Influence of fission fragment nuclear structure on scission configuration in252Cf (S.F.)

With the aim of investigating the influence of fragment nuclear structure e.g. shell closure configuration and odd-even nature on the scission configuration, fragment angular momenta have been deduced from the radiochemically determined independent isomeric yield ratios of the fission products¹¹¹Pd,¹³¹Te,¹³³Te,¹³⁴I and¹³⁸Cs in²⁵²Cf spontaneous fission. The fragments' angular momenta deduced are 8.8± 1.5, 5.8 ±1.0, 6.1±1.1, 11.5±1.1 and 9.8±1.2 ? respectively. The angular momenta data from this work and literature have been analysed to arrive at fragments' deformations at the scission bringing out the influence of the spherical 82n and deformed 66n and 88n shells. The fragment angular momenta were also seen to be inversely correlated to their elemental yields exhibiting odd-even fluctuations. This has been explained in terms of equilibration of the collective degrees of freedom in low energy fission.     

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.     

Decisive role of wriggling vibrations in the formation of angular and spin distributions of products originating from binary and ternary fission of oriented nuclei

It is shown that the multiplicities and angular and energy distributions of neutrons and photons evaporated from thermalized fragments originating from the spontaneous and low-energy induced fission of nuclei, the relative yields of ground and isomeric states of final fragments, and the features of delayed neutrons emitted upon the beta decay of the above fragments can successfully be described by employing nonequilibrium distributions of spins and relative orbital angular momenta of fission fragments formed in the vicinity of the scission point for the fissile nucleus being studied. It is also shown that these distributions, which are characterized by large mean values of the spins and orbital angular momenta directed orthogonally to the symmetry axis of the fissioning nucleus are successfully constructed upon simultaneously taking into account zero-mode transverse wriggling and bending vibrations of a fissile compound nucleus in the vicinity of its scission point, the wriggling vibrations being dominant. It is confirmed that the zero-mode wriggling vibrations considered immediately above are directly involved in the formation of the angular distributions of fragments originating from the spontaneous and low-energy fission of nuclei. This makes it possible to describe successfully such distributions for photofission fragments.     

Energetics of the fission process

The mass asymmetry of fragments from nuclear fission of heavy nuclei is reviewed. While mass asymmetry is a common and well-known phenomenon for low-energy fission of the lighter actinides, more recent experiments have demonstrated that, for the heaviest actinides, the mass distribution switches to a symmetric one. On the other hand, it has been discovered that, though for fissioning nuclei with mass numbersA225 the mass distribution is basically symmetric, an asymmetric component is clearly to be identified for nuclei down to the Pb-region. In the absence of a generally accepted dynamical theory of fission, the above experimental findings are discussed in terms of static energy considerations. Triggered from the outset by the structure of the potential energy surface at the saddlepoint, the energy balance at the scission point between the available energy (Q-value) of the reaction and the Coulomb and deformation energy of the nascent fragments is shown to steer the characteristics of the fragment mass distributions.     

Deformation parameter changes in fission mass yields within the systematic statistical scission-point model

The fission fragment mass-yields are evaluated for pre-actinide and actinide isotopes using a systematic statistical scission point model. The total potential energy of the fissioning systems at the scission point is presented in approximate relations as functions of mass numbers,deformation parameters and the temperature of complementary fission fragments. The collective temperature, Tcoll, and the temperature of fission fragments, Ti, are separated and the effect of collective temperature on mass yields results is investigated. The fragment temperature has been calculated with the generalized superfluid model. The sum of deformation parameters of complementary fission fragments has been obtained by fitting the calculated results with the experimental data. To investigate the transitions between symmetric and asymmetric modes mass yields for pre-actinide and heavy actinides are calculated with this model. The transition from asymmetric to symmetric fission is well reproduced using this systematic statistical scission point model. The calculated results are in good agreement with the experimental data with Tcoll= 2 Me V at intermediate excitation energy and with T_(coll)= 1MeV for spontaneous fission.Despite the Langevin model, in the scission point model, a constraint on the deformation parameters of fission fragments has little effect on the results of the mass yield.     

Recent studies in heavy ion induced fission reactions

Nuclear fission process involves large scale shape changes of the nucleus, while it evolves from a nearly spherical configuration to two separated fission fragments. The dynamics of these shape changes in the nuclear many body system is governed by a strong interplay of the collective and single particle degrees of freedom. With the availability of heavy ion accelerators, there has been an impetus to study the nuclear dynamics through the investigations of nucleus-nucleus collisions involving fusion and fission process. From the various investigations carried out in the past years, it is now well recognized that there is large scale damping of collective modes in heavy ion induced fission reactions, which in other words implies that nuclear motion is highly viscous. In recent years, there have been many experimental observations in heavy ion induced fission reactions at medium bombarding energies, which suggest possible occurrence of various non-equilibrium modes of fission such as quasi-fission, fast fission and pre-equilibrium fission, where some of the internal degrees of freedom of the nucleus is not fully equilibrated. We have carried out extensive investigations on the fission fragment angular distributions at near barrier bombarding energies using heavy fissile targets. The measured fragment anisotropies when compared with the standard saddle point model (SSPM) calculations show that for projectile-target systems having zero or low ground state spins, the angular anisotropy exhibits a peak-like behaviour at the sub barrier energies, which cannot be explained by the SSPM calculations. For projectiles or targets with large ground state spins, the anomalous peaking gets washed out due to smearing of the K-distribution by the intrinsic entrance channel spins. Recently studies have been carried out on the spin distributions of fission fragments through the gamma ray multiplicity measurements. The fission fragments acquire spin mainly from two sources: (i) due to rigid rotation of the nascent fragments at scission and (ii) due to statistical excitation of the spin bearing collective modes in the fissioning nucleus. One of the collective modes — the tilting mode depends on the K quantum number and is responsible for the emission angle dependence of fragment spin. In our studies, we have shown conclusively that the collective statistical spin modes get strongly suppressed for high K values corresponding to large rotational frequencies along the fission axis. These results bring out the importance of the dynamical effects in the heavy ion induced fusion-fission reactions. The present article will review the work carried out on the above aspects in heavy ion fission reactions as well as on the fission time scales, and some of the recent studies on the mass-energy correlations of fission fragments at near-barrier bombarding energies.     

Generation of angular momentum of fission fragments in a cluster model

Based on the dinuclear system concept, the role of bending vibrations in creation of the angular momentum of primary fission fragments is investigated. For ²⁵²Cf spontaneous fission, the angular momenta of the fragments are calculated as a function of the neutron multiplicity and compared with available experimental data. Different cluster compositions of the ²⁵²Cf fission modes at the scission point are considered.     

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.     

Correlations of fission fragment angular momentum with collective and intrinsic degrees of freedom

In the present work angular momenta of the fragments corresponding to¹³²I^m,g have been deduced from the radiochemically determined independent isomeric yield ratios and statistical model based analysis in neutron induced fission of²³⁵U,²³⁹Pu and²⁴⁵Cm and spontaneous fission of²⁵²Cf. These data along with similar data on¹³⁴I, reported earlier from this laboratory, bring out the effects of deformed 66n and spherical 82n shells on fragment angular momentum showing also an inverse correlation of the latter with elemental yields. Quantitative estimates of fragment scission point deformation and the coefficient of change of fragment angular momentum with kinetic/excitation energy have been deduced and are seen to be in good agreement with the expected theoretical estimates.     

Photofission of nuclei with allowance for wriggling vibrations of fissioning nuclei

It is confirmed that one source of the large relative orbital momenta L of fragments in spontaneous and stimulated low-energy nuclear fission is quantum transverse zero-point wriggling vibrations of the fissioning system near its scission point. The angular distributions of fragments of low-energy photofission of actinide nuclei, calculated using the quantum theory of fission, are compared. Vibrations are allowed for by using parameter C _w determined by Nix and Swiatecki. Agreement between the experimental and theoretical angular distributions for ²³⁴U, ²³⁶U, ²³⁸U, ²³⁸Pu, ²⁴⁰Pu, ²⁴²Pu nuclei is observed. The strong sensitivity of the theoretical angular distributions for ²³⁸Pu, ²⁴⁰Pu, ²⁴²Pu nuclei toward the choice of parameters of transient fissioning states at the external and internal fission barriers is demonstrated.     

Ternary fission of nuclei in the adiabatic approximation

On the basis of a generalization of integral formulas for nuclear-decay widths to the three-body case, the spontaneous and the low-energy induced ternary fission of nuclei are investigated by using the adiabatic approximation. The properties of energy distributions, of partial fission widths, and of the angular distributions of fission fragments are analyzed for the case of ternary fission. Conditions are found under which the angular distributions of two heavy fragments originating from ternary fission are similar to the analogous distributions of fragments originating from binary fission. The features of angular distributions are investigated, along with the parities and angular momenta of the third (light) ternary-fission fragment.     

Angular distributions,relative orbital angular momenta,and spins of fragments originating from the binary fission of polarized nuclei

The angular distributions of fragments originating from the binary fission of odd and odd-odd nuclei capable of undergoing spontaneous fission that are polarized by a strong magnetic field at ultralow temperatures and from the low-energy photofission of even-even nuclei that is induced by dipole and quadrupole photons are investigated. It is shown that the deviations of these angular distributions from those that are obtained on the basis of the A. Bohr formula make it possible to estimate the maximum relative orbital angular momentum of fission fragments, this estimate providing important information about the relative orientation of the fragment spins. The angular distributions of fragments originating from subthreshold fission are analyzed for the case of the ²³⁸U nucleus. A comparison of the resulting angular distributions with their experimental counterparts leads to the conclusion that the maximum relative orbital angular momentum of binary-fission fragments exceeds 20, the fragment spins having predominantly a parallel orientation. The possibility is considered for performing an experiment aimed at measuring the angular distributions of fragments of the spontaneous fission of polarized nuclei in order to determine both the spins of such nuclei and the maximum values of the relative orbital angular momenta of fission fragments.     

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.     

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.     

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.     

Even and odd amplitudes of distributions of third particles in nuclear fission

The principal values for the even and odd components of the amplitudes of the angular distributions of α particles emitted as the third particles in true low-energy ternary fission of nuclei are calculated within the quantum theory of fission using natural approximations for the dependence of the potential scattering phases of the α particle on its orbital momenta and experimental angular distributions, unperturbed by the fissioning nucleus rotation, of these third α particles. Knowing the angular dependences of these components, we can estimate the angular dependences of the T-odd ROT and TRI asymmetry coefficients for the ternary fission of actinide nuclei induced by cold polarized neutrons.     

Symmetric and asymmetric scission properties

Existence of two kinds of scission configurations associated with the symmetric and asymmetric fission modes is pointed out in the fission of actinides: elongated and compact configurations. Each symmetric and asymmetric scission property is discussed in terms of shape elongation evaluated from fragment total kinetic energy (TKE). It is found that the shape elongation associated with the asymmetric fission mode is nearly constant for a wide range of fissioning nuclei, while that with the symmetric one is also constant except for low-energy induced fission and spontaneous fission (SF) of heavy nuclei. Prom the systematic study of the scission properties, the bimodal fission observed in SF of the heavy actinides is interpreted as the presence of the two fission paths of the ordinary asymmetric mode and a strongly shell-influenced symmetric one.     

Angular momenta of fission fragments in the α-accompanied fission of 252Cf

For the first time, average angular momenta of the ternary fission fragments ^{100, 102}Zr, ¹⁰⁶Mo, ^{144, 146}Ba and ^{138, 140, 142}Xe from the α-accompanied fission of ²⁵²Cf were obtained from relative intensities of prompt γ-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of ²⁵²Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is ∼1.4 ℏ lower than in binary fission. Consequently, results indicate that the mechanism of the ternary α-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of ¹⁰⁶Mo and ¹⁴⁰Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed.