Fission probability

Why will nuclear fission probably never be used directly for powering automobiles How could it be used indirectly ... 

Fig. 3. Mass fission yield curves as function of excitation energy and degree of fission probability...

Fig- 1(a). Calculated maximum possible values of 3-delayed fission probabilities (in %) shown for the precursor nuclei. 

There was also great uncertainty of the production yields for SHEs. Closely related to the fission probability of SHEs in the ground-state, the survival of the compound nuclei formed after complete fusion was difficult to predict. Even the best choice of the reaction mechanism, fusion or transfer of nucleons, was critically debated. However, as soon as experiments could be performed without technical limitations, it turned out that the most successful methods for the laboratory synthesis of heavy elements are fusion-evaporation reactions using heavy-element targets, recoil-separation techniques, and the identification of the nuclei by generic ties to known daughter decays after implantation into position-sensitive detectors [13-15],... 

The epoxidation of enones by alkaline hydrogen peroxide is well known. Prolonged reaction causes C-C bond fission, probably by a Baeyer-Villiger mechanism. Applied to the 1 o,2a-epoxy-4,6-dien-3-one system (231), this... 

The two processes are radically different in nature it would indeed be a remarkable coincidence if both these probabilities and their rates of change with energy, were to be so very similar. However, as we have seen in Sect. 8, it is not necessary to assume that the total probability of inelastic neutron emission increases very rapidly with energy. If, as is much more likely, the total neutron width is approximately independent of neutron energy, it follows that the average fission probability is also approximately independent of energy. 

The deposition of Tc from weapon fallout has been estimated to be 540 + 50mBqm at 62°N. Frequently, carpets of mosses and lichens are used as bioindicators for the estimation of deposited radionuclides. The concentration of Tc in lichens (mBq per kg dry weight), the fission yields (Mt) for nuclear weapons testing, and the observed and theoretical Tc/ Cs radionuclide ratios are given in Figure 1. The present Tc/ Cs ratio is expected to be 3.2 X 10 " due to the physical decay of Cs. In general, the observed Tc/ Cs ratio is lower than expected from fission probably due to a shorter residence time for Tc in the lichen carpet. The concentration of Tc and the Tc/ Cs ratio in lichens has increased since 1975. Unusual mixtures of shortlived radioisotopes, e.g., Np and Mo, in fallout... 

The adjoint function and neutron importance. Equation (64) leads to an interesting interpretation of the adjoint function mo which may be used to gain an intuitive understanding of the results of perturbation theory. A neutron may be regarded as having an importance to the chain reaction that is proportional to the amplitude of the persistent mode that it eventually goes into. The adjoint function mo(a ) may then be called the importance of a neutron at a . It is also known as the iterated fission probability. A natural normalization is such that the importance is unity for one neutron distributed in the persistent mode. Equivalently, the average importance is unity for neutrons in the persistent mode. In this normalization... 

The iterated sequence of adjoint functions may be given a physical interpretation that is a natural extension of the Hurwitz-Brooks iterated fission probability concept (19) extended to subcritical as well as critical systems and to arbitrary detector characteristics as well as to a normalization based on the number of progeny in a generation. 

The complication that the transition state cannot be recrossed was dealt with theoretically by Kramers (1940), where the fission width is reduced relative to the Bohr-Wheeler estimate by saddle recrossing. As the recrossing probability increases with friction, the reduced fission probability can be cast in terms of the friction coefficient y. 

In the seven decades since the discovery of nuclear fission, experimental studies on low-energy fission have been restricted to about 80 fissionable nuclei. They represent only about 15% of all known nuclei with Z > 82. However, recently a novel experimental technique has been introduced. The fission of relativistic secondary projectiles has now been studied in flight. The benefit of the radioactive beams for studying the fission process is clear, but no fission probabilities below the fission barrier have been determined so far (Schmidt et al. 1994). 

Starting with a brief discussion of the theoretical model predictions for the fission potential as a function of the deformation of the nucleus, the consequences of the multiple-humped potential barrier on the fission probabilities will be discussed. During the last decade... 

The experimentally determined fission probabilities can then be compared to the results obtained with the expression above and the height and the curvature of the barrier can be determined. If the fission barrier is more complicated, then this simple formula cannot be used. More sophisticated calculations - including double- and triple-humped fission barriers - have been published recently by Sin et al. (2006, 2008). The situation is complicated by the presence... 

Bohr suggested that in a saddle-point configuration a nucleus is in a very cold state and that the spectrum of transition states resembles the spectra near the ground states of stably deformed nuclei. These transition states could cause resonances in the fission probability. Therefore, first the low-lying excited states of even-even nuclei shall be discussed briefly. 

Thanks to the resonant tunneling effect, such excited states (class-II and class-III) can be mapped by measuring the fission probability as a function of the excitation energy (see O Fig. 5.4). If one measures also the angular distribution of the fragments arising from fission induced by some reaction, then one can get information on the spin and if values of such excited states as well. 

For a pure and undamped transmission resonance, where the strength of the P-vihrational state is not distributed over the neighboring intrinsic states in the second minimum, the fission probability Pg of a class-I state can be described as (Glassel et al. 1976)... 

Undamped and damped transmission resonances. Panel (a) shows the Lorentzian of the fission probability for class-1 states. Panel (b) displays the strength function of the p-vibration in the case of damping into class-ll states. Constant level distances D, for states in the first and On for states in the second minimum were assumed... 

The hcoii corresponds to the P-phonon energy in the second minimum, while i(Oa,b denotes the curvature of the parabolic parameterization of the fission barrier. The experimentally accessible fission cross section cr can be obtained from the cross section for the formation of a compound state Id) in the first minimum and the fission probability... 

As shown in O Fig. 5.5, the fission probability is distributed among the class-I states. The width of the distribution is determined by barrier penetration probabilities (Pa and Pb)- If one wants to observe sharp transmission resonances in the fission probability, then one should go well below the fission barriers. A more detailed analysis of the transmission resonances will be... 

The measured proton energy spectrum from the (d,p) reaction in coincidence with the fission fragments (after subtraction of random coincidences) is shown in O Fig. 5.7a in terms of the excitation energy of the compound nucleus Pu. The spectrum is proportional to the product of the fission probability and the known smoothly varying (d,p) cross section, which shows no fine structure (Specht et al. 1969). 

In the third well of the potential, the reflection asymmetry permits almost degenerate levels of both parities in the rotational spectrum. These kinds of rotational levels have been nicely observed in the experimental fission probability of Th (Blons et al. 1975). Assuming that each of the observed resonances also contains a whole rotational band, the experimental results... 

The following free parameters were introduced (1) energy of the band head, (2) absolute intensity of the band, and (3) rotational parameter of the band. The last parameter was kept identical for all of the groups, i.e., the 5.28, 5.37 and 5.47 MeV groups. A fit to the measured spectrum was performed with the above parameters using the least squares method. The nonresonant part of the fission probability was taken into account as an exponential background. ... 

The HD states are characterized by the presence of alternating parity bands with very large moments of inertia because of the very large quadrupole and octopole moments (Blons et al. 1988). Assuming alternating parity bands with K = 3, 4, and 5 band heads, the fission probability between 5.2 and 5.5 MeV was fitted, resulting in the fit curve superimposed on the data in Pig. 5.14a. The corresponding normalized values are presented in Pig. 5.14c as a function of fi /20. The horizontal line represents the 99.9% (3(t) confidence level for the... 

The result of the analysis in the excitation-energy region between 5.05 and 5.2 MeV is shown in Fig. 5.15, where the prompt fission probability is displayed (panel a) together with the results of a fit by rotational bands similar to the procedure described above for the upper resonance region. Again the spin-dependent excitation probabilities of the rotational band members were based on DWBA calculations by Back et al. (1971) for E " = 5.1 MeV. 

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