Fissionability parameter

Thus, it is natural to express the fissionability of nuclei in terms of a parameter a, that is, this energy ratio, and is called the fissionability parameter. Thus... 

In our previous discussion, we showed that the fission barrier heights depend on Z2/A and thus so should the spontaneous fission half-lives. In Figure 11.4, we show the dependence of the known spontaneous fission half-lives on x, the fissionability parameter. There is an overall decrease in spontaneous fission half-life with increasing x, but clearly the spontaneous fission half-life does not depend only on Z2/A. One also observes that the odd A nuclei have abnormally long half-fives relative to the even-even nuclei. Also the spontaneous fission half-fives of the heaviest nuclei (Z > 104) are roughly similar with values of milliseconds. 

Figure 11.4 Spontaneous fission half-lives of even-even ( ) and even-odd (O) nuclides as a function of fissionability parameter, x. (From R. Vandenbosch and J. R. Huizenga, Nuclear Fission. Copyright 1973 Academic Press. Reprinted by permission of Elsevier.)...

What are the values of the fissionability parameter x for 209Bi, 226Ra, 232Th, 242Pu, and 252Cf ... 

Fig. 12. Reaction parameters of H-hexane conversion by nickel and Ni-Cu alloys. A, = log c at 330 C, A2 = log rs at 330 C, activation energy of the overall reaction fission parameter M, selectivity parameter S all as a function of alloy composition (in at. % Cu). r, is rate per cm2, rw rale per gram catalyst. From Ponec and Sachtler (14).

A much more pronounced increase in S and the fission parameter M is observed at 40 to 73% Cu, where S reaches values common for platinum in this region the A parameters change only little. The fission parameter M is defined as... 

FIG. 18. Reaction parameters for n-hexane conversion by Ni and Ni-Cu alloys at 330°C Ai = log rw (rate per gram of catalyst) A2 = log rs (rate per square centimeter of total surface) Eact is activation energy of the overall process S is the selectivity for producing Cg products M is a fission parameter whose value inversely reflects the degree of multiple fragmentation to methane (102). 

Figure 5.18. Half-life of spontaneous fission of even-even nuclei as a function of the fissionability parameter jA.

The mechanisms and data of the fission process have been reviewed recently by Leachman (70). Several different approaches have been used in an effort to explain the asymmetry of the fission process as well as other fission parameters. These approaches include developments of the liquid drop model (50, 51,102), calculations based on dependence of fission barrier penetration on asymmetry (34), the effect of nuclear shells (52, 79, 81), the determinations of the fission mode by level population of the fragments (18, 33, 84), and finally the consideration of quantum states of the fission nucleus at the saddle point (15, 108). All these approaches require a mass formula whereby the masses of the fission fragments far removed from stability may be determined. The lack of an adequate mass formula has hindered the development of a satisfactory theory of fission. The fission process is highly complex and it is not surprising that the present theories fall short of a full explanation. 

All of the members of the natural decay chains are unstable with respect to spontaneous fission, but the probabilities are small. The decay chains follow the side of the valley of stability where the fissionability parameter Z A is relatively small. However, fission is such an extraordinary event that even a few events can be detected, as long as they can be distinguished from events such as muon-induced fission. For the natural chains has the highest fraction of decays by spontaneous fission, 5.4 x 10. Although this leads to a multitude of natural decay chains consisting of fission followed by decays through fission product chains, the process will not be considered in this chapter. 

Blann, M., Komoto, T.T. Statistical fission parameters for nuclei at high excitation and angular momenta. Phys. Rev. C26, 472—485 (1982)... 

D. E. McMillan et al., A Measurement of Eta and Other Fission Parameters for U-S33, Pu-239, Pu-241, Relative to U-235 at Sub-Cadmium Neutron Energies, USAEC Report KAPL-1464, Knolls Atomic Power Laboratory, Dec. 15, 1955. 

The chronology of the development of nuclear reactors can be divided into several principal periods pre-1939, before fission was discovered (12) 1939—1945, the time of World War II (13—15) 1945—1963, the era of research, development, and demonstration (16—18) 1963—mid-1990s, during which reactors have been deployed in large numbers throughout the world (10,18) and extending into the twenty-first century, a time when advanced power reactors are expected to be built (19—23). Design of nuclear reactors has been based on a combination of theory, measurement of basic and derived parameters, and experiments with complete systems (24—27). 

The treatment of these simple associations directly follows that of the simple fission reactions discussed previously. For example, these reactions proceed via the formation of a loose transition state and without an activation energy barrier. The rates and rate parameters of simple associations can be determined either directly, by the application of bimolecular TST, or from their reverse, simple unimolecular fission reactions, through the use of the principle of microscopic reversibility. 

Many association reactions, as well as their reverse unimolecular decompositions, exhibit rate parameters that depend both on temperature and pressure, i.e., density, at process conditions. This is particularly the case for molecules with fewer than 10 atoms, because these small species do not have enough vibrational and rotational degrees of freedom to retain the energy imparted to or liberated within the species. Under these conditions, energy transfer rates affect product distributions. Consequently, the treatment of association reactions, in general, would be different than that of the fission reactions. 

Energy transfer limitations have long been recognized to affect the rates and mechanisms of fission and association reactions (Robinson and Holbrook, 1972 Laidler, 1987). In addition, it is increasingly being recognized that many exothermic bimolecular reactions can exhibit pressure-(density)-dependent rate parameters if they proceed via the formation of a bound intermediate. When energy transfer limitations exist, the rate coefficients exhibit non-Arrhenius temperature dependencies—i.e., the plots of ln(k) as a function of l/T are curved. 

Despite the apparent similarity of the Bohr and the Bethe stopping power formulae, the conditions of their validity are rather complimentary than the same. Bloch [23] pointed out that Born approximation requires the incident particle velocity v ze jh, the speed of a Is electron around the incident electron while the requirement of Bohr s classical theory is exactly the opposite. For heavy, slow particles, for example, fission fragments penetrating light media, Bohr s formula has an inherent advantage, although the typical transition energy has to be taken as an adjustable parameter. 

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