Cluster aspects of binary and ternary fission

On the basis of the statistical approach and calculation of the potential energy of the scission configurations, binary and ternary fissions are described. The text was submitted by the authors in English     

Sequential character of low-energy ternary and quaternary nuclear fission

An analysis of low-energy true ternary (quaternary) nuclear fission leads to the conclusion that these fission modes have a sequential two-step (three-step) character such that the emission of a third particle (third and fourth particles) and the separation of fission fragments occur at distinctly different instants, in contrast to the simultaneous emergence of all fission products in the case of onestep ternary (quaternary) fission. This conclusion relies on the following arguments. First, the emission of a third particle (third and fourth particles) from a fissile nucleus is due to a nonevaporative mechanism associated with a nonadiabatic character of the collective deformation motion of this nucleus at the stages preceding its scission. Second, the axial symmetry of the deformed fissile compound nucleus and the direction of its symmetry axis both remain unchanged at all stages of ternary (quaternary) fission. This circumstancemakes it possible to explain themechanism of the appearance of observed anisotropies and T — odd asymmeries in the angular distributions of products of ternary (quaternary) nuclear fission. Third, the T —odd asymmetry discovered experimentally in ternary nuclear fission induced by cold polarized neutrons obeys the T —invariance condition only in the case of a sequential two-step (three-step) character of true ternary (quaternary) nuclear fission. At the same time, this asymmetry is not a T —invariant quantity in the case of the simultaneous emission of products of true ternary (quaternary) nuclear fission from the fissile compound nucleus.     

Bimodal fission in binary and ternary spontaneous fission of 252Cf

The hot bimodal fission of ²⁵²Cf is reexamined with new high-statistics data. We constructed a γ-γ-γ coincidence cube for binary fission and LCP-gated γ-γ matrix for ternary fission. By identifying the secondary fission fragments from their γ-ray transitions, we measured the yields for various fission splits. The normal neutron yield distribution is found to be Gaussian for Xe-Ru. However, the binary fission split of Ba-Mo is found to exhibit a bimodal neutron distribution with the “hot mode” corresponding to ≈3.1% of the total yield. In α ternary fission, the first measurements of yields for specific fission splits are presented. The Te-α-Ru and Xe-α-Mo neutron yields fit well with a single mode, but the Ba-α-Zr split shows evidence for an enhanced hot mode with an intensity of ≈13.8% of the normal mode. The text was submitted by the authors in English.     

Quantum and thermodynamical aspects of binary and ternary fission

A short review is given of the recent developments in the quantum theory of low-energy fission. It is emphasized that angular anisotropy and various angular correlations of fission products are possible only if the fissioning nucleus remains nonthermalized during all the stages of fission from the saddle point to scission. The text was submitted by the authors in English.     

Mechanisms of transfer reactions in low-energy collisions with neutron-enriched nuclei

A mechanism of neutron transfer between nuclei in close low-energy collisions is established. It includes three stages: the transformation of the initial one-nuclear state into a two-nucleus state, the transitions of this state to other molecular states, and the transformation of those states into one-nuclear states in which nuclei are separated from one another. An explanation is offered for the fusion of nuclei in the ¹⁸O + ⁵⁸Ni reaction exceeding the cross section, relative to the ¹⁶O + ⁶⁰Ni reaction.     

Nuclear temperatures obtained from light-charged-particle yields in low-energy ternary fission

Nuclear temperatures were determined from yields of isotopes with 1 ?Z? 14 accompanying the spontaneous and neutron-induced fission of heavy elements. The mean temperature derived from the corresponding temperature distributions amounts to 1.10±0.15 MeV. Received: 10 August 2001 / Accepted: 5 October 2001     

Relativistic effects in ternary fission

Relativistic effects can explain the energy shift of - 6 keV reported by Ramayya et al. for the -ray de-exciting the first 2 ⁺ state, at 3368.03 keV, of the ¹⁰Be cluster emitted together with the fragments ¹⁴⁶Ba and ⁹⁶Sr in the ternary fission of ²⁵²Cf; the calculated shift is equal to -6.14 (0.16) keV. An explanation is presented for the apparent absence of Doppler broadening. For the configurations ¹³⁸Xe-¹⁰⁴Zr-¹⁰Be and ¹³⁶Te-¹⁰⁶Mo-¹⁰Be, recently reported by Hamilton et al. , observable shifts of the 3367.43 keV -line are predicted.Received: 2 June 2003, Revised: 14 January 2004, Published online: 10 August 2004PACS: 03.30. + p Special relativity - 23.20.-g Electromagnetic transitions - 25.85.-w Fission reactions     

Quantum and thermodynamic properties of spontaneous and low-energy induced fission of nuclei

It is shown that A. Bohr’s concept of transition fission states can be matched with the properties of Coriolis interaction if an axisymmetric fissile nucleus near the scission point remains cold despite a nonadiabatic character of nuclear collective deformation motion. The quantum and thermodynamic properties of various stages of binary and ternary fission after the descent of a fissile nucleus fromt he outer saddle point are studied within quantum-mechanical fission theory. It is shown that two-particle nucleon-nucleon correlations—in particular, superfluid correlations— play an important role in the formation of fission products and in the classification of fission transitions. The distributions of thermalized primary fission fragments with respect to spins and their projections onto the symmetry axis of the fissile nucleus and fission fragments are constructed, these distributions determining the properties of prompt neutrons and gamma rays emitted by these fragments. A new nonevaporation mechanism of third-particle production in ternary fission is proposed. This mechanism involves transitions of third particles from the cluster states of the fissile-nucleus neck to high-energy states under effects of the shake-off type that are due to the nonadiabatic character of nuclear collective deformation motion.     

Cold and hot binary and ternary fission yields in the spontaneous fission of 252Cf

The spontaneous fission (SF) of ²⁵²Cf has been studied via γ-γ-γ coincidence and light charged particle—γ-γ coincidence with Gammasphere. The yields of correlated Mo-Ba pairs in binary fission with 0–10 neutron emission have been remeasured with an uncompressed cube. The previous hot fission mode with 8–10 neutron emission seen in the Mo-Ba split is found to be smaller than earlier results but still present. New 0n binary SF yields are reported. By gating on the light charged particles detected in ΔE-E detectors and γ-γ coincidence with Gammasphere, the relative yields of correlated pairs in alpha ternary fission with zero to 6n emission are observed for the first time. The peak occurs around the α2n channel. A number of correlated pairs are identified in ternary fission with ¹⁰Be as the light charged particle. We observed only cold, 0n ¹⁰Be and little, if any, hot, xn ¹⁰Be channels.     

Dynamic and statistical simulation of the fission of highly excited atomic nuclei with allowance for the relaxation stage

Statistical and combined dynamic-statistical approaches to simulating the fission of excited nuclei are compared. It is shown that in the statistical approach, the complete suppression of the fission pro cess during time τ _s does not result in double consideration of the emission of light particles. The importance of dynamic simulation of fission at the stage of relaxation of fission rate R _f (t) to its quasistationary value is demonstrated.     

Possible parity-violating effects in ternary fission

Possible parity-violating effects are considered in ternary fission and estimated for different assumptions regarding the mechanism of the process. Here we shall consider differentP-violating effects in neutron-induced ternary fission. As shown in [1], all theP-violating effects in nuclear reactions proceeding via the compound-nucleus stage bear some features in common. All of them are characterized by the factors of dynamical enhancement (caused by the large density of compound-nucleus states), resonance enhancement defined by the ratio of the level spacing for the states of opposite of opposite parity to the width these states [1], and structural enhancement (or hindrance) factors in the exit or entrance channels. Since we believe that neutron-induced ternary fission proceeds via the compound-nucleus stage, one can apply here the basic methods and results [1] used for binary fission, with some modifications necessitated by the presence of 3 particles in the exit channel. Since, however, the analytic analysis of the 3-body problem is rather abstruse and difficult even in classical mechanics, we shall use some reasonable hypothesis about the mechanism of ternary fission in order to obtain the order of magnitude estimates forP-violating effects.     

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.     

Experiment aimed at the study of 252Cf binary and ternary fission

A new experiment devoted to the fission of ²⁵²Cf is described. It continued a series of our experiments based on correlation measurements of γ rays emitted by fission fragment pairs. The measurements of γ-γ and γ-γ-γ coincidences were done at Gammasphere with closed ²⁵²Cf sources. The open source was used for the first time in the last experiment. Fission fragment detectors were arranged in the center hole of Gammasphere. Correlations between fission fragment masses, total kinetic energy, and γ rays were observed. The first, preliminary results of data analysis are discussed. The text was submitted by the authors in English.     

Parity nonconservation in binary and ternary nuclear fission induced by polarized neutrons

Within the quantum-mechanical theory of the nuclear-fission process, the conditions of the emergence of coherent effects in the angular distributions of fragments originating from the binary and ternary fission of polarized nuclei are analyzed with allowance for the properties of transition fission states. In the case of ternary fission, the coefficients of P-odd asymmetry in the angular distributions of a light particle and a third particle, which is taken here to be an alpha particle, are calculated under the assumption that the third particle and two fragments are produced through a one-step mechanism. In order to confirm the ideas developed here, it is proposed to repeat, at a higher level of statistical accuracy, experiments devoted to seeking P-odd asymmetries for alpha particles in the ternary fission of nuclei.     

Quantum nature of ROT and TRI asymmetries in the ternary fission of nuclei

Effects of T-odd asymmetry in ternary-nuclear-fission reactions induced by polarized cold neutrons are considered within quantum theory. It is shown that the asymmetry coefficient can be expressed in terms of experimental angular distributions of third particles in reactions induced by unpolarized neutrons. The explicit form of this coefficient makes it possible to explain the difference in the magnitudes and signs of the TRI and ROT effects observed experimentally for different targets.     

T-odd asymmetries in the cold neutron-induced ternary fission of polarized target nuclei

T-odd asymmetries in the ternary fission of oriented target nuclei, induced by cold unpolarized neutrons and accompanied by emission of ?? particles, are described using quantum fission theory. The differential cross section for the reaction in question is obtained using the spin density matrix of the target nucleus by considering the Coriolis interaction of the spin of a fissioning compound nucleus with the orbital momentum of an ?? particle and interference from the fission amplitudes of various pairs of neutron resonances excited in the compound nucleus as the target nucleus captures a cold neutron. It is shown that in the case under consideration, T-odd asymmetries occur only at odd values of the target nucleus??s order of orientation. It is demonstrated that the concepts of TRI and ROT asymmetries are preserved while the absolute values of the coefficients for these asymmetries can change noticeably in comparison to the similar coefficients for the fission of unoriented target nuclei induced by cold polarized neutrons.     

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.     

Quantum mechanical method of fragment’s angular and energy distribution calculation for binary and ternary fission

In the framework of quantum-mechanical fission theory, the method of calculation for partial fission width amplitudes and asymptotic behavior of the fissile nucleus wave function with strong channel coupling taken into account has been suggested. The method allows one to solve the calculation problem of angular and energy distribution countation for binary and ternary fission. The text was submitted by the authors in English.     

An analysis of the binary and ternary fission of uranium induced by 12.2 GeV protons

In this work the binary and ternary fission of uranium induced by 12.2 GeV protons has been investigated with a polycarbonate detector registering the tracks of particles with mass numbersA>16. The basic characteristics of binary and ternary fission are discussed and the corresponding cross-sections are given. The values of the cross-sections for binary and ternary fission are calculated to be σ _b =(915 ± 120) mb and σ _t -(12.8 ± 2.5) mb, respectively.     

Unified quantum description of TRI and ROT effects in ternary fission

It is shown that consideration of the Coriolis interaction makes it possible to explain both T-odd effects observed in ternary fission induced by polarized neutrons. A possible reason for the difference in the effects observed for ²³³U and ²³⁵U targets is discussed.