Angular distributions of fragments originating from the spontaneous fission of oriented nuclei and problem of the conservation of the spin projection onto the symmetry axis of a fissile nucleus

The concept of transition fission states, which was successfully used to describe the angular distributions of fragments for the spontaneous and low-energy induced fission of axisymmetric nuclei, proves to be correct if the spin projection onto the symmetry axis of a fissile nucleus is an integral of the motion for the external region from the descent of the fissile nucleus from the external fission barrier to the scission point. Upon heating a fissile nucleus in this region to temperatures of T ≈ 1 MeV (this is predicted by many theoretical models of the fission process), the Coriolis interaction uniformly mixes the possible projections of the fissile-nucleus spin for the case of low spin values, this leading to the loss of memory about transition fission states in the asymptotic region where the angular distributions of fragments are formed. Within quantum-mechanical fission theory, which takes into account deviations from A. Bohr’s formula, the angular distributions of fragments are calculated for spontaneously fissile nuclei aligned by an external magnetic field at ultralow temperatures, and it is shown that an analysis of experimental angular distributions of fragments would make it possible to solve the problem of spin-projection conservation for fissile nuclei in the external region.     

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.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

On Ternary Fission Induced by Neutrons

Experiments on measuring the rotational effect of the ²³⁴U fissile nucleus at the scission point showed that the fissile nucleus rotates as a right screw with respect to the longitudinally polarized neutron beam direction in the ternary fission of the ²³³U target nucleus induced by polarized s-neutrons; in the binary fission of the same nuclei it rotates in the opposite direction. Moreover, it was found that ternary fission “prefers” the spin state of J = I +1/2. This phenomenon cannot be explained within the existing concepts of ternary fission as one of the two “final” states after neck rupture. The same “parent” ²³⁴U nucleus cannot rotate in opposite directions in the two different final states. It should be assumed that ternary fission is a special branch of descent from the saddle point to the point of neck rupture. It can also be assumed that this branch is formed at the saddle point in a configuration favorable for cluster formation. Why does it prefer the spin state of J = I + 1/2? This is an interesting question for further studies.

     

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.     

Nonuniform character of the population of spin projections K for a fissile nucleus at the scission point and anisotropies in the angular distributions of fragments originating from the induced fission of nuclei

It is shown that the emergence of anisotropies in the angular distributions of fragments originating from the spontaneous and induced fission of oriented actinide nuclei is possible only if nonuniformities in the population of the projectionsM (K) of the fissile-nucleus spin onto the z axis of the laboratory frame (fissile-nucleus symmetry axis) appear simultaneously in the vicinity of the scission point but not in the vicinity of the outer saddle point of the deformation potential. The possibilities for creating the orientation of fissile nuclei for spontaneous and induced fission and the effect of these orientations on the anisotropies under analysis are considered. The role of Coriolis interaction as a unique source of the mixing of different-K fissile-nucleus states at all stages of the fission process is studied with allowance for the dynamical enhancement of this interaction for excited thermalized states of the nucleus involved that is characterized by a high energy density. It is shown that the absence of thermalization of excited states of the fissile nucleus that appear because of the effect of nonadiabaticity of its collective deformation motion in the vicinity of the scission point is a condition of conservation of the influence that transition fission states formed at the inner and outer fission barriers exerts on the distribution of the spin projections K for lowenergy spontaneous nuclear fission. It is confirmed that anisotropies observed in the angular distributions of fragments originating from the fission of nuclei that is induced by fast light particles (multiply charged ions) are due to the appearance of strongly excited equilibrium(nonequilibrium) states of the fissile nucleus in the vicinity of its scission point that have a Gibbs (non-Gibbs) distribution of projections K.     

Mechanism of the appearance of angular distribution anisotropy for evaporation neutrons in center-of-mass systems emitting their thermalized fission fragments

Anisotropy in the angular distributions of cascade-evaporation neutrons in center-of-mass systems emitting their fission fragments is analyzed in the context of the quantum theory of fission. It is emphasized that such anisotropy is caused not by bending but by wriggling oscillations of the fissioning nucleus in the vicinity of its point of scission; these lead to the appearance of high-value spins of primary fission fragments [(J)\vec]₁\vec J_1 and [(J)\vec]₂\vec J_2 oriented in a plane perpendicular to direction [(n)\vec]₀\vec n_0 of the axis of symmetry of the fissioning nucleus at the instant of scission. This direction coincides with the asymptotic direction of the emission of fission fragments with a high degree of accuracy. The analytical dependences of the anisotropy coefficient on the orbital momentum l and total spin j in angular distributions of cascade-evaporation neutrons are calculated using the methods developed in analyzing angular distributions of cascade-evaporation gamma quanta. The proper spin of a neutron is shown to have almost no effect on the aforesaid anisotropy coefficient due to the weak dependence of the neutron transmission coefficient T _lj ([`(e)]\bar \varepsilon ) on the values of j.     

Effect of the orientation degree of freedom on the rate and time of fission of highly excited nuclei

The effect of the dimensionality of the dynamical model used on the fission rate and mean time is studied within a multidimensional stochastic approach to fission dynamics. These features of fission of excited compound nuclei are calculated within four-dimensional Langevin dynamics, where the coordinate K, which is the projection of the total angular momentum onto the symmetry axis of the nucleus being considered, is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, a} parametrization. The evolution of this orientation degree of freedom (K mode) is described in terms of the Langevin equation in the overdamped regime. The effect of the orientation degree of freedom on the rate and mean time of fission of compound nuclei is studied. The introduction of the orientation degree of freedom is shown to lead to a substantial decrease in the fission rate and, accordingly, to an increase in the mean fission time upon going over from the three- to the four-dimensional model. The reactions induced by the interaction of ¹⁴N and ¹⁶O projectile ions with ¹⁹⁷Au, ²⁰⁸Pb, ²³²Th, and ²³⁸U nuclei at energies above the Coulomb fusion barrier are considered. The effect of the increase in the fission time because of the introduction of the K mode is so strong that it compensates almost completely for an opposite effect from introducing, in the one-dimensional model, the second and third collective coordinates that take into account, respectively, the evolution of the neck in the nuclear shape and the mass asymmetry. Ultimately, the difference between the results in the four- and one dimensional problems is not more than 5 to 25% for the reactions considered here.     

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.     

Scission gamma rays

Gamma rays probably emitted by the fissioning nucleus ²³⁶U* at the instant of the break of the neck or within the time of about 10⁻²¹ s after or before this were discovered in the experiment devoted to searches for the effect of rotation of the fissioning nucleus in the process ²³⁵U($ \vec n $ \vec n , γf) and performed in a polarized beam of cold neutrons from the MEPHISTO Guideline at the FRM II Munich reactor. Detailed investigations revealed that the angular distribution of these gamma rays is compatible with the assumption of the dipole character of the radiation and that their energy spectrum differs substantially from the spectrum of prompt fission gamma rays. In the measured interval 250–600 keV, this spectrum can be described by an exponential function at the exponent value of α = −5 × 10⁻³ keV⁻¹. The mechanism of radiation of such gamma rays is not known at the present time. Theoretical models based on the phenomenon of the electric giant dipole resonance in a strongly deformed fissioning nucleus or in a fission fragment predict harder radiation whose spectrum differs substantially from the spectrum measured in the present study.     

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.     

Beyond the N = 50 shell closure: High-spin excitations of 87Kr and ground-state spin of 87Br

The ⁸⁷Kr nucleus has been produced as fission fragment in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. High-spin states of this neutron-rich isotope have been identified for the first time. Its level scheme has been obtained up to 6.3MeV excitation energy and spin I ∼ 23/2ℏ. Its structure is interpreted by analogy with those of the heavier isotones. The proposed configurations involve both proton and neutron excitations from several sub-shells located close to the Fermi levels, particularly νd_5/2, πp_3/2f_5/2 and πg_9/2. Moreover, a revised spin value of 5/2^- for the ⁸⁷Br ground state is proposed.     

P-odd asymmetries for the binary fission of oriented target nuclei, induced by cold polarized neutrons

P-odd asymmetries in binary fission of oriented target nuclei induced by cold polarized neutrons are described for the first time using methods of the quantum theory of fission. A spin matrix of the compound nucleus density is constructed with allowance for the interference of the fission amplitudes of various pairs of neutron resonances excited in the given nucleus during the capture of a cold polarized neutron by the oriented target nucleus. In the differential cross sections for this reaction we obtain not only P-odd T-even correlations with the angular dependence different from that of the earlier investigated correlations in the fission of unoriented target nuclei by polarized neutrons but also P-odd T-odd correlations that do not occur in the fission of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons.     

<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.     

High-spin excitations of 84 35Br49 and 85 35Br50: Mapping the proton sub-shells towards 78Ni

The ^{84, 85}Br nuclei have been produced as fission fragments in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. The high-spin states of the odd-odd ⁸⁴Br nucleus have been identified for the first time, the observed structure being built on the known 6^- isomeric state. High-spin states of ⁸⁵Br have been observed up to 5.4MeV excitation energy and spin I ∼ 21/2. From angular correlation analysis, spin values have been assigned to most of the ⁸⁵Br excited states up to 4MeV. None of these excited states has been found to exhibit a delayed decay having T _1/2 > 10ns. All the observed states in ^{84, 85}Br can be described by various proton excitations involving at least the two sub-shells ( πf _5/2 and πp _3/2) located just above the Z = 28 shell closure.     

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.      

Angular and spin distributions of primary fission fragments

It is demonstrated that the formation of the fissile nucleus prescission configuration with two fission prefragments connected by a neck is possible only with the simultaneous appearance of high values of relative orbital moments [(L)\vec]\vec L of the abovementioned prefragments, independently of their form. It is found that conservation of the fissile nucleus spin when its values are low leads to the formation of high values of prefragment spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 that are oriented antiparallel to the moment [(L)\vec]\vec L and perpendicular to the fissile nucleus symmetry axis. It is shown that for two deformed fission prefragments, the pumping mechanism of high values of their relative moments [(L)\vec]\vec L and spins [(J)\vec]₁\vec J_1, [(J)\vec]₂\vec J_2 is due to the combined influence of bending- and wriggling- vibrations, the latter predominating. It is found that the high values of spherical fission prefragments are not related to thermal excitations but is determined by the excitation of the initial high-spin double quasiparticle states, due to the nonadiabatic collective deformation motion of the fissile nucleus in the vicinity of its rupture point.     

Manifestation of the nuclear viscosity effects in induced fission reactions at excitation energies below 30 MeV

A large set of experimental observables for the ²³²Th(α, xnf)reaction was analyzed theoretically within the dynamic-statistical approach, making it possible to interconsistently consider the manifestation of nuclear viscosity, the double-humped structure of the fission barrier, and the phenomenon of shell effect damping with temperature. Analyses were performed for the energy dependence of the finite lifetime effect in the investigated reaction, obtained using the crystal blocking technique; the fission probability isotopes produced in this reaction during the development of a neutron emission cascade; and the anisotropy of angular distributions of fission fragments. It is shown that this analysis allows us to obtain information regarding nuclear viscosity and its energy dependence at relatively low excitation energies (<30 MeV).     

Negative resistivity anomaly of unstable 4f impurities in metals

The minimum of the resistivity of dilute alloys with unstable Ce and Pr impurities is usually attributed to an abnormal increase of the spin scattering cross section of the inner 4f electron at low temperatures (4f Kondo effect). By comparison with the resistivity increments of stable rare earth impurities, we show that nearT=0 the anomalous increment is in fact consistent with simple potential scattering from the outer 5d6s valence electrons of fractional valent impurities. The observed decrease of the increment at elevated temperatures is too large to be due to 4f spin scattering in the unitarity limit or to a valence change. This decrease therefore implies some kind of shunting of the impurity potential scattering by an unknown mechanism connected with the valence instability of the impurity.