Fast fission mechanism and duality of the diffusion process

The reaction of ²³⁸U with ¹²C was studied radiochemically with the purpose of elucidating fast fission characteristics. From the difference in the mass distribution below and above the critical energy where fast fission is predicted to set in, fast fission component was extracted in far-asymmetric mass region and interpreted as the mass diffusion following the Fokker-Planck equation. Anomalous charge dispersion widths in the corresponding mass region and a sudden increase of the whole mass distribution width at the critical energy were also observed to support the above result. The reaction time of fast fission deduced from the width and position of the mass distribution was 5×10⁻²¹s as well by taking into account the effect of neutron emission during the diffusion process, which turned out to be more than one order of magnitude longer than the corresponding life time of typical deep inelastic scattering but substantially short compared to ordinary fusion-fission life time. Evaluation of the driving potential for mass drift required dinuclear configuration be of an elongated or deformed form for fast fission in contrast to a more compact form for the deep-inelastic process. Received: 11 November 1997     

Resonances in the isomeric and prompt fission probabilities of240Pu

The prompt and isomeric fission probabilities of²⁴⁰Pu have been studied using the²³⁹Pu(d,p) reaction. A number of resonances are observed in the subbarrier population of the 4 ns fission isomer for excitation energies between 4.0 and 6.2 MeV. Apart from a structure at 4.3 MeV, they do not coincide with transmission resonances found in prompt fission. Calculations with an extended doorway state model which simultaneously reproduce the measured delayed and prompt fission probabilities yield revised fission barrier parameters as well as spectroscopic information on fission and gamma widths of highly excited states in the second minimum.     

Cross section for the subthreshold fission of 236U

The cross section for ²³⁶U fission in the neutron-energy range E _n = 0.001–20 keV was measured by using the INR RAS (Institute of Nuclear Research, Russian Academy of Sciences, Moscow) LSDS-100 neutron spectrometer of the lead slowing-down spectrometer type. The resonance fission areas of the resonances at 5.45 eV and 1.28 keV were found, and the fission widths of these resonances were evaluated. The cross section for the ²³⁸U(n, f) fission process was measured, and the threshold sensitivity of the LSDS-100 to small values of fission cross sections was estimated. The well-known intermediate structure in the cross section for the neutron-induced subbarrier fission of ²³⁶U was confirmed.     

Inelastic deuteron breakup followed by fission at intermediate energy

The results of experimental and theoretical studies of the double-differential proton and neutron spectra measured in coincidence with fission fragments in the deuteron-induced reaction on a ²³⁸U target at E _d =65 MeV are presented. These spectra measured in the forward direction are analyzed in the plane-wave Born approximation by using the modified model of stripping into a continuum. The pre-neutron emission fission fragment mass distributions were measured for the (d, f), (d, pf), and (d, nf) reaction channels. The enhancement of highly asymmetric mass division in the (d, pf) channel for the low-energy part of the breakup proton spectrum was observed. The (d, pf) channel can be used to imitate the neutron-induced fission at intermediate energy. The fission characteristics were analyzed in the model taking into account nuclear friction and relevant fission modes.     

Identification of gamma transitions from He and Be ternary fission fragments

He and Be ternary fission processes of ²⁵²Cf have been studied in two experiments with the Gammasphere detector array with light charged particle detectors surrounding the source. From α-γ double gated spectra, neutron multiplicity distributions were determined for related α ternary fission pairs. In going from binary to α ternary SF for approximately the same mass splittings (A ≈ 104–146) the average neutron multiplicity decreases about 0.7 AMU. In the first light charged particle (LCP) γ-γ experiment, the ¹⁰Be spectrum was cutoff below 27 MeV and in the recent experiment, below 18 MeV. For high energy (E > 27 MeV) ¹⁰Be ternary fission, the data indicate that the largest yields go via the cold process (zero neutron evaporation). In the recent experiment with E cutoff of 18 MeV, the ¹⁰Be ternary SF was observed for zero to 4n emissions. It seems that in some cases like ¹³⁶Te, the On channel is the strongest and in the other cases like ¹⁰⁰Zr the 1n or 2n channel dominates. Clearly, there is a shift to lower average number of neutrons emitted for ¹⁰Be compared to α ternary SF. The ¹⁰⁴Zr and ¹³⁶Te cases where zero neutron emission occurs may be related to the fact that these nuclei are near the limits of the more neutron rich Zr and Te nuclei observed. The ¹³⁶Te is more spherical than the heavy partners in the other pairs and this may influence the 0n channel. Finally, the 0n channel may be more enhanced in the first data with the higher ¹⁰Be energy cutoff, leading to lower excitation energy. Also, we confirmed the 3368 keV peak with the FWHM of 60 keV emitted from the moving Be particles in the Doppler effect corrected spectrum.     

Sequential fission angular distributions from mass-asymmetric heavy-ion reactions

The angular distributions of sequential fission fragments have been measured for the reactions of ⁴⁰Ar with ¹⁹⁷Au and ²³⁸U as a function of reaction Q-value and charge transfer. These angular, distributions are used to study the angular momentum and alignment of the deep-inelastic products which undergo fission. All of the fission fragment angular distributions are strongly focused into the plane defined by the beam and the projectile-like fragment velocity vectors. The in-plane angular distributions from reactions with uranium are isotropic for small energy losses and become anisotropic as the energy loss increases. For large negative Q-values, the in-plane anisotropy increases as the deep-inelastic products become more symmetric. The variation of the in-plane anisotropy with mass asymmetry for the two systems in this work was compared to a compilation of previous work and a consistent pattern was found. These alignment data are compared to equilibrium statistical calculations.     

The influence of pairing and nuclear structure on the thermal-neutron-induced fission of235U

The mass separated fission product beam provided by the mass separator “Lohengrin” has been used to determine the nuclear charge distribution for the thermal-neutron-induced fission of²³⁵U for all light fission products in the region 80≦A≦107. The measurements were performed at the most probable kinetic energy of the fission products. By using the known fission product mass yields, the independent yields for a total number of 100 nuclides were obtained under the condition of the most probable kinetic energy. The proton pairing effect modulates the average nuclear charge of the fission fragments and the isobaric charge distribution widths in a regular fashion. The probabilities of breaking a pair and of forming fragments with an energetically unfavourable neutron-to-proton ratio are found to compete with each other. Both probabilities depend on the mass split and reach their maximum values in the region of the most probable masses. The odd-even-proton effect is found to vary smoothly between 16% for the most abundant mass splits and 40% for the rare mass splits. The odd-even-neutron effect exhibits maxima nearN=50 andN=60, where it reaches 16%. These maxima and the extremely low Tcyield (0.13±0.05%) are discussed with regard to fragment shell effects.     

Total spontaneous and isomer fission half-lives of U,U and Pu

Using the recently proposed coupled channel decay theory, we have reproduced here the observed absolute yield curves; total decay probabilities from the spontaneous and the isomeric fission states of ²³⁴U, ²³⁶U, and ²⁴⁰Pu, and the average kinetic energies. Our predicted yield curve for the decay of isomer fission state seems to be in agreement with preliminary observation.     

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.     

Cross section for the subbarrier fission of <Superscript>244</Superscript>Cm

The cross section for ²⁴⁴Cm fission induced by neutrons of energy in the range between 0.07 eV and 20 keV was measured by using the lead slowing-down spectrometer (LSDS-100) of the Institute for Nuclear Research (Russian Academy of Sciences, Moscow). The parameters of the resonance areas were determined for the lowest eight s-wave neutron resonances, and the respective fission widths were evaluated. Also, the parameters of the intermediate structure in the cross section for the subbarrier fission of ²⁴⁴Cm nuclei were evaluated. The results were compared with available data and recommendations based on evaluations.     

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.     

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.     

Quaternary fission

Quaternary fission is a nuclear reaction where the two customary fragments from fission are accompanied by two light charged particles. The process has been investigated at the ILL, Grenoble, for thermal neutron induced fission of ²³³U and ²³⁵U. The light particles were identified to be α particles and H isotopes (mostly tritons). Two different types of processes could be disentangled: in one of these processes all four charged particles are born in coincidence while the second process is in fact merely a special case of ternary fission where the ternary particle decays into two charged particles before reaching the detectors.     

Symmetric and asymmetric fission of Ac isotopes near the fission threshold

Fission probabilities and fragment anisotropies were investigated for fission of ²²⁷Ac and ²²⁸Ac by means of direct reactions with a ³He beam on a ²²⁶Ra target. Triple-humped mass distributions are found also for excitation energies where second-chance fission is excluded. The fission barrier is higher for symmetric fission compared to that for asymmetric fission by 1.2 and 2.0 MeV, respectively, suggesting that the character of the mass split is already predetermined at the saddle point.     

Competition between fission and neutron emission by diffusion model

Magnitudes and relative signs of amplitudes for three inelastic proton channels have been determined for 42 3/2⁺ resonances in⁵⁷Co in the rangeE _p =3.1–4.0 MeV. Amplitude and width channel correlations have been obtained for each pair of channels. One of the amplitude correlations is large and highly significant. Comparisons between these data and statistical theories of nuclear levels are presented for both widths and products of amplitudes; in general, agreement is good. The widths for one channel and amplitude products for one pair of channels appear energy-dependent, with most of the strength concentrated in the lowest 200 keV.     

The study of prompt and delayed muon induced fission

The ratios of prompt to delayed fission yields for the isotopes²³³U,²³⁴U,²³⁵U,²³⁶U,²³⁸U,²³⁷Np,²⁴²Pu, and²⁴⁴Pu and the fission probabilities relative to each other have been investigated experimentally. Using the value of the total fission probability for²³⁷Np the absolute probabilities for prompt and delayed fission have been determined. The fission probabilities per muon captureP _fc have been derived for all the isotopes and compared with an evaluation based on excitation functions from theory.     

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.     

Quantum description of quaternary nuclear fission

The quantum theory of binary and ternary fission is generalized to the case of recently observed quaternary nuclear fission. Formulas for the amplitudes of partial fission widths and angular and energy distributions of quaternary fission products are derived with allowance for strong channel coupling. The nonevaporation mechanism for formation of light particles is used to explain the experimentally observed decrease in the probability for emission of light particles (α, α), (α, t), and (t, t) as compared with the product of emission probabilities for the same particles in ternary fission. It is concluded that in quaternary fission, as in ternary fission, light particles escape from the neck of the fissioning nucleus much earlier than scission of the nucleus into heavy fragments occurs.     

Parity nonconservation and Brosa modes in nuclear fission

The parity nonconserving (PNC) asymmetry coefficient for the angular distribution of fragment emission from binary fission of²³³U irradiated by polarized thermal neutrons has been measured. Complementary fragments were detected by a double ionization chamber with high resolving power. The experiment was carried out at the high flux reactor of the ILL, Grenoble. Integrated over all masses and energies of light fragments from asymmetric fission of²³⁴U^h, the PNC asymmetry coefficient is found to be =(3.29±0.31) × 10^–4.The positive sign of indicates a preferential emission of light fragments parallel to the spin of neutrons inducing fission. Theory claims that PNC effects are sensitive to the properties of the fission barrier. On the other hand, one may wonder whether characteristics of eventual fragments are already specified at the barrier. The measurement of PNC asymmetries for distinct mass-energy ranges of fragments has been utilized to answer this question. Mass-energy distributions of fragments were analyzed along the lines of the Brosa model of fission as a superposition of individual modes. Within experimental uncertainty no mode dependence of asymmetric fission could be disclosed. The result is in keeping with the Brosa model where asymmetric modes bifurcate only once the standard fission barrier has been passed.     

Mass and energy dependence of pion-induced fission

Data for fission induced by pi meson beams from 80 to 500 MeV are presented for nuclei from Fe through Pu as measured by solid state track detectors. The general trends for binary fission withπ ⁺ are reproduced fairly well by a calculation in the ‘high excitation’ limit with standard level density and fission barrier parameters, butπ ^? data are underpredicted. A universal dependence of the binary fission probabilities with the fissility (Z±1)²/A is found to be valid for both pion beam charges for all beam energies below the delta resonance. Probabilities for observing three fragments withπ ⁺ are not reproduced by a ternary fission application of the model found to work for binary fission.