstable LCP in common ternary fission (“pseudo” QF). Experimentally the two varieties of QF have been distinguished by exploiting the different patterns of angular correlations between the two outgoing LCPs. The experiments described in the present paper are the first to demonstrate that both types of reactions, true and pseudo QF, occur with quite comparable probabilities. As a new result also, the kinetic-energy distributions related to the two processes have been shown to be significantly different. For all QF reactions which could be explored, the yields for ²⁵²Cf(sf) were found to be roughly by an order of magnitude larger than the yields found in the ²³³U(n_th, f ) and ²³⁵U(n_th, f ) reactions. An interesting by-product has been the measurement of yields of excited LCPs which allows to deduce nuclear temperatures at scission by comparison to the respective yields in the ground state.     

Mechanisms for emission of4He in the reactions of 334 MeV40Ar with238U

Emission of⁴He in the reaction 334 MeV⁴⁰Ar+²³⁸U has been studied by triple coincidence measurements that allow the separate identification of fusion fission and sequential fission. For the⁴He evaporative spectra from fusion fission the composite system is shown to be the predominant contributor; whereas, for sequential fission the dominant emission is from the fragments. This result demonstrates a correlation between evaporative emission probability and lifetime expectancy of the composite system. To account for the observed⁴He spectra two other mechanisms are necessary in addition to nuclear evaporation. At forward angles, the⁴He spectra from both fusion fission and sequential fission exhibit higher intensities and larger energies than those expected from purely evaporative processes. This forward-peaked component must be related to a very rapid or pre-thermalization stage of the reaction. At backward angles yet another component is observed for fusion fission. As it is sensitive to the fragment masses but does not carry the kinematic shift characteristic of their full acceleration, this component must originate near to the time of scission. The average⁴He energy for this component is approximately 17 MeV (c.m.), and its intensity is correlated with a plane perpendicular to the fission fragment separation axis. These signatures are similar to those for long range alpha particle emission in low energy fission. Alpha particles evaporated from the composite nuclei in fusion-fission reactions are shown to be preferentially associated with fission events which result in the more symmetric masses. This result is consistent with the notion that mass asymmetric fission is a faster process than symmetric fission. Such a correlation between mass asymmetry and lifetime is an essential part of the “fast fission” or “quasifission” idea, which has attracted much current attention.     

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.     

Evidence for nonequilibrium particle emission before symmetric disintegration of a composite system formed in the 16O+40Ca reaction at 230 MeV

Measurement of fragment-fragment correlations in the reactions of 230 MeV ¹⁶O with ⁴⁰Ca and 280 MeV³²S with ²⁴Mg have been used to isolate processes in which symmetric decay follows nonequilibrium emission of one or two alpha particles. At the higher energy per nucleon. in contrast to previous observations for lower velocity projectiles, nonequilibrium emission followed by symmetric decay has approximately the same probability as the symmetric fission following complete fusion.     

Energy partition in nuclear fission

A scission point model (two spheroid model TSM) including semi-empirical, temperature-dependent shell correction energies for deformed fragments at scission is presented. It has been used to describe the mass-asymmetry-dependent partition of the total energy release on both fragments from spontaneous and induced fission. Characteristic trends of experimental fragment energy and neutron multiplicity data as function of incidence energy in the Th — Cf region of fissioning nuclei are well reproduced. Based on model applications, information on the energy dissipated during the descent from second saddle of fission barrier to scission point have been deduced.     

Fission modes in charged-particle induced fission

The population of the three fission modes predicted by Brosa's multi-channel fission model for the uranium region was studied in different fissioning systems. They were produced bombarding²³²Th and²³⁸U targets by light charged particles with energies slightly above the Coulomb barrier. Though the maximum excitation energy of the compound nucleus amounted to about 22 MeV, the influences of various spherical and deformed nuclear shells on the mass and total kinetic energy distributions of fission fragments are still pronounced. The larger variances of the total kinetic energy distributions compared to those of thermal neutron induced fission were explained by temperature dependent fluctuations of the amount and velocity of alteration of the scission point elongation of the fissioning system. From the ratio of these variances the portion of the potential energy dissipated among intrinsic degrees of freedom before scission was deduced for the different fission channels. It was found that the excitation remaining after pre-scission neutron emission is mainly transferred into intrinsic heat and less into pre-scission kinetic energy.     

The scission neutron spectrum of252CF (SF)

The scission neutron spectrum was obtained as a difference between the integral experimental fission neutron spectrum evaluated by Mannhart based on measurements in the laboratory reference system from several authors in the different neutron energy ranges, and the laboratory fission neutron spectrum stemming only from those neutrons which are evaporated from the fully accelerated fission fragments. The scission neutron spectrum was represented by a Weisskopf evaporation spectrump _s(? _l )=P ₀/(T _s)²·?_l·exp(??_l/T_s). A least squares fit gave for the fraction of scission neutrons with respect to all fission neutrons a value ofp ₀=(0.011±0.003) and for the pseudo scission neutron temperature a value ofT _s=(0.20±0.03) MeV. The low pseudo temperature is compatible with a cold nuclear matter of the prescission configuration. The low energy of the scission neutrons indicates that they come from a slowly moving source. The width of the distribution suggests that the source is small: radius of about 5 fm. This information conforms with the idea of satellite droplets which are formed when the neck snaps.     

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.