Subthreshold photofission of even-even nuclei

Within quantum-mechanical fission theory, the angular distributions of fragments originating from the subthreshold photofission of the even-even nuclei ²³²Th, ²³⁴U, ²³⁶U, ²³⁸U, ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu are analyzed for photon energies below 7 MeV. Special features of various fission channels are assessed under the assumption that the fission barrier has a two-humped shape. It is shown that the maximum value of the relative orbital angular momentum L _m of fission fragments can be found upon taking into account deviations from the predictions of A. Bohr’s formula for the angular distributions of fission fragments. The result is L _m ≈ 30. The existence of an “isomeric shelf” for the angular distributions of fragments from ²³⁶U and ²³⁸U photofission in the low-energy region is confirmed.     

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.     

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.     

<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.     

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.     

Combined dynamical and statistical approach to describing induced fission of heavy nuclei

A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV and the d+^242,240Pu reactions at deuteron energies in the range E _d = 20–30 MeV, fission times in the α + ²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV, and angular distributions of fission fragments in the α + ²³⁸U, ²³⁷Np reactions at alpha-particle energies in the range E _α = 20–100 MeV.     

P-odd,T-odd asymmetries in the binary and ternary fissioning of oriented target nuclei by cold polarized neutrons

Since P-odd and T-odd asymmetries are generally not observed during the fissioning of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons, analogous asymmetries in angular distributions of products from binary and ternary fissioning of oriented target nuclei by cold polarized neutrons are thoroughly analyzed within the quantum theory of fission for finding these correlations. It is demonstrated that these correlations occur only when interference of the compound fissioning nucleus states with different spins is considered. Contributions from target nucleus orientations of different orders to coefficients of the asymmetries in question for fission fragments are estimated. Characteristics of analogous asymmetries for prescission and evaporation third particles are analyzed.     

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.     

Mass distribution in the bremsstrahlung-induced fission of Th,U and Pu

The yields of various fission products in the 10 MeV bremsstrahlung-induced fission of ²³²Th, ²³⁸U and ²⁴⁰Pu were determined using a recoil catcher and off-line γ-ray spectrometric techniques. From the yield data, mass yield distributions were obtained using charge distribution corrections. The higher yields of fission products around mass numbers 133–135, 138–140, 143–145 and their complementary products in the neutron and bremsstrahlung-induced fission of ²³²Th, ²³⁸U and ²⁴⁰Pu were interpreted based on nuclear structure effects. From the mass yield distribution, the peak-to-valley (P/V$P/V$) ratio was also obtained for the above fissioning systems. The present data, along with data from the literature on different bremsstrahlung- and mono-energetic neutron-induced fissions of ²³²Th and ²³⁸U are interpreted to examine the influence of excitation energy on the peak to valley ratio. For the same compound nucleus ²⁴⁰Pu^?, the data in the 10–30 MeV bremsstrahlung-induced fission of ²⁴⁰Pu were compared with similar data of thermal to 14 MeV neutron-induced fission of ²³⁹Pu and the spontaneous fission of ²⁴⁰Pu to examine the role of excitation energy due to bremsstrahlung radiation and mono-energetic neutrons.     

Effects of rotation of fissioning nuclei in the angular distributions of prompt neutrons and gamma rays originating from the polarized-neutron-induced fission of 233U and 235U nuclei

The results of an experiment devoted to searches for effects of rotation of fissioning nuclei in the angular distributions of prompt neutrons and gamma rays originating from the polarized-neutron-induced fission of ²³³U nuclei are presented. The effects discovered in these angular distributions are opposite in sign to their counterparts in the polarized-neutron-induced fission of ²³⁵U nuclei. This is at odds with data on the relative signs of respective effects in the angular distribution of alpha particles from the ternary fission of the same nuclei and may be indicative of problems in the model currently used to describe the effect in question. The report on which this article is based was presented at the seminar held at the Institute of Theoretical and Experimental Physics and dedicated to the 90th anniversary of the birth of Yu.G. Abov, corresponding member of Russian Academy of Sciences, Editor in Chief of the journal Physics of Atomic Nuclei.     

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.     

Relative measurements of photofission cross sections with the use of a bremsstrahlung spectrum

This survey is devoted to the investigation of fission probability by measuring photofission yields using a bremsstrahlung spectrum of the microtron with the relative measurement method in the region of energies from the threshold to the upper boundary of the fissility plateau (E < 11 MeV). The results were obtained using a unique technique for nineteen nuclei from ²³²Th to ²⁴⁹Cf. For some nuclei in the threshold energy region, detailed measurements were performed which provided the possibility of observation of new resonances in the photofission cross section. The observed resonance effects are discussed. For ²³⁴U and ^{238, 240, 242}Pu, theoretical analysis was performed to obtain the fission barrier parameters for fission channels with particular quantum states. Data of other measurements of photofission cross sections are given, along with the results obtained in the surveyed series of measurements. The data obtained using the relative measurement method is compared with data for other reactions that result in fission of the nuclei under study.     

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.     

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.     

Photofission of 238Pu, 240Pu, and 242Pu in the energy range 5–10 MeV

The cross sections for the photofission of plutonium isotopes ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu in the energy range 5–10 MeV have been measured by using a beam of bremsstrahlung photons from the microtron installed at the Institute of Physics and Power Engineering (Obninsk). The energy regions below the fission barrier and above 6 MeV have been scanned with pitches of 0.05 and 0.1 MeV, respectively. In deriving the absolute cross section for ²³⁸Pu photofission, ²³⁸U photofission has been employed as a reference reaction. In measurements involving ²⁴⁰Pu and ²⁴²Pu nuclei, the neptunium isotope ²³⁷Np, which is characterized by a more regular dependence of the photofission cross section on excitation energy than ²³⁸U, has been chosen for the first time as a reference nucleus. The measured cross sections as functions of energy show resonance structures in the vicinity of the fission threshold that are consistent with those previously observed in the energy dependences of fissilities for corresponding direct reactions. The partial-wave cross sections for the J ^π K = 1^?0, 1^?1, and 2⁺0 photofission channels have been determined as functions of energy. At energies below some 5.5 MeV, the total cross section for photofission of each plutonium isotope being studied receives a significant contribution from quadrupole interaction. Within the one-dimensional model of a two-humped fission barrier, the parameters of the barriers for ²³⁸Pu, ²⁴⁰Pu, and ²⁴²Pu have been extracted from data and have then been compared with estimates based on previous measurements.     

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.     

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.     

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.     

ANGULAR DISTRIBUTIONS OF FISSION FRAGMENTS AND THE SHAPES OF THE SADDLE POINT OF COMPOUND NUCLEI

We have measured the angular distributions of fission fragments for a series of compound nuclei formed in the bombardment of ¹⁶⁹Tm, ¹⁷⁵Lu, ¹⁸¹Ta, ¹⁹⁷Au, ²⁰⁹Bi, ²³²Th and ²³⁸U by 78 MeV ¹²C ions and in the bombardment of natural lead by 96.6, 92.2, 88.1, 79.0 and 75.6 MeV ¹⁴N ions with mica track detectors. All the measured angular distributions can be fitted by the theoretical formula given by Halpern and Strutinski. The effective moments of inertia of the fissioning nuclei at the saddle point are derived from the angular distribution anisotropies. A comparison is made for the shapes of experimental saddle point with the theoretical predictions by the liquid drop model.     

Hyperfine interactions and charge distributions of actinide ions recoiling into vacuum

The angular distribution of conversion electrons from the 4⁺→2⁺ transition in the ground-state rotational band of²⁴⁰Pu has been measuredvia the²³⁸U (α,2n)²⁴⁰Pu reaction. The electrons are emitted in flight from the Pu nuclei recoiling into vacuum atv/c?0.2%. The attenuation of the angular distribution by extranuclear fields is found to be less than 20% within 120 ps. The hyperfine interactions are discussed with particular attention to the high charge states of actinide recoil ions following internal conversion. Charge distributions ranging up to 45⁺ have been observed for²⁴⁰Cm nuclei in the²³⁹Pu(α,3n) reaction.