Liquid drop model of multiply charged metal cluster fission

Qualitative similarities and differences between metal cluster and nuclear fission are discussed in terms of the liquid drop model. Points covered include the dependence onz ²/n of the relative fission rate, the critical size, and the competition between fission and evaporation.     

Shell correction study of fission of doubly charged silver clusters

Fission of doubly charged silver clusters is investigated by the method of shell corrections. The following fission events are considered: Ag ₂₂ ²⁺ → Ag _n ⁺ + Ag _{22 ?n} ⁺ , (n=11, 10, 9, 8); Ag ₂₁ ²⁺ → Ag _n ⁺ + Ag _{21 ?n} ⁺ , (n=10, 9, 8, 7); Ag ₁₈ ²⁺ → Ag _n ⁺ + Ag _{18 ?n} ⁺ , (n=9, 8, 7, 6). It is found that the shell correction energy is comparable to or larger than the deformation energy of the liquid drop. Threshold energies for the fission events are calculated and compared with the experimental abundance spectra obtained by Katakuse et al. (1990). Correspondence between the calculated threshold energies with the shell corrections and the experimental abundance is very good, showing products from lower threshold fission channels yield more abundance. The threshold energies without the shell corrections are almost constant irrespective of the fission channels and cannot explain the experimental abundance. Abundance of some products are too small to be accounted for only by the threshold energies. The low abundance of those products may be explained by the presence of competing fission channels that have similar minimal energy paths. It is found in fission of Ag ₁₈ ²⁺ that the shell correction overwhelms the Coulomb energy and the fission channel to Ag₈ + Ag ₁₀ ²⁺ is preferred over the fission channel to Ag ₈ ⁺ + Ag ₁₀ ⁺ .     

Variational RRKM theory calculation of thermal rate constant for carbon—hydrogen bond fission reaction of nitro benzene

The present work provides quantitative results for the rate of unimolecular carbon-hydrogen bond fission reaction of benzene and nitro benzene at elevated temperatures up to 2000 K. The potential energy surface for each C-H (in the ortho, meta, and para sites) bond fission reaction of nitro benzene was investigated by ab initio calculations. The geometry and vibrational frequencies of the species involved in this process were optimized at the MP2 level of theory, using the cc-pvdz basis set. Since C-H bond fission channel is barrier less reaction, we have used variational RRKM theory to predict rate constants. By means of calculated rate constant at the different temperatures, the activation energy and exponential factor were determined. The Arrhenius expression for C-H bond fission reaction of nitro benzene on the ortho, meta and para sites are k(T) = 2.1 × 10¹⁷exp(?56575.98/T), k(T) = 2.1 × 10¹⁷exp(?57587.45/T), and k(T) = 3.3 × 10¹⁶exp(?57594.79/T) respectively. The Arrhenius expression for C-H bond fission reaction of benzene is k(T) = 2 × 10¹⁸exp(?59343.48.18/T). The effect of NO₂ group, location of hydrogen atoms on the substituted benzene ring, reaction degeneracy, benzene ring resonance and tunneling effect on the rate expression have been discussed.     

Determination of the 238U spontaneous fission decay constant without neutron irradiation

We have developed a methodology for measuring the decay constant of the spontaneous fission of ²³⁸U, l_f, using nuclear particle track detectors where thermal neutron irradiation is unnecessary. This methodology is based on the fact that the radiation damage caused by spontaneous fission of trans-uranium elements bearing a mass number close to 238 are similar to ²³⁸U spontaneous-fission ones. Loading a thick source of uranium (thickness greater than the fission fragment range) with a small amount of a suitable trans-uranium element (for instance, ²⁴²Pu, which presents a spontaneous fission half-life of 6.75^.10¹⁰ y), it is possible to determine the observation efficiency of a particle-track detector for fission fragments. Procedures concerning our thick source manufacture and uniformity tests of the trans-uranium distribution are also presented. These results make it possible for the exposure of thick uranium sources (without trans-uranium element) to lead to a l_f value.     

Simple metal clusters

The response of alkali cluster ions to an optical excitation is investigated for two different photon energy domains. Below the ionization potential giant resonances in the photoabsorption cross-section are observed for closed shell species. Above the ionization potential, the ionization process competes with the photofragmentation process. The number of valence electrons determines both the behavior of the photoabsorption spectrum and the evolution of the ionization cross-section with the cluster size. The stability of the clusters against an excess of charge is examined through the observation of an asymmetric fission of Na _n ⁺⁺ . Experimental results are discussed in term of an electrostatic model giving an estimate of the critical size of stability and of the height of the coulombic barrier.     

Fine structure of mass and charge distribution in low energy fission

Studies of finer details in mass and charge distribution fission leads to a better understanding of the fission process. Experimental determination of independent and cumulative yields using radiochemical techniques as well as mass spectrometers and fission product recoil separators form the basis of such studies. It has been established that closed shells as well as an even number of nucleons influence both mass and charge distributions. The magnitudes of these effects may be estimated from existing experimental yield data and various fission models. Using our measurements of several fission yields and those existing in the literature we have calculated even-odd proton and neutron effects for various low energy fissioning systems. Where enough data existed, direct calculations were made, whereas for other cases the Z_p-model of WAHL has been used. It is found that the even-odd proton effect is well established and pronounced in thermal neutron fission of²³⁵U and²³³U. Lesser effects were found for reactor neutron induced fission of²³²Th, thermal neutron fission of²³⁹Pu and spontaneous fission of²⁴⁵Cm and²⁴⁹Cf. No effect seems to exist in the thermal neutron fission of²⁴¹Pu and the spontaneous fission of²⁵²Cf. The even-odd neutron effect is found to be much lower than the corresponding proton effect in²³⁵U and²³³U fissions and is nonexistent in the rest of the fissioning systems.     

Fission studies in the reaction of <Superscript>19</Superscript>F with <Superscript>209</Superscript>Bi at 99.2 MeV

Fission product yield studies in the reaction of 99.2 MeV ¹⁹F with ²⁰⁹Bi have been carried out for the first time using gamma-ray spectrometry. The cross sections for the production of fission products have been determined. The yield distribution of fission products was found to be symmetric and broad with FWHM around 22 mass units and peak near mass 111. The average number of neutrons emitted per fission has been found to be around 6.7. The comparison of the fission products yield distribution of ²⁰⁹Bi using projectiles like ⁴He, ¹²C, ¹⁶O, and ¹⁹F have shown that the mass of symmetric peak increases as the mass of the compound nucleus increases. The high fission yield around mass 112 has been attributed to the presence of deformed neutron shells. The total fission cross section and width of the mass distribution have been found to be low in case of ¹⁶O induced fission as compared to the ⁴He, ¹²C, and ¹⁹F induced fission of ²⁰⁹Bi.     

Fission product yields in the fast-neutron fission of238U

The fission yields of 38 fission products in the fast-neutron induced fission of²³⁸U have been determined using a rapid, multiscaling gamma-ray spectroscopic method. To obtain absolute yields for fission products having half-lives ranging from 32 s to 40 d, a total of 56 multi-scaling gamma-ray spectra were collected using various irradiation and cooling periods. Gamma-rays and photopeak areas of interest were assigned to the fission products by their energies and half-lives. Fission product activities were evaluated from spectral data using growth and decay calculations and fission yields were determined by normalizing the¹⁴⁰Ba yield to the average value from reported data. The depleted uranium target, covered with a boron-cadmium thermal neutron shield, was used to keep interference from the fission of²³⁵U minimal. Results for the cumulative fission yields, including 17 mostly short-lived fission products measured for the first time, are compared with previous measurements and with the recommended yields in recent evaluations. The agreement, and some discrepancies, in the comparisons are discussed. No explicit even-odd pairing effects are observed in the fission yield data for fast-neutron induced fission of²³⁸U.     

Measurements of fission yield in 8 MeV bremsstrahlung induced fission of 232Th and 238U

The cumulative yields (i.e. the sum of isobaric independent yield up to the isobar of interest) for various fission products have been determined in the 8 MeV bremsstrahlung induced fission of ²³²Th and ²³⁸U by using off-line gamma ray spectrometric technique. From the cumulative yields of the fission products, their mass-chain yields (i.e. the sum of independent yields of all the isobars) were obtained by using charge distribution correction. The mass-chain yields in the ²³²Th(γ, f) and ²³⁸U(γ, f) reactions were compared with the data of similar excitation energy in the ²³²Th(n, f) and ²³⁸U(n, f) reactions to examine the effect of nuclear structure. From these data, it was found that the yields of fission products for the mass numbers 133–134, 138–140 and 143–144 as well as their corresponding complementary products are significantly higher than other fission products. Higher yields of the fission products around the mass numbers 133–134 and 143–144 were explained from the standard I and standard II asymmetric mode of fission, which indicates the role of shell closure proximity. However, the amplitude of yields for the mass numbers 133–134 and 143–144 are reverse in the ²³²Th(γ, f) and ²³²Th(n, f) reactions than in the ²³⁸U(γ, f) and ²³⁸U(n, f) reactions, which has been explained from the point of shell combinations of the complementary fragments.     

Separation of gram quantities of uranium from fission products by extraction chromatography

The separation of gram quantities of uranium from fission products has been investigated by extraction chromatography. The separation which is based on the difference in distribution coefficients between uranium and the fission products on a tributyl phosphate (TBP) resin in nitric acid medium, was carried out by means of high acidity feed and stepwise elution on a TBP chromatography column. The results show that this technique is capable to separate 5 g of uranium from a large quantity of fission products. The recovery of uranium is more than 99%. The decontamination factors of g- and b-activities were 2.1^.10³ and 2.3^.10³, respectively.     

Spontaneous fission yields for 238U in molybdenum measured in Archaean zircons

The relative cumulative fission yields of ^95,97,98,100Mo produced by spontaneous fission of ²³⁸U contained in Archaean zircons, were measured by sensitive thermal ionization mass spectrometry (TIMS). The relative yields for ^95,97,98,100Mo are 0.58 : 1.08 : 1.04 : 1.0, respectively. Combined with mass spectrometrically-determined ^{99,101,102,104}Ru fission yields,¹ the mass distribution from 95￡A￡104 can be delineated. Assuming an “absolute” fission yield of 6.1±0.4% for the cumulative fission yield at mass 97, it is possible to express the Mo and Ru relative spontaneous fission yields for ²³⁸U as “absolute” values. There is no evidence for a significant isotope anomaly at mass 98. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fission yields of molybdenum in the Oklo natural reactor

The isotopic compositions of molybdenum in six uranium-rich samples from the Oklo Zone 9 natural reactor were accurately measured by thermal ionization mass spectrometry. The samples were subjected to an ion exchange separation process that removed the isobaric elements zirconium and ruthenium, with high efficiency and a low blank. Molybdenum possesses seven isotopes of which ^92,94,96Mo are unaffected by the fission process, enabling the raw data to be corrected for isotope fractionation by normalising to ⁹²Mo/⁹⁶Mo, and to use ⁹⁴Mo to correct for the primordial component in each of the fission-produced isotopes. This enables the relative fission yields of Mo to be calculated from the isotopic composition measurements, to give cumulative fission yields of 1:0.941:0.936:1.025 for ^95,97,98,100Mo, respectively. These data demonstrate that the most important nuclear process involved in reactor Zone 9 was the thermal neutron fission of ²³⁵U. The consistency of the relative cumulative fission yields of all six samples from different locations in the reactor, implies that Mo is a mobile element in the uraninite comprising Zone 9, and that a significant fraction of molybdenum was mobilized within the reactor zone and probably escaped from Zone 9, a conclusion in agreement with earlier published work.     

Preparative scale mass spectrometry: A brief history of the calutron

Calutrons were developed in the laboratory of E. O. Lawrence at the University of California at Berkeley. They were a modification of the cyclotrons he had invented and used in his Noble Prize winning investigations of the atomic nucleus. At the time their construction was undertaken, calutrons represented the only certain means of preparing enriched uranium isotopes for the construction of a fission bomb. The effort was successful enough that every atom of the 42 kg of ²³⁵U used in the first uranium bomb had passed through at least one stage of calutron separation. At peak production, the first stage separators, α tanks, yielded an aggregate 258-g/d ²³⁵U enriched to about 10 at. % from its natural abundance level of 0. 72 at. %. The second stage separators, β tanks, used the 10 at. % material as feedstock and produced a total 204-g/d ²³⁵U enriched to at least 80 at. %. The latter, weapons grade, material was used in fission bombs. Under typical operating conditions, each α tank operated at a uranium beam intensity at the collectors of approximately 20 mA and each β tank at a beam intensity of approximately 215 mA at the collectors. Bulk separation of isotopes for bomb production ceased in 1945. Since that time calutrons have been used to separate stable isotopes, but on a more limited scale than wartime weapons production. Stable isotope separations since 1960 have taken place using one modified beta tank.     

Plutonium-244 dating

Re-examination of a vast amount of xenon isotope data which have been accumulated since the 1960s reveals that the so-called CCF (carbonaceous chondrite fission) xenon is a mixture of²⁴⁴Pu fission xenon and a severely mass-fractionated primordial xenon, whose isotopic composition has been further altered by neutron-capture and spallation reactions, which occurred in the vicinity of a supernova that most likely exploded sometime more than 4.8 billion years ago. The integrated flux of 10 KeV (stellar temperature) neutrons to which the xenon was exposed appears to have been in excess of 10²³ n/cm².     

Scission shapes of pair fragments in asymmetric and symmetric fission modes

Scission shapes composed of two touching spheroids in asymmetric and symmetric fission modes have been deduced from static potential calculations with the experimental fragment total kinetic energy and excitation energies for a typical fragment pair of ¹⁰³Nb and ¹³⁰Sn in the proton-induced fission of ²³²Th. It was found that the fragment deformation of the heavy fragment ¹³⁰Sn in the symmetric fission mode was extremely large compared with that in the asymmetric fission and those of the complementary fragment ¹⁰³Nb. Such scission shapes also provide internal excitation energies of pair fragments in the two fission modes. The deduced total internal excitation energies of complementary fragments for the two fission modes are nearly the same as the excitation energy of the fissioning nucleus. The results suggest that the two fission modes are strongly characterized by the degrees of fragment deformation of the heavy fragments, not by the total internal excitation energies at scission.     

Thermal homolytic fission of the MoMo bond in (h5 -C5H5)2Mo2(CO)6

Kinetic studies of reactions of the MoMo bonded complex (h⁵-C₅H₅)₂Mo₂(CO)₆ in decalin show that it undergoes reversible homolytic fission and that the activation enthalpy required to break the MoMo bond is 135.9 ± 2.2 kJ mol^?1.     

The use of hydrochloric acid in separating95Zr−95Nb activity from uranium fission products on silica gel

Dissolution of a neutron-irradiated uranium target in a medium of 6N HCl containing a few drops of very dilute HNO₃ yielded a matrix solution which on running on a silica gel column allowed the complete adsorption of the⁹⁵Zr−⁹⁵Nb activity formed in the fission process. The⁹⁵Zr−⁹⁵Nb activity is cleanly and totally eluted with 0.5% oxalic acid solution. None of the uranium or the activity of the other fission products was found to be adsorbed on the column.     

Xe-135 production from Cf-252

The presence of ¹³⁵Xe is often used as an indicator that fission has occurred, and is used to help enforce the Comprehensive Test Ban Treaty. There are no known commercial suppliers, though it can be acquired. Readily available standards of this isotope are very useful. ¹³⁵Xe can be produced through fission, or by neutron capture on ¹³⁴Xe. At the INL, scientists have previously transported fission products from an electroplated ²⁵²Cf thin source for the measurement of nuclear data of short-lived fission products using a technique called He-Jet collection. A similar system has been applied to the collection of gaseous ¹³⁵Xe, and ¹³³Xe, in order to produce standards of these isotopes.     

INAA of Zr,La, Ce and Nd in geological samples in the presence of different uranium concentratios

Rock samples which contain relatively high concentrations of uranium may create problems of interference produced by fission products, when instrumental neutron activation analysis is used. The isotopes⁹⁵Zr,¹⁴⁰La,¹⁴¹Ce, 143Ce and 147Nd, which are commonly used in the neutron activation analysis of the corresponding elements, are also produced as fission products of²³⁵U. For each of these radioisotopes, a contribution factor is calculated theoretically and meaured experimentally using geological samples with different uranium contents.     

Determination of uranium fission interference factors for INAA

Instrumental neutron activation analysis (INAA) is a very suitable technique for the determination of several elements in different kinds of matrices. However, when the sample contains high uranium concentration this method presents interference problems of uranium fission products. The same radioisotopes used in INAA are formed in uranium fission. Among these radioisotopes are ¹⁴¹Ce, ¹⁴³Ce, ¹⁴⁰La, ⁹⁹Mo, ¹⁴⁷Nd, ¹⁵³Sm and ⁹⁵Zr. The purpose of this study was to evaluate uranium fission interference factors to be used in the INAA of environmental and geological samples containing high levels of U. The obtained interference factors agreed with literature reported values. The results point to the viability of using these experimentally determined interference factors for the correction of uranium fission products.