Description of true and delayed ternary nuclear fission accompanied by the emission of various third particles

The mechanisms and the features of the main types of nuclear ternary fission (that is, true ternary fission, in which a third particle is emitted before the rupture of the fissioning nucleus into fragments, and delayed ternary fission, in which a third particle is emitted from fission fragments going apart) are investigated within quantum-mechanical fission theory. The features of T-odd asymmetry in true ternary nuclear fission induced by cold polarized neutrons are investigated for the cases where alpha particles, prescission neutrons, and photons appear as third particles emitted by fissioning nuclei, the Coriolis interaction of the spin of the polarized fissioning nucleus with the spin of the third particle and the interference between the fission amplitudes for neutron resonances excited in the fissioning nucleus in the case of projectile-neutron capture being taken into account. For the cases where third particles emitted by fission fragments are evaporated neutrons or photons, T-odd asymmetries in delayed ternary nuclear fission induced by cold polarized neutrons are analyzed with allowance for the mechanism of pumping of large fission-fragment spins oriented orthogonally to the fragment-emission direction and with allowance for the interference between the fission amplitudes for neutron resonances.     

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.     

Mechanisms of excitation of <Emphasis Type="Italic">T</Emphasis>-odd correlations for prescission gamma rays and structure of these correlations

Conditions for the appearance and observation of prescission gamma rays emitted by a fissioning nucleus prior to its separation into fission fragments were investigated within quantum-mechanical fission theory. It is shown that these conditions are realizable in the gamma decay of isovector electric giant dipole resonances in a fissile nucleus that are excited because of nonadiabaticity of the collective deformation motion of the nucleus at the ultimate stages of its prefission evolution. Angular and energy distributions of prescission gamma rays emitted by unpolarized fissioning nuclei are analyzed. Features of T-odd correlations in angular distributions of gamma rays arising in the fission of unpolarized target nuclei that is induced by polarized cold neutrons are investigated, and it is shown that these correlations are similar in nature to T-odd ROT correlations discovered earlier for alpha particles emitted in the ternary fission of nuclei.     

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.     

<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.     

Mechanisms for the appearance of prescission γ-rays and their related T-odd asymmetries

Conditions for the appearance and observation of prescission γ-rays emitted by a fissioning nucleus before its separation into fission fragments were investigated within the quantum theory of fission. It was demonstrated that these conditions can be fulfilled in the γ-decay of giant electric isovector dipole resonances in a fissioning nucleus that become excited due to the nonadiabaticity of the collective deformation motion of the nucleus at the final stages of its prefission evolution. Angular and energy distributions of prescission γ-rays emitted by unpolarized fissioning nuclei were analyzed. Characteristics of T-odd asymmetries in angular distributions of prescission γ-rays were investigated for fission of unpolarized target nuclei induced by polarized cold neutrons, and these correlations were shown to be similar in nature to the T-odd ROT correlations earlier found for α-particles emitted in ternary nuclear fission.     

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.     

Rotation of fissioning nuclei in reactions with polarized neutrons

Advantages and disadvantages of taking into account rotation of polarized nuclei in classical trajectory calculations of ternary fission are considered. Expressions for polarization of the fissioning deformed compound nucleus which allow for the quantum number K in the fission channel are derived.     

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.     

Emission order of light particles and light fragments from hot nuclei followed by binary fission

Emission orders of light charged particles and Li fragments from highly excited fissioning nuclei in the reaction of ⁴⁰Ar+¹⁹⁷Au at E _beam /A=25 MeV have been studied by measuring difference velocity distributions of two correlated particles at small relative angles in coincidence with two fission fragments. By comparing the data with three-body trajectory calculations, we found that high velocity deuterons are emitted prior to high velocity Li fragments but low velocity deuterons are emitted after low velocity Li fragments. On the other hand, no preferential emission was observed among light particles, such as protons and deuterons. Furthermore, the emission orders are found to depend only weakly on the mass asymmetry of fission fragments. Received: 3 June 1997 / Revised version: 23 July 1997     

<Emphasis Type="Italic">T</Emphasis>-odd angular correlations in the emission of prompt gamma rays and neutrons in nuclear fission induced by polarized neutrons

Study of the T-odd three-vector correlation in the emission of prompt neutrons from ²³⁵U fission by polarized cold neutrons has been continued at the facility MEPHISTO of the FRM II reactor (Technical University of Munich). The sought correlation was not found within experimental error of 2.3 × 10⁻⁵. The upper limit for the asymmetry coefficient has been set to |D _n | < 6 × 10⁻⁵ at 99% confidence level, whereas for ternary fission correlation coefficient D _α = (170±20) × 10⁻⁵. This limit casts doubt on a model that explains the three-vector correlation in ternary fission by the Coriolis mechanism. At the same time, five-vector correlation in the emission of prompt fission neutrons has been measured, which describes the rotation of the fissioning nucleus at the moment it breaks (ROT effect). At the angle 22.5° to the fission axis, the correlation coefficient was found to be (1.57 ± 0.20) × 10⁻⁴, while at the angle of 67.5° it is zero within the experimental uncertainty. The existence of ROT effect in the emission of prompt fission neutrons can be explained by the anisotropy of neutron emission in the rest frame of the fragment (fission fragments are aligned with respect to the axis of deformation of the fissioning nucleus), similar to the mechanism of ROT effect in the emission of prompt γ-rays.     

P-odd, P-even, and T-odd asymmetries in true quaternary fission of nuclei

The coefficients of P-odd, P-even, and T -odd asymmetries for a third and a fourth prescission particle emitted in the true quaternary fission of nuclei that was induced by polarized cold neutrons were studied on the basis of quantum-mechanical fission theory. By using non-evaporation (nonadiabatic) mechanisms of light-particle emission, these coefficients were compared with the analogous coefficients for prescission third particles emitted in the ternary fission of 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.     

New data on the ternary fission of 252Cf from the Gammasphere facility

Ternary fission of ²⁵²Cf was studied at Gammasphere using eight ΔE×E particle telescopes. Helium, beryllium, boron, and carbon light charged particles (LCPs) emitted with kinetic energy more than 9, 21, 26, and 32 MeV, respectively, were identified. The 3368-keV γ transition from the first 2⁺ excited state in ¹⁰Be was found and the population probability ratio N(2⁺)/N(0⁺) = 0.160 ± 0.025 was estimated. No evidence was found for 3368-keV γ rays emitted from a triple molecular state. For the first time, charge distributions are obtained for ternary fission fragments emitted with helium, beryllium, and carbon LCPs.     

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.     

P-odd,T-even symmetries for products of the spontaneous fissioning of oriented nuclei

P-Odd, T-even asymmetries in angular distributions of products from the binary and ternary spontaneous fissioning of nuclei oriented in strong magnetic fields at ultralow temperature are described for the first time by means of the quantum theory of fission. Using the spin density matrix of a fissioning nucleus and considering the notable octupole deformations of the nucleus that appear in the vicinity of its scission point, we show that coefficients of the asymmetries in question are governed by the orientation parameters of a fissioning nucleus with Q = 1 and Q = 3. The coefficients obtained in this work are compared to the analogous coefficients in the fissioning of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons.     

The quantum and thermodynamical characteristics of fission taking into account adiabatic and nonadiabatic modes of motion

In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed. The text was submitted by the author in English.     

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.     

Basic results of investigations of scission neutrons in nuclear fission at low excitation energies

To estimate the main characteristics of neutrons emitted shortly before the scission of a fissioning nucleus, various experiments sensitive to the presence of these scission neutrons in thermal-neutron-induced fission of ²³⁵U and spontaneous fission of ²⁵²Cf were performed. The results of the experiments were analyzed within theoretical calculations allowing for various possible neutron-emission mechanisms, including the possibility of the emergence of neutrons from the scission of a nucleus.     

Probabilities for the emission of light particles and their energy and angular distributions for true quaternary nuclear fission

On the basis of quantum-mechanical fission theory, the features of true quaternary nuclear fission are studied by treating this fission process as a sequence of three processes following one another in the course of time. The first two processes are the escape of the first and then the second of the two light particles emitted from the neck of a fissioning nucleus because of a nonadiabatic character of the collective deformation motion of this nucleus. Finally, the third process is the separation of the fissioning nucleus into two rather heavy fission fragments. The differences that arise in the emission probabilities and in the angular and energy distributions upon going over from the first emitted to the second emitted prescission third and fourth particles are analyzed by invoking experimental data on the spontaneous and thermalneutron-induced fission of nuclei, and it is shown that these differences are caused by the changes both in the geometric configuration of the fissioning nucleus and in the shell structure of its neck after the first prescission particle is emitted from it.