Potential energy surfaces and lifetimes for spontaneous fission of heavy and superheavy elements from a variable density dependent mass formula

The potential energy surface for spontaneous fission is calculated using realistic density distributions for finite nuclei. Particular emphasis is placed on the region of the potential between the saddle and scission point. The method involves computing the energy of the system using an energy density functional consistent with varible density distributions and nuclear masses and obtained from a statistical many body theory. The results show that there exists an external or scission barrier to the fission process. Lifetimes and mass distributions which are computed using these potential energy surfaces are found to be in adequate agreement with observations for ²³⁴U, ²³⁶U, ²⁴⁰Pu, ²⁴⁴Cm, ²⁴⁸Cf, and ²⁵²Cf. Our predicted upper limit for the spontaneous fission half-lives of elements 112 and 114 is one year but the calculation indicates that these could be considerably shorter than a year.     

Investigation of polar emission in 252Cf and 235U + nth fission

The energy distributions and relative intensities of protons, deuterons, tritons and α-particles emitted along the fission axis during spontaneous fission of ²⁵²Cf were measured simultaneously with both fission fragment energies. The absolute intensity of particles, the mass distribution of fragments, the total kinetic energy and total excitation energy of both fragments were subsequently deduced from the experimental data. Statistical model calculations based on a hypothesis that the polar particles are evaporated from fission fragments have been performed for ²⁵²Cf and ²³⁶U fission. Although some experimental results agree remarkably well with the evaporation hypothesis, the considered model cannot describe many features of the polar emission phenomenon.     

Correlations of fission fragment angular momentum with collective and intrinsic degrees of freedom

In the present work angular momenta of the fragments corresponding to¹³²I^m,g have been deduced from the radiochemically determined independent isomeric yield ratios and statistical model based analysis in neutron induced fission of²³⁵U,²³⁹Pu and²⁴⁵Cm and spontaneous fission of²⁵²Cf. These data along with similar data on¹³⁴I, reported earlier from this laboratory, bring out the effects of deformed 66n and spherical 82n shells on fragment angular momentum showing also an inverse correlation of the latter with elemental yields. Quantitative estimates of fragment scission point deformation and the coefficient of change of fragment angular momentum with kinetic/excitation energy have been deduced and are seen to be in good agreement with the expected theoretical estimates.     

Dependence of light charged particles parameters on Z2/A in ternary fission

Emission of light charged particles from ternary fission of²⁴⁸Cm,²⁵²Cf and²³⁵U+n _th has been measured by a CsI(T1) counter. Relative probabilities and parameters of p, t,α energy spectra in triple fission were extracted and compared with earlier reference results.     

Dependence of light charged particles parameters on Z2/A in ternary fission

Emission of light charged particles from ternary fission of ²⁴⁸Cm, ²⁵²Cf and ²³⁵U+n_th has been measured by a CsI(Tl) counter. Relative probabilities and parameters of p, t, α energy spectra in triple fission were extracted and compared with earlier reference results.     

Fission-fragment energy correlation measurements for the spontaneous fission of 244Cm

Fission-fragment mass and kinetic energy distributions and their correlations have been measured for the spontaneous fission of ²⁴⁴Cm. About 3.54 × 10⁵ fission events were collected. The global mass distribution shows shoulders at μ_H ≈ 134 and μ_H ≈ 143?144. The peak/valley ratio is 86. The dip ΔE_K value at symmetry is 13.4 ± 1.5 MeV. In the yields for high-kinetic-energy selected events, the masses 139 and 144 dominate. The results of ²⁴⁴Cm are compared with the other isotopes of Cm and discussed in terms of the structures present in the potential energy surface of the fissioning system caused by the structures in the nascent fragments.     

Variation of even-odd proton effects with excitation energy in fission of 252Cf: Confirmation of fine structure in v(A)

The existence of even-odd proton effects (fine structure) in νv(A) of individual fragments from ²⁵²Cf(sf) has been confirmed by analysis of previously reported data. The fine structure is seen to increase in amplitude as the fragment excitation energy decreases, a behaviour similar to the well-known behaviour of the mass yield curve. The present mass yield data also show these effects, as expected. Conversely, our total kinetic energy data TKE(A), not previously reported, show very little even-odd proton effect. It is shown that energy balance considerations, also, support the existence of even-odd proton effects in neutron emission from ²⁵²Cf(sf).     

Cross sections for the photofission of <Superscript>243</Superscript>Cm, <Superscript>245</Superscript>Cm, <Superscript>249</Superscript>Bk,and <Superscript>249</Superscript>Cf isotopes in the energy range from the threshold to 10–12 MeV

The relative method was used to measure the photofission cross sections for ²⁴³Cm and ²⁴⁹Cf isotopes in the energy range from 6 to 12 MeV, for ²⁴⁵Cm in the energy range from 5 to 10 MeV, and for ²⁴⁹Bk in the energy range from 5.5 to 10 MeV. The measurements were performed with an energy step of 50 to 200 keV by using the microtron installed at the Institute of Physics and Power Engineering (Obninsk). The cross section for ²³⁸U photofission was used as a reference in these measurements. Data on the cross sections for ²⁴³Cm, ²⁴⁵Cm, and ²⁴⁹Bk photofission were obtained for the first time, while data on the cross section for ²⁴⁹Cf photofission were obtained for the first time only in the energyregion E<10 MeV. The data on the ²⁴⁵Cm nucleus suggest that, in the energy region around 6 MeV, the cross section for its photofission has a maximum, which is likely to be due to the low-energy resonance structure of the dipole-photoabsorption cross section. For ²⁴⁹Cf, an anomalously large value of the photo fission cross section is observed in the region of the first maximum of the giant dipole resonance (E≈11 MeV). By comparing the energy dependences obtained for the fissilities of the ²⁴³Cm and ²⁴⁹Bk isotopes from photofission data with the fissilities from direct-reaction data, it is found that the observed fission thresholds agree and that there is a plateau-like dependence at energies above 7.5 MeV. For the ²⁴⁵Cm and ²⁴⁹Cf nuclei, there are no similar data for performing such a comparison. Data on the fissilities as obtained from the present series of relative measurements that employ the microtron bremsstrahlung spectrum are analyzed.     

On the kinetic energy of fission fragments with even and odd numbers of protons

In order to compare the distributions of the prompt energy release in the fission of a doubly even nucleus into even-Z and odd-Z fragments, the spectra of fragment kinetic energy and the coincident K X-rays were measured in a two-parameter mode with high statistical accuracy for the case of ²⁵²Cf spontaneous fission. By means of computer spectrum decomposition techniques data were obtained for average kinetic energies of fragments with even and odd atomic number. The comparison did not show any noticeable correlation of the mean fragment kinetic energy with oddness or evenness of the fragments.     

Angular distributions of light charged particles from 252Cf fission in the ranges 0–46° and 134–180°

Alpha particles, tritons, deuterons and protons accompanying ²⁵²Cf fission were registered in coincidence with both fission fragments by means of a system containing two-dimensional position-sensitive silicon detectors. Angular distributions, kinetic energy spectra of light charged particles as well as mass distributions of fission fragments in coincidence with light charged particles were measured. The experimental results are compared with some theoretical models.     

Nuclear molecules in ternary fission

Experimental results on particle accompanied cold fission of ²⁵²Cf suggest the existence of a short-lived quasi-molecular state. Within our three-center phenomenological model, described in this paper, we found a possible explanation based on a new minimum in the deformation energy at a separation distance very close to the touching point. Half-lives of some quasimolecular states which could be formed in ¹⁰Be accompanied fission of ²³⁶U, ²³⁶Pu, ²⁴⁶Cm, ²⁵²Cf, ^252,256Fm, ^256,260No, and ²⁶²Rf are roughly estimated.     

Ternary fission fragmentation of <Superscript>252</Superscript>Cf for all possible third fragments

The ternary fragmentation of ²⁵²Cf for all possible third fragments has been investigated using the recently proposed three-cluster model within a spherical approximation and satisfying the condition A ₁ 3 \geq A ₂ 3 \geq A ₃ . The most probable ternary configurations in the fission of ²⁵²Cf accompanied with all possible third fragment mass numbers from A ₃ = 1 to 84 are predicted and their independent and overall relative yields are calculated. The calculations of the properly charge minimized potential energy surface (PES) and yield reveal that even-mass third fragments are more favored than odd ones. In the most probable configuration having the minimum in the potential energy and the maximum in yield, among the three fragments, at least one (or two) of the fragment(s) associates itself with the neutron (or proton) closed shell and in some cases even with the doubly closed shell. The calculated relative yields imply that next to ¹⁴C (the heaviest third fragment observed in the spontaneous ternary fission of ²⁵²Cf , ^{34, 36, 38}Si , ^{46, 48}Ar , and ^{48, 50}Ca are presenting themselves as the most favoured cases to be observed as the third particle in the spontaneous ternary fission of ²⁵²Cf .     

Coherent bremsstrahlung and GDR width from Cf cold fission

The energy spectrum of the high energy γ-rays in coincidence with the prompt γ-rays has been measured for the spontaneous fission of ²⁵²Cf. The nucleus–nucleus coherent bremsstrahlung of the accelerating fission fragments is observed and the result has been substantiated with a theoretical calculation based on the Coulomb acceleration model. The width of the giant dipole resonance (GDR) decay from the excited fission fragments has been extracted for the first time and compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism. The extracted GDR width is significantly smaller than the predictions of TSFM.     

Generation of angular momentum of fission fragments in a cluster model

Based on the dinuclear system concept, the role of bending vibrations in creation of the angular momentum of primary fission fragments is investigated. For ²⁵²Cf spontaneous fission, the angular momenta of the fragments are calculated as a function of the neutron multiplicity and compared with available experimental data. Different cluster compositions of the ²⁵²Cf fission modes at the scission point are considered.     

Prescission neutrons in the fission of 235U and 252Cf nuclei

Experimental data obtained previously for the energy-angular distribution of neutrons originating from the fission of ²⁵²Cf (spontaneous fission) and ²³⁵U (thermal-neutron-induced fission) nuclei are analyzed, the angle being measured with respect to the direction of fission-fragment motion. A regularity common to all independent experiments is revealed: at an angle of about 90°, there exists an excess of neutrons (30% for ²⁵²Cf and 60% for ²³⁵U) that does not admit explanation within the model of neutron emission from fully accelerated fragments. Two possible explanations of this experimental fact—neutron emission during the acceleration process and the existence of an additional source of neutrons (predominantly, prescission neutrons)—are considered. It is shown that the latter conjecture describes the observed features for both nuclei more adequately. The total yield of prescission neutrons and their energy and angular distributions are determined.     

Multiplicity distribution of prompt gamma rays in spontaneous ternary fission of252Cf

The first and the second moments of the multiplicity distribution of prompt gamma rays in spontaneous ternary fission of²⁵²Cf have been measured by the multiple coincidence technique. While both these moments were found to be nearly independent of the energy of the light charged particle accompanying the fission fragments, the width of the multiplicity distribution was larger than that in the case of normal binary fission by about 20%.     

Charge distributions in low-energy nuclear fission and their relevance to fission dynamics

Radiochemical and energy loss techniques have been used to measure fragment charge distributions in the systems ²²⁹Th(n_th, f), ²³⁵U(n_{3 MeV}, f) and ²⁵²Cf(s, f). Together with those previously obtained [^{233, 235}U(n_th, f) and ^{239, 241}Pu(n_th, f] the results show that these charge distributions depend very sensitively on both the fissioning species and the initial excitation energy. Very strong even-odd effects are present, for example in the charge distribution of ²²⁹Th(n_th, f) while they almost disappear in ²³⁵U(n_{3 MeV}, f). In the ²²⁹Th(n_th f) and ²⁵²Cf(s, f) cases, kinetic energy distributions of the fragments have been obtained. Fragments with even charges are more energetic, on average, than fragments with odd charges. The results are discussed in terms of a rather small probability for pair breaking during the transition from saddle-point to scission. The relationship between even-odd effects in charge distributions and fine structures in mass distributions is also investigated.     

New data on the ternary fission of 252Cf from the Gammasphere facility

Ternary fission of ²⁵²Cf was studied at Gammasphere using eight ΔE×E particle telescopes. Helium, beryllium, boron, and carbon light charged particles (LCPs) emitted with kinetic energy more than 9, 21, 26, and 32 MeV, respectively, were identified. The 3368-keV γ transition from the first 2⁺ excited state in ¹⁰Be was found and the population probability ratio N(2⁺)/N(0⁺) = 0.160 ± 0.025 was estimated. No evidence was found for 3368-keV γ rays emitted from a triple molecular state. For the first time, charge distributions are obtained for ternary fission fragments emitted with helium, beryllium, and carbon LCPs.     

Neutron-neutron angular correlations in spontaneous fission of <Superscript>252</Superscript>Cf

An experiment has been carried out to study neutron-neutron angular correlations in spontaneous fission of ²⁵²Cf. Angular dependences of the number of neutron-neutron coincidences obtained in the experiment were compared with the results of the Monte Carlo calculations for various neutron detection thresholds in the range 425–1600 keV. It was inferred that 10–11% of the total number of prompt neutrons from ²⁵²Cf (s.f.) in the laboratory system were emitted isotropically and may probably be interpreted as neutrons directly associated with the instant of scission of the nucleus. The analysis allowed their energy distribution to be determined as well. A similar method was also used to describe the angular correlation of prompt neutrons that accompanied the reaction ²³⁵U(n _th ,f).     

Collinear cluster tripartition channel in the reaction 235U(n th, f)

Investigation of the ²³⁵U(n _th, f) reaction using the miniFOBOS double-arm time-of-flight spectrometer of fission fragments confirmed manifestations of the earlier unknown many-body, at least ternary, decay involving almost collinear decay-product escape, which were first observed in the spontaneous fission of ²⁵²Cf(sf). The use of variables sensitive to the nuclear charge of fission fragments allowed the reliability of identification of decay events to be increased and new decay modes to be revealed.