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.     

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.     

Effect of the Input Channel of Heavy-Ion Reactions on Fission-Fragment Spins

Within a dynamical approach, the average spins of fission fragments originating from the ¹²C + ^235,236U and ¹³C + ²³⁵U complete fusion reactions at c.m. energies in the range of E_c.m. = (55–75) MeV are analyzed as a function of energy. Particular attention is given to the process of formation of initial distributions for the components of the total angular momentum of compound nuclei. It is shown that substantial distinctions in the behavior of average spins of fission fragments for different fusion reaction channels are expected to be observed in the range of subbarrier energies.

     

The effect of angular momentum coupling on the angular distribution of fission fragments

We examine what information can be obtained from fission angular distributions through precise measurements and an analysis in terms of the simple statistical model of Ericson. We report on the systematics of the decoupling angle and present the role of the angular momentum coupling between the entrance and the exit channel. The results indicate that the directional coupling of the angular momentum in the entrance and the exit channel is always strong for heavy-ion induced fission, and the angular momentum coupling plays a decisive role on the angular distribution of fission fragments. The average channel spins of fission fragments 〈I_f〉 are deduced through the decoupling angles determined experimentally. They agree well with γ-multiplicity measurements.     

<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.     

Investigation of the reaction <Superscript>208</Superscript>Pb(<Superscript>18</Superscript>O, <Emphasis Type="Italic">f</Emphasis>): Folding angular distributions of fission fragments and gamma-ray multiplicity

Correlations between folding angular distributions of fission fragments and the gamma-ray multiplicity are studied for ¹⁸O + ²⁰⁸Pb interactions at energies of the beam of ¹⁸O ions in the range E _lab = 78–198.5 MeV. The probabilities are determined for complete-and incomplete-fusion processes inevitably followed by the fission of nuclei formed in these processes. It is found that the probability of incomplete fusion followed by fission increases with increasing energy of bombarding ions. It is shown that, for the incomplete-fusion process, folding angular distributions of fission fragments have a two-component structure. The width of folding angular distributions (FWHM) for complete fusion grows linearly with increasing energy of ¹⁸O ions. The multiplicity of gamma rays from fission fragments as a function of the linear-momentum transfer behaves differently for different energies of projectile ions. This circumstance is explained here by the distinction between the average angular momenta of participant nuclei in the fusion and fission channels, which is due to the difference in the probabilities of fission in the cases where different numbers of nucleons are captured by the target nucleus.     

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.     

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.     

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.     

Probing the tilting mode in fission with γ-ray multiplicity techniques

The γ-ray multiplicities of the fragments from a number of ⁴He-induced fission reactions have been measured as a function of fragment emission angle. The value of M_γ is found to vary with angle in qualitative agreement with the predictions of statistical models of fission-fragment angular distributions. The observed variation is rather weak, on the order of 5%. The data are compared with several models. Calculations assuming a rigidly rotating, transition-state nucleus predict a much stronger angular dependence of the fragment spin than indicated by the data. The agreement is significantly improved if a fragment-spin enhancement effect is included in these calculations. The fragment spins are explored within the framework of the statistical scission model and the collective mode model. Both of these models predict large fragment spins and thus a relatively weak angular dependence of the total fragment spin. Neither model provides a completely satisfactory explanation of the data. Depending on the assumptions made in the calculations, the models either predict too strong an angular dependence of the total fragment spin or spins which seem incompatible with M_γ.     

Angular momenta of fission fragments in the α-accompanied fission of 252Cf

For the first time, average angular momenta of the ternary fission fragments ^{100, 102}Zr, ¹⁰⁶Mo, ^{144, 146}Ba and ^{138, 140, 142}Xe from the α-accompanied fission of ²⁵²Cf were obtained from relative intensities of prompt γ-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of ²⁵²Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is ∼1.4 ℏ lower than in binary fission. Consequently, results indicate that the mechanism of the ternary α-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of ¹⁰⁶Mo and ¹⁴⁰Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed.     

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.     

Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.     

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atE _cm ^inc =750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.     

Angular distribution of fission fragments in reactions of complete fusion of deformed nuclei

Formation of angular distributions of fission fragments for the ¹⁶O + ²³²Th and ¹²C + ^235,236U reactions has been analyzed within a dynamic approach. In this approach, the component of the total angular momentum along the fission axis K is considered as a fluctuating quantity and the corresponding relaxation time is assumed to be the main parameter controlling the evolution of this mode. Particular attention is paid to the analysis of the effect of initial distributions over K (formed during fusion) on the angular distribution of fission fragments of nuclei having fission barriers comparable with the nuclear temperatures.     

Average spins of primary fission fragments

The average spins at which final fragments are formed after fission following fusion of ¹⁹F with ¹⁹⁷Au have been measured directly from spectroscopic studies of discrete γ-ray lines. The final fragment spins can be translated into average spins at which primary fragments are formed by adding changes due to statistical γ-ray emission and post-fission neutron emission. The average primary fragment spins show marked variations with fragment mass. Possible causes for the structure are discussed within the framework of the statistical scission model of heavy-ion induced fission.     

Dynamical approach to calculating angular distributions of fission fragments

A dynamical approach is proposed for calculating the angular distributions of fission fragments. The relaxation time for the degree of freedom associated with the projection of the total angular momentum of the nuclear system onto the symmetry axis and the coefficient of damping of the fission mode are the basic parameters of this approach. Experimental data on the anisotropy of the angular distributions of fission fragments and on the multiplicities of prescission neutrons are analyzed within the proposed model for ¹⁶O+²⁰⁸Pb (E _lab=110–148 MeV), ¹⁶O+²³²Th (120–160 MeV), ¹⁶O+²⁴⁸Cm (110–148 MeV), and ¹⁶O+²³⁸U (96–148 MeV). The relaxation time and the damping coefficient are estimated at τ_K=(5–6)×10^?21 s and β=4×10²¹ s^?1, respectively.     

Measurement of the fission moment of inertia of medium mass nuclides

Measurements have been made, by means of mica nuclear track detectors, of the distributions in tracklength and the angular distributions with respect to the beam direction for the fission fragments from the systems Ag, Te and Au plus 80-MeV alpha particles. Analysis of the tracklength distributions indicated that, in each case, full momentum transfer from the incident projectile characterized those interactions that led to fission. Angular-momentum dependent statistical model calculations for the decay of the respective compound nuclei then provided information on fission-evaporation competition in the de-excitation processes, and in particular the distribution in nuclear temperature and angular momentum at which the fission events took place. This information was then employed in the analysis of the measured fission fragment angular distributions, and to extractK ₀ ² values. From these, the moments of inertia of the fission saddle point shapes were calculated, and the results are in good agreement with theoretical estimates.