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.     

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.     

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.     

Fission fragment angular momentum in ODD-Z fissioning systems

Independent isomeric yield ratios of ¹²⁸Sb, ¹³⁰Sb, ¹³², ¹³¹Te, ¹³³Te, ¹³²I, ¹³⁴I, ¹³⁶I, ¹³⁵Xe and ¹³⁸Cs have been determined in the fast neutron induced fission of ²³⁷Np and ²⁴¹Am using radiochemical and gamma spectrometric technique. From the independent isomeric yield ratios, fragment angular momenta (J_rms) have been deduced using spin-dependent statistical model analysis. Comparison of these data with the literature data for even-Z fissioning systems shows the following important features: (i) Angular momenta for fragments with spherical 82n shell and even-Z products are lower compared to the fragments with out the 82n shell and odd-Z products indicating the effect of nuclear structure. (ii) Angular momentum of even-Z products in all the fissioning systems are comparable where as for odd-Z products it is slightly higher in the odd-Z fissioning systems than in the adjacent even-Z fissioning systems. This indicates the role of single particle on fragment angular momentum in odd-Z fissioning systems. Received: 26 March 1999 / Revised version: 16 October 1999     

Experimental studies of nuclear fission dynamics near the scission point

Conditions for formation of angular and energy distributions of light particles emitted in ternary fission of ^{233, 235}U, ²³⁹Pu, and ²⁴⁵Cm nuclei induced by cold polarized neutrons have been studied in the course of investigating T-odd asymmetry in emission of these particles with respect to the plane formed by the fission axis and the polarization axis of the fissioning nucleus. The results obtained lead to the conclusion that in ternary fission charged particles are emitted by the fissioning nuclear system rotating around the polarization direction.     

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.     

Odd-even effect in fragment angular momentum in low-energy fission of actinides

Quantitative explanation for the odd-even effect on fragment angular momenta in the low-energy fission of actinides have been provided by taking into account the single particle spin of the odd proton at the fragment’s scission point deformation in the case of odd-Z fragments along with the contribution from the population of angular momentum bearing collective vibrations of the fissioning nucleus at scission point. The calculated fragment angular momenta have been found to be in very good agreement with the experimental data for fragments in the mass number region of 130–140. The odd-even effect observed in the fragment angular momenta in the low-energy fission of actinides has been explained quantitatively for the first time.      

<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.     

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.     

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.     

Influence of collective rotational degrees of freedom in medium energy fission

In the present work rms angular momenta have been deduced for the fission fragments corresponding to¹³¹Te^m,g and¹³³Te^m,g in²³²Th(α _{40 MeV},f) and²³⁸U(α _{40 MeV},f) systems from the radiochemically determined independent isomeric yield ratios and statistical model based analysis. For¹³¹Te and¹³³Te the rms angular momenta deduced are 5.9±1.0 and 7.9±1.2 ? respectively in²³²Th(α _{40 MeV},f) and 7.2±0.6 and 8.0±0.8 ? respectively in²³⁸U(α ₄₀ MeV,f). Comparison of the present data with the literature data for these fragments in the same compound nuclei²³⁶U^* and²⁴²Pu^* at lower excitation energies shows increase in the fragment angular momentum with increasing excitation energy and angular momenta of the fissioning nuclei. Fragment angular momentum deduced theoretically for asymmetric and deformed fragments on the basis of thermal equilibration of the collective rotational degrees e.g., rigid rotation, wriggling, tilting, bending and twisting modes considering the effect of multichance fission, are in good agreement with the experimental observations.     

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.     

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.     

Fragment angular distributions from fission of238U,209Bi and197Au by 140-MeV4He Ions

The fission fragment angular distributions from reactions of 140-MeV⁴He ions with²³⁸U,²⁰⁹Bi and¹⁹⁷Au have been studied. From the anisotropies in the angular distributions, values for? _eff, the effective moment of inertia at the fission saddle point, have been estimated and compared with results obtained at lower bombarding energies. The derivation of? _eff values has included corrections for the effects of incomplete fusion mechanisms on the orbital angular momentum distribution of the fissioning nuclei and for neutron evaporation prior to fission. The results are also compared with heavy-ion-induced fission data for systems of similar fissility. Also, examination of the forward-backward symmetry of the²³⁸U angular distribution substantiates other results which show that the fraction of fission reactions which follow complete fusion of the target and projectile is less than 0.5 for 140-MeV⁴He-ion bombardment of²³⁸U.     

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.     

原子核的对相互作用对裂变碎块角分布的影响

我们把Migdal的关于基态原子核转动惯量的半经典近似的推导,推广到激发态(T≠0)情形;并由此计算了裂变碎块角分布参数K₀²。与实验数据比较的结果表明:在现有近似下,原子核的对相互作用能解释U区裂变核在低激发能(E_exc≤15MeV)时,K₀²“反常”小的现象,同时利用对相互作用与角动量的依赖关系,可以定性地解释Pb附近裂变核并没有这种“反常”现象。     

Analysis of angular momentum dependence of fission fragment mass-energy distribution within Langevin dynamics

Dependence of fission fragment mass-energy distribution on the angular momentum is studied within Langevin dynamics. The calculations are performed in the framework of the generalized temperature-dependent finite-range liquid drop model. The analysis is done for five compound nuclear systems representing heavy fissioning nuclei, medium fissioning nuclei, and a light fissioning one with the angular momentum varied in a wide range from l = 0 to 70?. The coefficients d〈E _K 〉/dl ² and $d\sigma _{{\rm E}_{\rm K} }^2 /dl^2 $ are extracted. Previous analysis of the dσ _M ² /dl ² coefficient is generalized. Excitation energy dependence of the fission fragment mass-energy distribution is also found. The qualitative comparison of the extracted values with the experimental data reveals good agreement for all the cases. The calculated values of the coefficients dσ _M ² /dl ² and $d\sigma _{{\rm E}_{\rm K} }^2 /dl^2 $ are functions of the angular momentum, in contrast to the experimental estimations.     

An interpretation of the structure of subthreshold fission cross section of240Pu

The structure recently observed in the subthreshold fission cross section of²⁴⁰Pu is interpreted as being due to intermediate states of the fissioning nucleus associated with the second minimum of the potential energy as a function of deformation postulated byStrutinsky.     

Formation and decay of hot nuclei

Formation and decay properties of composite-like nuclei produced by ⁵⁸Ni projectiles bombarding ²³²Th target nuclei are investigated at different energies by means of fission fragment angular correlation measurements. Experimental results are compared to the excition model and excitation energies in the fissioning nuclei are deduced. By comparing the present data with the results on other systems, the influences of entrance channel conditions and composite-like nuclei temperatures are discussed to explain the evolution of the high linear momentum transfer region. The coexistence of both massive transfer mmechanism and head-on collisions followed by preequilibrium is suggested.     

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.