Investigation of Ternary Fission of <Stack><Subscript>98</Subscript><Superscript>252</Superscript></Stack>Cf Using Three-Cluster and Unified Ternary Fission Models

Using three-cluster and unified ternary fission models, the ternary fission of ₉₈²⁵²Cf is studied. We applied collinear and equatorial configurations to study the ternary fission of ₉₈²⁵²Cf when the third fragment is ₃¹⁰Li. The nuclear potential energy in the three-cluster model and unified ternary fission model is calculated respectively, using Yukawa plus exponential and proximity formalisms. The relative yields of different fragmentation channels are calculated. Our results reveal that the ternary fragmentation potential of the three fragments and the relative yields depend on the configuration of three fragments and usedmodel. Two models predict that the lowest driving potential and highest relative yield take place for the fragment combination ₅₁¹³²Sb + ₄₄¹¹⁰Ru + ₃¹⁰Li. Also, the values of driving potential and relative yield are not equal in the three-clustermodel and unified ternary fission model. For fragment combination ₅₁¹³²Sb + ₄₄¹¹⁰Ru + ₃¹⁰Li, the relative yield based on the three-cluster model in collinear configuration is maximum, whereas the unified ternary fission model in equatorial configuration predicts the lowest relative yield.     

Kinetic energies of cluster fragments in ternary fission of <Superscript>252</Superscript> Cf

The kinetic energy distribution and potential energies of fragments from the collinear cluster tripartition (CCT), the “true” ternary fission of ²⁵²Cf, have been calculated. It is assumed that the breakup of the nucleus into three fragments happens sequentially in two steps from a hyper-deformed shape. In the first step a first neck rupture occurs of the parent radioactive nucleus, forming two fragments (one of them is usually ¹³²Sn) and, in the second step, one of the two fragments breaks into two other fragments, resulting finally in three fragments (the experiment is based on a binary coincidence where a missing mass is determined). We show the result for the principal combination of the three spherical fragments (semi-magic isotopes of Sn, Ca, Ni) observed recently experimentally. These isotopes are clusters with high Q -values, which produce the highest yields in the ternary fission bump. It is shown that the kinetic energies of the middle fragments have very low values, making their experimental detection quite difficult. This fact explains why the direct detection of true ternary fission with three fragments heavier than A > 40 has escaped experimental observation.     

Coaxial Fission of Nuclei to Three Commensurate Fragments

Trajectory calculations of the angular distribution of fragments originating from the spontaneous true ternary fission of ²⁵²Cf nuclei are performed with allowance for the rotation of the fissile-nucleus axis. This rotation arises upon scission because of the formation of fragment spins despite the conservation of zero total angular momentum at all fission stages. The calculations in question lead to the conclusion that a collinear tripartition is the most probable in spontaneous true ternary fission of ²⁵²Cf nuclei. This confirms experimental data, thereby creating the basis that is necessary for obtaining deeper insight into them.     

New experimental studies on the quaternary fission of <Superscript>233, 235</Superscript>U(n<Subscript>th</Subscript>, f ) and <Superscript>252</Superscript>Cf (sf )

Experiments have been performed for studying quaternary fission (QF) in spontaneous fission of ²⁵²Cf, on the one hand, and for the neutron-induced fission reactions ^{233, 235}U(n_th, f ), on the other hand. In this higher-multiplicity fission mode, by definition, four charged products appear in the final state. In other words, as a generalization of the ternary-fission process, not only one but two light charged particles (LCPs) are accompanying the splitting of an actinide nucleus into the customary pair of fission fragments. In the two sets of measurements, which have used quite different approaches, the yields of several QF reactions with α-particles and tritons as the LCPs have been determined and the corresponding kinetic-energy distributions of the α-particles measured. The QF process can appear in two basically different ways: i) the simultaneous creation of two LCPs in the act of fission (“true” QF) and ii) via a fast sequential decay of a single but particle-unstable LCP in common ternary fission (“pseudo” QF). Experimentally the two varieties of QF have been distinguished by exploiting the different patterns of angular correlations between the two outgoing LCPs. The experiments described in the present paper are the first to demonstrate that both types of reactions, true and pseudo QF, occur with quite comparable probabilities. As a new result also, the kinetic-energy distributions related to the two processes have been shown to be significantly different. For all QF reactions which could be explored, the yields for ²⁵²Cf(sf) were found to be roughly by an order of magnitude larger than the yields found in the ²³³U(n_th, f ) and ²³⁵U(n_th, f ) reactions. An interesting by-product has been the measurement of yields of excited LCPs which allows to deduce nuclear temperatures at scission by comparison to the respective yields in the ground state.     

Charge distribution studies in the fast-neutron-induced fission of <Superscript>232</Superscript>Th, <Superscript>238</Superscript>U, <Superscript>240</Superscript>Pu and <Superscript>244</Superscript>Cm

Charge distribution studies for heavy-mass fission products were carried out in the fast-neutron-induced fission of ²³²Th, ²³⁸U, ²⁴⁰Pu and ²⁴⁴Cm using radiochemical and gamma-ray spectrometric techniques. The width parameter( σ_Z/σ_A), the most probable charge/mass ( Z _P/A _P), the charge polarization (ΔZ) and the slope of charge polarization [ δ(ΔZ)/δA ^′] as a function of the fragment mass (A ^′) were deduced. The average charge dispersion parameter ( 〈σ_Z〉) and proton odd-even effect ( δ_p) were also obtained for these fissioning systems. The 〈σ_Z〉 and δ_p values in the fissioning systems ²⁴¹Pu ^* and ²⁴⁵Cm ^* were determined for the first time. The δ(ΔZ)/δA ^′ value is also determined for the first time in the fissioning systems ²³⁹U ^* , ²⁴¹Pu ^* and ²⁴⁵Cm ^* . These data along with the literature data for even-Z fissioning systems such as ²³⁰Th ^* , ²³²Th ^* , ²³³U ^* , ²³⁴U ^* , ²³⁶U ^* , ²³⁸U ^* , ²³⁹Pu ^* , ²⁴⁰Pu*, ²⁴²Pu ^* , ²⁴⁶Cm ^* , ²⁵⁰Cf ^* and ²⁵²Cf(SF) are discussed in terms of nuclear structure effect and dynamics of descent from the saddle to the scission point. The role of the excitation energy in low-energy fission is also discussed. Received: 26 July 2002 / Accepted: 3 December 2002 / Published online: 3 April 2003 RID="a" ID="a"Present address: Emeritus Scientist (CSIR) Bhabha Atomic Research Centre, Nuclear Recycle Group, WIP Building, Trombay, Mumbai-400085, India; e-mail: rhiyer@magnum. barc.ernet.in Communicated by D. Schwalm     

Ternary fission within statistical approach

The ternary system with a light nucleus between two heavy fragments is assumed to appear from the binary configuration near scission. The formation of a third light nucleus in the binary system is considered. The calculated charge distributions in spontaneous ternary fission of ²⁵²Cf and in induced ternary fission of ⁵⁶Ni are compared with the available experimental data. The neutron multiplicity from the fission fragments is described. The fine structures of the TKE-mass distribution are predicted.     

Quenching of the E1 strength in <Superscript>149</Superscript>Nd

Lifetime measurements of excited states in ¹⁴⁹Nd have been performed using the advanced time-delayed b \beta g \gamma g \gamma(t) method. Half-lives of 14 excited states in ¹⁴⁹Nd have been determined for the first time or measured with higher precision. Twelve new g \gamma -lines and 5 new levels have been introduced into the decay scheme of ¹⁴⁹Pr based on results of the g \gamma g \gamma coincidence measurements. Reduced transition probabilities have been determined for 40 g \gamma -transitions in ¹⁴⁹Nd . Configuration assignments for 6 rotational bands in ¹⁴⁹Nd are proposed. Enhanced E1 transitions indicate that the ground-state band and the band built on the 332.9keV level constitute a pair of the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands. Potential energy surfaces on the (b₂,b₃)\ensuremath (\beta_{2},\beta_{3}) -plane have been calculated for the lowest single quasi-particle configurations in ¹⁴⁹Nd using the Strutinski method and the axially deformed Woods-Saxon potential. The predicted occurrence of the octupole-deformed K = 5/2 configuration is in agreement with experiment. Unexpectedly low |D₀|\ensuremath \vert D_0\vert values obtained for the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands may result from cancellation between the proton and neutron shell correction contributions to |D₀|\ensuremath \vert D_0\vert .     

Cluster ion emission from LiF induced by MeV N<Superscript>q+</Superscript> projectiles and <Superscript>252</Superscript>Cf fission fragments

Ion cluster desorption yields from LiF were measured at PUC-Rio with ≈0.1 MeV/u N ^q+ (q = 2,4,5,6) ion beams by means of a time-of-fight (TOF) mass spectrometer. A ²⁵²Cf source mounted in the irradiation chamber allows immediate comparison of cluster emissions induced by ≈65 MeV fission fragments (FF). Emission of (LiF) _n Li⁺ clusters are observed for both the N beams and the ²⁵²Cf fission fragments. The observed cluster size n varies from 1 to 6 for N ^q+ projectiles and from 1 to ≈40 for the ²⁵²Cf-FF. The size dependence of the Y(n) distributions suggests two cluster formation regimes: (i) recombination process in the outgoing gas phase after impact and (ii) emission of pre-formed clusters from the periphery of the impact site. The corresponding distribution of ejected negative cluster ions (LiF) _n F⁻ closely resembles that of the positive secondary (LiF) _n Li⁺ ions. The desorption yields of positive ions scale as Y(n) ∼ q ⁵. A calculation with the CASP code shows that this corresponds to a cubic scaling ∼S _e ³ with the electronic stopping power S _e , as predicted by collective shock wave models for sputtering and models involving multiple excitons (Frenkel pair sputtering). We discuss possible interpretations of the functional dependence of the evolution of the cluster emission yield Y(n) with cluster size n, fitted by a number of statistical distributions.     

Digital signal processing application to <Superscript>252</Superscript>Cf(sf) reaction products spectroscopy

The emission of prompt fission neutrons in spontaneous fission of ²⁵²Cf was studied by the application of digital data processing for the first time. The study was aimed at comparing the obtained results with those from the pioneering work of Budtz-Jorgensen and Knitter. By using a twin Frisch grid ionization chamber for fission fragment detection and a neutron scintillator (NE213) for the detection of neutrons, a total of about 10⁷ neutron coincidences were registered. The fission-fragment kinetic energies were measured using a fast (80 MHz) waveform digitizer that provided 10-bit amplitude resolution. Standard analog NIM modules were used for neutron time-of-flight and pulse shape measurements. A time-to-digital converter (TDC) with 1-ns resolution and a pair of gated charge-to-digital converters with 12-bit amplitude resolution were also used. The fission fragment signals were analyzed by means of digital signal processing algorithms. Data on prompt fission neutron energies were obtained by using a time-of-flight (TOF) spectrum unfolding procedure applicable to list-mode data.     

Analysis of fragment mass distribution in asymmetric area at fission of <Superscript>235</Superscript>U induced by thermal neutrons

The fragment mass yields in fission of ²³⁵U induced by thermal neutrons for A = 145–160 and E_K = 50–75 MeV were measured using a mass spectrometer. The fine structure is observed at A = 153, 154 and E_K = 50–60 MeV. The obtained results were described in the framework of a model based on the dinuclear system concept. The analyzed correlation between the total kinetic energy and mass distribution of fission fragments is connected with the shell structure of the formed fragments of fission. From this correlation and the time dependence of the calculated mass distribution of the binary reaction products, one can conclude that the descent time from a saddle point to a scission point for the more deformed fragments is longer than that for fragments of more compact shape.     

Dynamical decay process of <Superscript>219, 220</Superscript>Ra<Superscript>*</Superscript> formed in <Superscript>10, 11</Superscript>B + <Superscript>209</Superscript>Bi reactions

The excitation functions for both the evaporation residue and fission have been calculated for ¹⁰B + ²⁰⁹Bi and ¹¹B + ²⁰⁹Bi reactions forming compound systems ^{219, 220}Ra^* , using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of the nuclei included in it. In addition to this, the excitation functions for complete fusion (CF) are obtained by summing the fission cross-sections, neutron evaporation and charged particle evaporation residue cross-sections produced through the axn\ensuremath \alpha xn and pxn\ensuremath pxn (x = 2, 3, 4) emission channels for the ²¹⁹Ra system at various incident centre-of-mass energies. Experimentally the CF cross-sections are suppressed and the observed suppression is attributed to the low binding energy of ^{10, 11}B which breaks up into charged fragments. The reported complete fusion (CF) and incomplete fusion (ICF) excitation functions for the ²¹⁹Ra system are found to be nicely fitted by the calculations performed in the framework of DCM, without invoking a significant contribution from quasi-fission. Although DCM has been applied for a number of compound nucleus decay studies in the recent past, the same is being used here in reference to ICF and subsequent decay processes along with the CF process. Interestingly the main contribution to complete fusion cross-section comes from the fission cross-section at higher incident energies, which in DCM is found to consist of an asymmetric fission window, shown to arise due to the deformation and orientation effects of formation and decay fragments.     

Nuclear-charge polarization at scission in proton-induced fission of <Superscript>233</Superscript>U

The primary and the secondary fragment mass yields and neutron multiplicity in the 11.5MeV proton-induced fission of ²³³U were determined by a double time-of-flight method. The most probable charges of the secondary fragments in the isobaric chains with A = 126 , 127, 129, 132, and 136 have been derived from the secondary mass yields together with the literature values of the fractional cumulative and independent yields measured radiochemically. The nuclear-charge polarization of primary fragments at scission was obtained by correcting the secondary fragment mass for neutron evaporation. The results show that the nuclear-charge polarization is mostly determined by the minimum potential energy of nuclei at scission and that this behavior is nearly independent not only of mass and excitation energy but also of neutron-to-proton ratios of the fissioning nuclei.     

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).     

Characteristics of spontaneous fission of <Superscript>250</Superscript>No

This study describes an experiment on investigating the properties of spontaneous fission of shortlived neutron-deficient nuclei synthesized in the reaction of complete fusion ⁴⁸Ca + ²⁰⁴Pb = ²⁵²No*. The experiment is performed using the SHELS separator and the beam of multicharged ions at U-400 accelerator (LNR, JINR). Two activities undergoing spontaneous fission, which can be related to the ground and isomeric states of ²⁵⁰No nucleus, are registered. The half-lives, total kinetic energies of fission fragments, and neutron multiplicities are measured for the short-lived nuclei. The average number of neutrons per fission for the activity with t _1/2 = 5.1 ± 0.3 μs is = 4.38 ± 0.13 μs, and for nuclei with the half-life t _1/2 = 36 ± 3 μs it is xxxxx.     

Fragment dependence of high energy γ-ray emission in the spontaneous fission of 252Cf

The high energy γ-ray emission accompanying the spontaneous fission of ²⁵²Cf has been measured in coincidence with individual fission fragments selected by discrete γ-ray transitions. The enhancement of the γ-ray emission probability in the energy range E_γ= 3–8 MeV has been observed for the fission fragments in the region of nearly symmetric mass splitting, confirming results reported in previous investigations. The γ-γ coincidence technique employed in the present work clearly demonstrate that the major contribution to this enhancement is caused by the fission channels where one fragment is near to the N= 82 or Z= 50 shell closures. The high energy γ-ray emission probability does not show any significant dependence on the number of neutrons emitted in the fission process, supporting the hypothesis that high energy γ-rays are mainly emitted from the fragments after the neutron evaporation. Received: 22 December 1998     

Correlation between fractional independent yields and neutron-to-proton ratio of fission products in low energy fission

Fractional independent yields of fission products in the thermal neutron-induced fission of²³³U,²³⁵U,²³⁹Pu,²⁴¹Pu and in the spontaneous fission of²⁵²Cf have been correlated with the neutron-to-proton ratio of the fission products. The yields of the products from a fissioning system, when plotted as a function of neutron-to-proton (N/Z) ratio of fission preducts, fall on two Gaussian distribution corresponding to light and heavy fission products. The centroids of the distribution or the most probable value of neutron-to-proton ratio is found to be very close to theN/Z of the fissioning nucleus. From the most probable value ofN/Z the various parameters of charge distribution e.g. most probable massA _p, most probable chargeZ _p, the mass dispersionσ _Aand the charge dispersionσ _Zhave been obtained and are in good agreement with the experimental values ofA _pandZ _p.     

Geometrical and dynamical state of the 252Cf nucleus at the scission point as determined from the experimental results of ternary fission

Resuits on the geometrical and dynamical states of fission fragments and α-particles are presented for the most probable mode of ternary fission, at the instant of release of the light particle. The distributions of the relevant physical quantities are obtained by means of a program calculating the trajectories of three point charges. A total of about 2 × 10⁵ combinations of the parameters, derived by subdividing the quantities into physically significant intervals, are used. The computed values are compared with experimental results and the distributions of the parameters are weighted by the spectrum of the α-parlicles. The dynamics of the system undergoing fission at scission point are characterized by the following quantities: (i) The total kinetic energy of fragments. (ii) The kinetic energy of the α-particle. (iii) The distance between the centres of charge of the fragments, (iv) The abscissa and Ordinate of the α-particle emission point, (v) The emission angle of the α-parlicle with respect to the line of flight of the light fragment. The distributions of above quantities are presented for the most probable model of spontaneous ternary fission of ²⁵²Cf The results obtained are discussed and relevant information on the dynamical properties of the last fission stage is presented.     

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.     

Level structures in the <Stack><Subscript>49</Subscript><Superscript>107</Superscript></Stack>In nucleus and their microscopic description

Excited states of the ₄₉¹⁰⁷In nucleus were populated through the ⁷⁸Se ( ³²S , p2n) fusion-evaporation reaction at beam energy, E _lab = 125 MeV. The de-excitations were studied using in-beam g \gamma -ray spectroscopic techniques involving the Compton-suppressed clover detector array. The level scheme of ¹⁰⁷In consisting of about seven bands is established up to spin ∼ 45/2ℏ with the addition of 25 new transitions. Spins and parities of various levels have been assigned through the DCO and polarization measurements. The level structures observed in ¹⁰⁷In have been interpreted in the framework of a microscopic theory based on the deformed Hartree-Fock (HF) and angular-momentum projection techniques. Various bands are reproduced in band mixing calculations with the configurations involving high-W \Omega p \pi g _9/2 and n \nu d _5/2 orbits, and low-W \Omega p \pi g _7/2 , n \nu g _7/2 and n \nu h _11/2 orbits.     

Nuclear-charge polarization at scission in the 12 MeV proton-induced fission of <Superscript>232</Superscript>Th

The most probable charges of secondary fragments, produced after neutron evaporation from primary fragments, have been evaluated using fractional cumulative and mass yields in the 12MeV proton-induced fission of ²³²Th . The nuclear-charge polarization of primary fragments at scission has been obtained by correcting the most probable charge of secondary fragments for neutron evaporation. The fragment mass dependence of the nuclear-charge polarization at scission shows good agreement with that for thermal neutron-induced fission of ²³⁵U , indicating that the nuclear-charge polarization is nearly insensitive to mass and excitation energy of the fissioning nucleus for asymmetric fission in the actinide region.