Symmetric and Asymmetric Fission

Abstract

Fission yields have been calculated assuming as a first approximation that they are proportional to the product of the level densities of a pair of binary fission products. The level densities have been calculated with the simplified shell-model methods of Newson and Duncan. The calculations predict a single symmetric peak when the mass of the fissioning nucleus, Ao<Ni-\-Zi-}-N2-\-Z 2 =50-f-28+82+50=210 (in agreement with the observed fission yields for bismuth and lighter elements), and three maxima in the fission yield curves for heavier compound nuclei. The peak corresponding to approximately equal-size binary fission products is very much higher than is observed experimentally. This is undoubtedly due to the fact that in asymmetric fission a core corresponding to 82 neutrons and 50 protons remains intact in the heavier fission product, whereas for symmetric fission this core I T has been pointed out by Fong 1 that the fission yield of a particular mass number should be proportional to the level density of the fission product of the same or slightly greater mass number multiplied by the level density of the accompanying fission product. Starting from this assumption and inferring level densities from low-energy neutron resonances, Fong calculated a remarkably good fit to the experimentally measured thermal fission yields for U 235 . Cameron 2 also found an excellent fit starting from the same general idea. However, neither of these authors has extended his calculations to other fissionable nuclides. This is probably because the neutron resonance data gives a level density at a very different (several Mev) excitation energy from that of the fission products. Level densities are so sensitive to excitation energy that this correction tends to become an empirical fitting of experimental data with the use of many free parameters. 2 On the other hand, Fong and Cameron achieved enough success to make it seem very likely that the fundamental assumption of their calculations was at least approximately correct.The shell model suggests two principal types of fission 3 : (1) We define (binary) asymmetric fission by the relations: 50<N h N 2 >S2, 28<Z h and Z 2 >50, or after neutron emission, 77<Ai and yl 2 >132. (2) We define (binary) symmetric fission by: 28<Zi<Z 2 <50 and 50<Ni<N 2 <:S2 so that A 2 <132; this second mode is less favorable energetically because of the breakup of the "double magic core" 5oSn 82 132 of the heavier fragment. (3) The remaining cases, ternary and very asymmetric binary fission (where Ai=Ni+Zi<77) have extremely small yields and will not be discussed or 1 is disrupted at the cost of several Mev. Since correction for this energy effect involves a number of unknown factors, the calculated yields for symmetric fission have been reduced by the same empirical factor in all calculations. An additional parameter, n, is introduced in correcting for excitation energy of the fission products and for possible departures from equilibrium. These calculations, which involve only two free parameters, explain...

Fission Yields in the Thermal Neutron Fission of 233U,235U,239Pu and 241Pu

“…THIND and TOMLINSON [9] had pointed out that a depression in the mass yield curve, around mass numbers 110 and 125 in the cumulative yields in the fission of ^^^U and ^^^Th should exist based on fine structure in the neutron evaporation. Results of calculations by NEWSON [10] also predict similar trend. However these effects are not believed to exist since there are no such dips in all the fissioning systems.…”

Relative yields of stable tin isotopes in neutron-induced fission

“…This has now been confirmed by the experimental work of lyer et al (1963) and more recently by Ganapathy and Kuroda (1966). Newson (1961), by extending the work of Fong (1956) and Cameron (1958) to a number of fissionable nuclides, showed that a symmetric peak could be theoretically predicted in most of these nuclides if one assumed that the fission yields are proportional to the product of the level densities of a pair of binary fission fragments.…”

“…2) within the limitations imposed by experimental errors. Thind and Tomlinson (1969) predicted that there should be fine structure in the cumulative mass yield curve in the symmetric mass region Can. J. Phys.…”

“…On this hypothesis, fine structure in the cumulative yield curve could occur even when the prompt mass vield distribution is free from such structure, provided that variations exist in the neutron emission as a function of mass. Thind and Tomlinson (1969) point out that the existence of fine structure in the symmetric region of the cumulative fission yield curve might result from variations in the neutron emission with mass curve, rather than from the prompt mass yield distribution, which may in itself show no fine structure at all. Neither the variation of neutron emission as a function of fragment mass, nor the prompt mass yield distribution have been experimentally determined in the symmetric trough, although Whetstone (1964) has reported a distribution of neutron emission with mass in this region.…”

“…For example, if the cumulative and primary yields are known, the neutron yield as a function of mass of the fragments may be calculated, as shown by Farrar and Tomlinson (1962) and independently by Terrell (1962).…”