Mass Division Research Articles

Asymmetric Fission in the Two-Center Model

Four-dimensional potential energy surfaces have been calculated in the asymmetric two-center model for $^{252}\mathrm{Fm}$, $^{258}\mathrm{Fm}$, $^{264}\mathrm{Fm}$, and $^{236}\mathrm{U}$. Symmetric fission is found to be preferred in $^{258}\mathrm{Fm}$, consistent with a recent observation; symmetric mass division is strongly preferred in $^{264}\mathrm{Fm}$. Asymmetric fission is preferred in $^{252}\mathrm{Fm}$, and in $^{236}\mathrm{U}$ for which the fission path is investigated in more detail. The development of asymmetry in the fission of $^{236}\mathrm{U}$ is described.

Interpretation of mass asymmetry in fission based on deformation energy surfaces

The deformation energy surfaces of fissioning nuclei have been studied to quantitatively interpret the experimentally observed mass asymmetry in fission. These studies use the calculated deformation energy surfaces which have recently been shown to have reflection asymmetric saddle-point shapes in the second (outer) fission barriers of actinide nuclei. Quantitative estimates of the mass asymmetry in fission, characterized by the peak-to-valley mass-yield ratio, have been calculated from an analysis of the fission probabilities over the outer barrier. The probability distributions were determined using the simple Fermi-gas level density and the WKB barrier-penetration formulae. Good correlations have been obtained for all known radiochemically determined peak-to-valley ratios of doubly even fissioning nuclei for which deformation energy surface calculations are available. One is able to understand by this analysis the recently discovered apparently anomalous results that the thermal-neutron-induced fission of 257Fm yields a symmetric mass division while the spontaneous fission of 256Fm is fission asymmetric. Apossible explanation for the triple-peaked mass-yield fission of nuclei near 226Ra is proposed based also on the deformation energy surfaces. Further experiments are suggested to test the present theory, in particular, to discriminate between analyses based on the fission barrier in the deformation energy surfaces and those based on fragment shell effects.

Calculation of Kinetic Energy and Most-Probable Charge in Fission

Kinetic energies and most-probable charges in fission were calculated for 235 U+n, 252 Cf and 226 Ra+p by applying the statistical model by Fong. The mass formula by Myers and Swiatecki was employed to evaluate fragment deformation energies. The most-probable scission configuration for a given mass division was obtained by maximizing the effective intrinsic excitation energy of the complementary fragments which was given as a function of their charges and deformation parameters. The general trends of the kinetic energy distribution and the charge distribution in fission could be reproduced fairly well.

XI.—Correlations in alpha-Particle-accompanied fission

SynopsisThe attempt is made to exhibit the necessary correlations between fragment excitation (or prompt neutron number), fragment kinetic energy, and a-particle energy, in α-particle-accompanied ternary fission. Treating a single mode of mass and charge division on the assumption that the ternary process develops directly out of an intermediate binary phase, and using the mutual electrostatic potential energy of the nascent binary fragments of this phase and the additional kinetic energy developed at the moment of α-particle emission as independent variables, various formal results are obtained and discussed in the light of the experimental evidence.In terms of a classical description, it appears likely that (for a given mode of division) the nuclear configuration at a-particle release in ternary fission is subject to much smaller variations than is the nuclear configuration at scission in binary fission in the corresponding mode. Possible inadequacies of this classical description are very briefly discussed.

Adiabatic Theory of Fission

Assuming that the fission process from the saddle point to the scission point is adiabatic with respect to the degrees of freedom of elongation and rotation of the nucleus as a whole, and that the state wave function remains a quasi-particle vacuum throughout the process, the time dependent Hartree-Fock-Bogolyubov theory is developed. A representation of the nucleon destruction operator in terms of the fragment single particle wave functions is introduced, which is suitable for the description of the density localization of the nucleus. Furthermore, it is assumed that the nascent fragments interact through the exchange of the valence nucleons near the Fermi energy and that the remaining nucleons form inert closed cores of the fragments. A simple model of the equations of motion for the density matrices is solved, and it is shown that the valence nucleon system has an asymmetric oscillation mode which leads to asymmetric mass divisions of the nucleus.

Reflection Symmetry and Fission Mass Ratios

It is shown that the collective potential energy surfaces for rapid deformations leading to nuclear scission favor asymmetric mass division. A "walk-run" fission process is proposed, in which a slow deformation to the saddle-point shape is appropriately described by the liquid-drop model, and a rapid collective deformation then carriers the nucleus from saddle point to scission. The most probable mass ratio decreases with decreasing $\frac{{Z}^{2}}{A}$, in qualitative agreement with empirical fact.

Ranges and Kinetic Energies of Fragments from Fission ofU238Induced by 14.5-MeV Neutrons

The average ranges of eight fission-product recoils in uranium, including both symmetric and asymmetric fragments, have been measured radiochemically from 14.5-MeV-neutron-induced fission of $^{238}\mathrm{U}$, using the thick-target technique. The measured average ranges, corrected for anisotropy, scattering, and edge effects, are, in mg/${\mathrm{cm}}^{2}$ U: $^{91}\mathrm{Sr}$: 10.21\ifmmode\pm\else\textpm\fi{}0.42, $^{99}\mathrm{Mo}$: 11.20\ifmmode\pm\else\textpm\fi{}0.29, $^{113}\mathrm{Ag}$: 9.63\ifmmode\pm\else\textpm\fi{}0.33, $^{115}\mathrm{Cd}$: 9.90\ifmmode\pm\else\textpm\fi{}0.97, $^{117}\mathrm{Cd}$: 9.36\ifmmode\pm\else\textpm\fi{}0.45, $^{121}\mathrm{Sn}$: 9.47\ifmmode\pm\else\textpm\fi{}0.87, $^{139}\mathrm{Ba}$: 7.60\ifmmode\pm\else\textpm\fi{}0.14, and $^{140}\mathrm{Ba}$: 8.14\ifmmode\pm\else\textpm\fi{}0.28. Using Niday's range-velocity relation, these ranges were converted to kinetic energies of the fragments to determine if there exists a deficit in total kinetic energy release at symmetric mass division. A dip was observed in the range-versus-mass curve, but the magnitude of this dip was smaller than what was previously reported in thermal-neutron fission of $^{235}\mathrm{U}$. The maximum total kinetic energy release at mass ratio 1.36 was found to be 176.7\ifmmode\pm\else\textpm\fi{}3.3 MeV, and the deficit in the energy release, corresponding to the observed dip in the range-mass curve, at symmetric fission was estimated to be 17\ifmmode\pm\else\textpm\fi{}5 MeV.

The ratio of asymmetric to symmetric fission in fission of 239Pu by neutrons of energies from 30 keV to 14.7 MeV

Radiochemical measurements have been made of the peak-to-valley ratio of the mass yield curve for neutron induced fission of 239Pu at neutron bombarding energies ranging from 30 keV to 14.7 MeV, and the results compared with similar measurements on 235U. For both target nucleides, the ratios all show a similar non-linear dependence on nuclear temperature at excitation energies below that at which intrinsic nucleonic levels become available. Once such levels are available, a more or less linear dependence on nuclear temperature is seen. This behaviour suggests that the mass asymmetry is governed primarily by the transition state spectrum, at least at low energies, and calculations have been made to check one of the experimentally measured ratios in 239Pu fission. The calculations are based on the α 3 symmetries of the levels of the transition state spectrum up to 300 keV, beyond which present knowledge of the spectrum is too sketchy to allow further calculation. This limited calculation agrees moderately well with the trend in the experimental results and so, as far as it goes, supports the applicability of the channel theory of fission to the mass division.

Coincident Time-of-Flight Measurements of the Velocities of Fission Fragments from Charged-Particle-Induced Fission

Measurements have been made of the velocities of the coincident fission fragment pairs emitted in the 25.7- and 29.5-MeV ${\mathrm{He}}^{4}$-induced fission of ${\mathrm{U}}^{233}$ and ${\mathrm{Th}}^{230}$, the 25.7- and 29.5-MeV ${\mathrm{He}}^{4}$-induced fission of ${\mathrm{Th}}^{232}$, and the 12.0- and 14.0-MeV ${\mathrm{H}}^{2}$-induced fission of ${\mathrm{Th}}^{230}$. Previously unpublished data for the 21.8-MeV ${\mathrm{He}}^{4}$-induced fission of ${\mathrm{U}}^{233}$ and ${\mathrm{Th}}^{232}$ are also included. A decrease in average total fragment kinetic energy for symmetric mass division is observed in each case. The relatively large yield of symmetric mass divisions in this work permits a reliable measurement of this effect. The distributions of fragment velocities, masses, and kinetic energies are consistent with the hypothesis of two competing modes of fission. A comparison is made of the primary mass yields obtained in the present work with the yields obtained by radiochemical methods to determine the dependence of prompt neutron emission on fragment mass. The neutron emission found, although subject to poorly known and possibly large uncertainties in the radiochemical data, appears to show a rather pronounced structure of just such a nature as might be attributed to fragment-shell effects that persist to these high excitation energies. Such a structure is not observed, however, when the present primary mass data are compared with mass distributions derived from recent fragment double-energy measurements. The time-of-flight mass distributions were corrected for the influence of the prefission neutron emission and the detection solid angle. As a part of the correction, the dependences of the yield of symmetric mass divisions on the excitation energy of the fissioning nuclei were estimated for each of the target-projectile systems.

Alpha-Particle-Induced Fission ofTh230,Th232, andU233

Measurements were made of the kinetic energies of coincident-fission fragment pairs emitted in the 22.1-, 25.7-, and 29.5-Mev He/sup 4/-induced fission of Th/sup 230/, Th/sup 232/, and U/sup 233/ to determine the mass and total kinetic-energy distributions of the fragments. The results are found to be consistent with the hypothesis of two distinct fission modes, corresponding to predominantly symmetric and predominantly asymmetric mass divisions. From a comparison of the mass distributions obtained from doubleenergy measurements with the mass distributions obtained from double-velocity time-of-flight measurements, it is possible to deduce the average number of prompt neutrons emitted as a function of the fragment mass. These results are also found to be qualitatively consistent with the twomode hypothesis. (auth)

Mass-Energy Relations in the Fission of Highly Excited Heavy Nuclei

Mass-energy relations in the fission of the compound nucleus ${\mathrm{Fm}}^{254}$ have been studied at excitation energies in the range from 58 to 116 MeV. This compound nucleus was produced by bombardments of ${\mathrm{Th}}^{232}$, ${\mathrm{U}}^{238}$, and ${\mathrm{Pu}}^{242}$ with the heavy ions ${\mathrm{Ne}}^{22}$, ${\mathrm{O}}^{16}$, and ${\mathrm{C}}^{12}$, respectively. The kinetic energies of the two fission fragments from each event were measured by using semiconductor detectors. From these energies the masses and total kinetic energies were calculated.The mass distributions were studied as a function of the total kinetic energy. The bell-shaped mass distributions narrowed rapidly as the kinetic energies of the fragments increased. The quantitative behavior of this narrowing suggests that most of the initial excitation energy of the compound nucleus is not available either for conversion into kinetic energy of the fragments or for the production of asymmetric mass divisions that are energetically unfavorable.

Coincident Time-of-Flight Measurements of the Velocities ofCf252Fission Fragments

The primary object of the experiment was to improve the absolute accuracy of the determination of the mean values of the distributions in fragment velocity, mass, and kinetic energy. Absolute uncertainties attained are estimated to be about plus or minus 0.5% for the velocity measurements ( approximates plus or minus 1% for the energy measurements); statistical uncertainties on the distribution mean values are considerably smaller. Mean velocities of 1.036 and 1.375 cm/nsec, mean mass numbers of 143.61 and 108.39 amu, and mean kinetic energies of 80.01 and 105.71 Mev, respectively, were obtained for the heavy- and light-fragment groups. The mean total-fragment kinetic energy was found to be 185.7 Mev, and the mean mass ratio, 1.334. Perturbations, suggesting fine structure, are found in the primary mass yields. Associated perturbations are observed in the average total-fragment kinetic energy (E /sub K/(R /sub A/)) for the corresponding mass divisions. A decrease in (E/sub K/(R/sub A/)) near symmetric mass division, extending over five or six mass pairs and reaching about 20 Mev at a mean mass ratio of 1.0, was observed; but the absolute uncertainty is large. (auth)

Dependence of fission fragment kinetic energies and neutron yields on nuclear structure

It is suggested that the dip in kinetic energy and the saw-tooth structure in the prompt neutron yields for thermal neutron fission of U 235 result from the influence of the shell structure of the eventual fragments on the deformations at the scission configuration. A simple model embodying this assumption has been explored in order to clarify the effects involved. Fragments which have a closed-shell structure prefer to retain a spherical shape at the scission configuration, whereas fragments which are soft with respect to deformation are more distorted at the scission configuration. From such a model it is seen how rather modest variations in the deformation energy as a function of distortion are exploited by the Coulomb repulsion between the eventual fragments to produce much larger effects on kinetic energies and neutron yields. This model, utilizing parameters determined from the U 235 experimental data, accounts for the qualitative features of the kinetic energy release and neutron yields for other fissioning nuclei from Bi to Cf. It is concluded that the structure in the kinetic energy release and neutron yields is primarily related to the shell structure of the final fragments rather than to differences associated with hypothetical symmetric and asymmetric modes. The large deficit in kinetic energy observed for U 235 near symmetry is attributed to the fact that both of the neutron-rich primary fission fragments for these mass divisions lie in a region characterized by an unusually low resistance towards deformation.

Energetics of Charged Particle-Induced Fission Reactions

Measurements with a semiconductor detector system and a two-dimensional analyzer have yielded information on the mass distributions and the details of the kinetic energy reiease from a series of charged particle-induced fission reactions. The fissioning compound nuclei range from thallium for which the mass distributions are symmetric, to plutonium for which the fission is predominantly asymmetric. In an intermediate region, the charged particle-induced fission of Ra/sup 226/ yields comparable contributions of symmetric and asymmetric fission. The results are quantitatively consistent with a two-mode hypothesis for the fission process and indicate that within each mode the distance between the charge centers of the two fragments at the scission point is approximately the same for all mass divisions. The results show a lower total kinetic energy release from symmetric fission than from asymmetric fission, indicating that the distance between the charge centers at the scission point is about 10% greater for the symmetric mode than for the asymmetric mode. (auth)

Asymmetric Fission of Bismuth

An asymmetric mode of mass division in the mass region 66-73 has been observed in the fission of ${\mathrm{Bi}}^{209}$ with 36-Mev protons. About 0.3% of the fissions contribute to this mode. At 58 Mev no evidence for asymmetric fission (0.05% of total fissions) as a separate mode could be found. The fission cross sections at 36 and 58 Mev are 1.9 and 11.3 mb, respectively. The narrowness of the 36-Mev asymmetric peak leads to the suggestion that the asymmetric fission of bismuth results from the fission of a single nuclear species and from a closed-shell effect, similar to the fine structure observed in low-energy fission of heavy elements. This asymmetric fission is considered to occur from states of relatively high excitation energy. However, the possibility of asymmetric fission also occurring from states of low excitation energy, whether following neutron evaporation or as a consequence of an inelastic proton interaction, cannot be ruled out. The symmetric fission observed with both 36- and 58-Mev protons is consistent with the results obtained by Fairhall in the fission of bismuth with 22-Mev deuterons.

Tripartition in the Spontaneous-Fission Decay ofCf252

The long-range alpha particles associated with the spontaneous-fission decay of californium-252 have been studied by means of nuclear-emulsion techniques. The alpha energy spectrum was found to peak at about 19 Mev with a half-width of 10 Mev, and the preferential angle of emission was found to be slightly less than 90 deg with respect to the light fission fragment. These results support the view that alpha emission occurs at the time of scission and that the direction is determined by the extent of electrostatic repulsion by the fragments. A trend toward a more nearly symmetric mass division in fission accompanied by alpha emission is indicated. The frequency of occurrence of the long-range alpha particles was observed to be 1 in 415\ifmmode\pm\else\textpm\fi{}10% binary fissions.Ternary events consisting of two heavy fragments and one light fragment of short range were observed, but the frequency with which these events occur was not measured. A parallel search was made for ternary-fission events in which fragmentation into comparable masses occurs.

Prompt-Neutron Emission from Single Fission Fragments

With a ${\mathrm{Cf}}^{252}$ source placed at the edge of a large cadmium-loaded liquid scintillator, it has been possible to obtain a measure of the number of prompt neutrons emitted from a single fission fragment of measured mass. The mass determination results from a concurrent time-of-flight measurement of the two fragment velocities. The 30-in. scintillator has a high detection efficiency, little dependent on the energy of the neutrons, and permits detection in a full hemisphere about the direction of one of the fragment flight paths. The average number of neutron counts per fission is found to increase with the mass number of the fragment approaching the neutron detector in much the same way in both the light- and heavy-fragment groups, with a sharp decrease occurring in passing from the light to the heavy group. A correction for the geometry of the neutron detection, assuming isotropic emission of the neutrons in the fragment frames, enhances slightly the sawtooth dependence of $\overline{\ensuremath{\nu}}(A)$ and gives for the ratio of the average number of neutrons from the light fragment to that from the heavy fragment $\frac{{\overline{\ensuremath{\nu}}}_{L}}{{\overline{\ensuremath{\nu}}}_{H}}=1.02\ifmmode\pm\else\textpm\fi{}0.02$. One is led to believe that either the emission of the neutrons is far from isotropic or that the slightly lighter fragments possess considerably more excitation energy than the slightly heavier fragments when the mass division is nearly symmetric. Perhaps a new picture of the mass division is indicated.

STUDIES ON INSECT SPERMATOGENESIS

1. In Euschistus the mitochondrial material of the primary spermatocytes occurs in the form of threads which are definitely oriented toward the centrioles in the prophases of the maturation divisions.2. Due to this very definite arrangement, the threads are so distributed during the anaphases that each daughter cell contains one half of the mitochondrial material.3. The mitochondria are not divided autonomously on the spindle but as a result of their position or the mechanical action of the constricting cell wall.4. The Golgi apparatus of the spermatocytes is extensively developed, occurring in the form of scattered Golgi bodies.5. During the maturation divisions these bodies undergo a process of autonomous fragmentation into dictyosomes which are arranged in a definite relation to the spindle and are then distributed in equal groups to the daughter cells. The arrangement and distribution of the Golgi elements during division is clearly dependent upon the centrioles.6. In the spermatids the Golgi elements are condensed into a single body, the acroblast, from which the acrosome of the mature sperm is derived.7. The remnant of the acroblast (or Golgi remnant) ultimately breaks free from the acrosome and is lost in the cytoplasm of the tail probably taking no further part in the formation of the sperm.8. The centrioles of the spermatid are, as in most (all?) animals, paired, and in this case remain in the "neck" region of the mature sperm.On the basis of the facts brought out in this study it is suggested that:1. The regularity in the division of the cytoplasmic elements of the cell, as illustrated by the mitochondria and Golgi bodies of Euschistus, is not the result of chance but is accomplished by a definite mechanism focused in the centrioles, and may perhaps partake of the nature of a meristic, as contrasted to a mass division.2. The acrosome of the animal sperm is probably universally formed in connection with the Golgi apparatus, and has nothing whatever to do with spindle fibers or other cell parts. It is to be considered as much a characteristic part of the sperm, having a definite morphological value, as are the nucleus and mitochondria.3. The idiosome plus the Golgi apparatus of vertebrates and pulmonates is to be considered as the homologue of the scattered Golgi bodies of insects, the idiosomic substance and the Golgi material being in some way intimately related, possibly in the sense of an essentially single cell organ of duplex chemical nature.