New approximation of the energy dependences of total cross sections for proton-induced fission of actinide nuclei

The energy dependences of the cross sections for the fission of ²³²Th to ²³⁹Pu nuclei that is induced by protons of energy in excess of 50 MeV are proposed to be approximated by the sum of two functions. Of these, the first decreases exponentially with increasing proton energy. It represents the contribution of two-step fission, which competes with particle evaporation. The second function decreases exponentially as the energy grows to about 200 MeV, whereupon it increases up to an energy of 1 or 2.5 GeV. After that, it again decreases for ²³²Th to ²³³U nuclei or remains nearly unchanged for ²³⁷Np and ²³⁹Pu nuclei. This function is likely to represent the sum of the contributions from three modes of single-stage fission.     

On the role of energy separated in fission process,excitation energy and reaction channels effects in the isomeric ratios of fission product <Superscript>135</Superscript>Xe in photofission of actinide elements

In this work we present the isomeric ratio of fission product ¹³⁵Xe in the photo-fission of actinide elements ²³²Th, ²³³U and ²³⁷Np induced by end-point bremsstrahlung energies of 13.5, 23.5 and 25.0 MeV which were determined by the method of inert gaseous flow. The data were analyzed, discussed and compared with the similar data from literature to examine the role of energy separated in fission process, excitation energy and reaction channels effects.     

Stochastic model of tilting mode in nuclear fission

A model of induced nuclear fission was developed with consideration of thermodynamically fluctuating orientation degree of freedom (tilting) of deformed nuclei. This model was applied to analysis of the experimental angular anisotropy of fission fragments in the ¹⁶O + ²³²Th, ²³⁸U, ²⁴⁸Cm, ²⁰⁸Pb, ²⁰⁹Bi; ¹²C + ²³⁶U; ¹⁹F + ²⁰⁸Pb; and ¹¹B + ²³⁷Np reactions. Information on the equilibrating time of the tilting mode was obtained. The text was submitted by the authors in English.     

Total cross sections for fission of heavy nuclei by intermediate-energy protons

The results of measuring total cross sections for proton-induced fission of ^natPb, ²⁰⁹Bi, ²³²Th, ²³³U, ²³⁵U, ²³⁸U, ²³⁷Np, and ²³⁹Pu nuclei at proton energies from 200 to 1000 MeV are reported. The measurements were carried out in steps of ≈100 MeV. Complementary fission fragments were detected in coincidence by two parallel-plate avalanche gas counters placed in the beam line on both sides of the thin target close to it. Energy and isotope dependences of the fission cross sections are analyzed.     

Yield of fission fragments from the photofission of actinide nuclei

Yields of the ¹⁰¹Mo, ¹³⁵I, and ^135m Cs isotopes from the photofission of the actinide nuclei ²³²Th ²³⁸U, and ²³⁷Np are measured. These fission fragments have specific nuclear structure features or are of practical use. The measurements are performed in the bremsstrahlung from the microtron of the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research (JINR) at an electron energy of 22 MeV. The yields of the fragments are measured by the activation method using a γ radiation HPGe detector.     

Multimode approach to 241Am and 237Np fission induced by 660-MeV protons

The results obtained by measuring cross sections for the formation of fragments originating from ²⁴¹Am and ²³⁷Np fission induced by 660-MeV protons are presented. The charge and mass distributions of fragments are analyzed within the multimode-fission model, symmetric and asymmetric fission channels being separated. The contributions of various fission components are estimated, and the fission cross sections for the ²⁴¹Am and ²³⁷Np nuclei are calculated along with the fissilities of these nuclei.     

Study of mass spectra of light-actinide fission isotopes Kr and Xe in the framework of a new statistical approach

Results on light-actinide fission fragments Kr and Xe yields calculated within the framework of a new statistical approach are presented. The proposed statistical method is derived from the equilibrium condition of the ensemble of all possible fission fragments. Using ²³⁷Np isotope as an example, we investigate the influence of excitation energy (nuclear temperature) and nuclear particle emission on the formation of mass fission channels. The results obtained are compared with the experimental data on Kr and Xe isotope yields at the fission of Th, U, Np, and Pu.     

Cross sections and barriers for nuclear fission induced by high-energy nucleons

The cross sections for the fission of ²³²Th, ^235,238U, ²³⁷Np, and ²³⁹Pu target nuclei that was induced by 20- to 1000-MeV neutrons and protons were calculated. The respective calculations were based on the multiconfiguration-fission (MCFx) model, which was used to describe three basic stages of the interaction of high-energy nucleons with nuclei: direct processes (intranuclear cascade), equilibration of the emerging compound system, and the decay of the compound nucleus (statistical model). Fission barriers were calculated within the microscopic approach for isotopic chains formed by 15 to 20 nuclei of the required elements. The calculated fission cross sections were compared with available experimental data. It was shown that the input data set and the theoretical model used made it possible to predict satisfactorily cross section for nuclear fission induced by 20- to 1000-MeV nucleons.     

Study of some characteristics of the thermal-neutron-induced sub-barrier fission of 231Pa, 232Th and 237Np

Some characteristics of the thermal-neutron-induced fission of ²³¹Pa, ²³²Th and ²³⁷Np were studied using a highly pure thermal-neutron beam of the Grenoble High Flux Reactor. For the thermal-neutron-induced-fission cross section we obtained 20 ± 4 mb for ²³⁷Np, 19 ± 4 mb for ²³¹Pa and less than 2.5 μb for ²³²Th, in agreement with calculations based on a double humped fission barrier. We also determined a mean total fission fragment kinetic energy of 172.8 + 2.5 MeV for ²³⁷Np, which fits into the semi-empirical systematic of $\text{E}\text{?}{}_{\mathrm{<mtext>K</mtext>}}$ versus $\text{Z}{}^2\text{/A}{}^{\mathrm{<mtext>case1</mtext><mtext>3</mtext>}}$. Finally, we determined LRA/B ratios of (1.94±0.17) × 10^?3 for ²³⁷Np and (1.67±0.11) × 10^?3for ²³¹Pa, in disagreement with the theoretical predictions of Feather, but consistent with the semi-empirical systematic of Halpern.     

Cross sections for 209Bi, 232Th, 235U, 238U, and 237Np fission induced by intermediate-energy protons and deuterons

The cross sections for ²⁰⁹Bi, ²³²Th, ²³⁵U, ²³⁸U, and ²³⁷Np fission induced by protons of energy in the range 1.0–3.7 GeV and by deuterons of energy 1.0 GeV were measured. The results are compared with data from other experiments, with available estimates, and with the predictions of theoretical models.     

Independent yields of Kr and Xe fragments in the photofission of <Superscript>237</Superscript>Np and <Superscript>243</Superscript>Am odd nuclei

Results are presented that were obtained by measuring the independent yields of Kr (A = 89–93) and Xe (A = 135–142) appearing as fragments in the photofission of ²³⁷Np and ²⁴³Am odd nuclei. The respective experiments were performed in a beam of bremsstrahlung photons from electrons accelerated to an energy of 25 MeV at the microtron of the Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research (JINR, Dubna). Use was made of the procedure involving the transportation of fragments emitted from the target by a gas flow along a capillary and the condensation of inert gases in a cryostat at liquid-nitrogen temperature. The identification of Kr and Xe appearing as fragments was performed by the gamma spectra of their daughter products. The mass-number distributions of the independent yields of Kr and Xe isotopes were obtained, along with those for the complementary fragments (Y and La in the fission of ²³⁷Np and Nb and Pr in the fission of ²⁴³Am).     

Mass asymmetry dependence of angular distribution in237Np(α29 and 44 MeV,f): single particle effect

Angular distributions of fission products have been measured as a function of mass asymmetry in the odd-Z ²³⁷Np(α_{29 and 44 MeV},f) system using a recoil-catcher technique and off-line gamma spectrometry. Higher angular anisotropies were observed for the asymmetric mode products compared to the symmetric mode products at both energies. Average anisotropies for individual modes are lower than those for neighbouring even-even fissioning nucleus²⁴²Pu due to odd-nucleon spin effect. Present data have been analysed according to the transition state model assuming two modes of fission with characteristic saddle-shapes, barriers and multichance fission probabilities. It is seen that angular distributions for the symmetric and asymmetric modes are decided at and well past the corresponding saddle points respectively. Odd-nucleon spin contribution (〈k ²〉) to the tilting mode variance have been deduced. For (²⁴¹)Am fission, 〈k ²〉 values for the asymmetric and symmetric modes are ≤ 14 and > 14 ?² respectively. The 〈k ²〉 value averaged over several nuclei from preactinide (²⁰¹Ti) to actinide (²⁴⁸Cf) is 11.5 ± 4.2 ?². Average 〈k ²〉 value is in close agreement with the theoretical estimate.     

Fission fragment angular distribution in alpha-particle-induced fission of actinide elements

Using Lexan polycarbonate plastic as the fission fragment track detectors, the fragment angular distributions have been measured in the cases of fission of²³²Th and²³⁸U induced by alpha particles of various energies ranging from 40 to 70MeV obtained from the 88″ variable energy cyclotron at Calcutta. The center-of-mass angular distributions have been calculated and fitted by a series of Legendre polynomials. TheW(10°)/W(90°) ratios (defined as anisotropy) were measured at several energies for both the targets. These data are utilized in calculation of the energy dependence ofK ₀ ² , the standard deviation of the distribution in the angular momentum projection on the nuclear symmetry axis at the saddle point. Values of Γ _f /Γ _η , i.e. the ratio of the fission width to neutron emission width have been determined for²³²Th and²³⁸U nuclei. The integral cross-section for alpha induced fission in each target was determined by numerical integration of the respective center-of-mass angular differential cross-sections. The results were compared with similar data available in the literature which served to resolve some of the discrepancies observed in earlier measurements. The results were also compared with theoretical cross-sections.     

Energy Dependence of the Most Stable Nuclei Production in Proton-Induced 238U and 232Th Fission

Using the available experimental data, production cross sections of the most stable nuclei have been calculated for the proton-induced fission of ²³⁸U and ²³²Th at 12, 20, 35, 50, 96 MeV in case of ²³⁸U and at 8, 9.3, 12, 19.55, 32.2, 44.7, 53 MeV for ²³²Th. The analysis has been carried out for the fission fragment mass ranges corresponding to N/Z ratios in the ranges 1.33 ± 0.09 and 1.32 ± 0.08 for ²³⁸U and ²³²Th respectively. Results have been compared with the ones generated indirectly by employing GEF nuclear reaction code, version 2017/1.1. From the production cross sections point of view, for the same energy, ²³²Th is found to be a better target than ²³⁸U for producing nuclei A around the symmetric mass peak, while ²³⁸U comes out to be a better one than ²³²Th for producing the fission fragments around the asymmetric peaks of the mass distribution.

     

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.     

Photonuclear reactions of actinides in the giant dipole resonance region

Photonuclear reactions at energies covering the giant dipole resonance (GDR) region are analyzed with an approach based on nuclear photoabsorption followed by the process of competition between light-particle evaporation and fission for the excited nucleus. The photoabsorption cross-section at energies covering the GDR region is contributed by both the Lorentz-type GDR cross-section and the quasi-deuteron cross-section. The evaporation-fission process of the compound nucleus is simulated in a Monte Carlo framework. Photofission reaction cross-sections are analyzed in a systematic manner in the energy range of ∼ 10-20 MeV for the actinides ²³²Th , ²³⁸U and ²³⁷Np . Photonuclear cross-sections for the medium-mass nuclei ⁶³Cu and ⁶⁴Zn , for which there are no fission events, are also presented. The study reproduces satisfactorily the available experimental data of photofission cross-sections at GDR energy region and the increasing trend of nuclear fissility with the fissility parameter Z ²/A for the actinides.     

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.     

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.     

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.