Delayed fission

The r-process path is terminated by (neutron-induced or yd-delayed) fission near A max = 270, feeding matter back into the process at around Amax/2, followed by recycling as long as the neutron supply lasts, assuming sufficient seed nuclei to start the process off. The number of heavy nuclei is thus doubled at each cycle, which could take place in a period of a few seconds, yd-delayed fission also occurs after freeze-out, when the yd-decay leaves nuclei with A > 256 or so with an excessive positive charge (see Eq. 2.90). 

If the time scale of neutron capture reactions is very much less than 3 -decay lifetimes, then rapid neutron capture or the r process occurs. For r-process nucleosynthesis, one needs large neutron densities, 1028/m3, which lead to capture times of the order of fractions of a second. The astrophysical environment where such processes can occur is now thought to be in supernovas. In the r process, a large number of sequential captures will occur until the process is terminated by neutron emission or, in the case of the heavy elements, fission or (3-delayed fission. The lighter seed nuclei capture neutrons until they reach the point where (3 -decay lifetimes have... 

We discuss RPA calculations of the Gamow-Teller properties of neutron-rich nuclei to study the effect of B"delayed fission and neutron emission on the production of Th, U and Pu chronometric nuclei in the astrophysical r-process. We find significant differences in the amount of -delayed fission when compared with the recent calculations of Thielemann et al. (1983). 

KRU81]). The B strength function for nuclei along the decay back paths [coupled with neutron separation energies (Sn), fission barrier heights (Bf) and B"decay Q-values (Qg)] determines the amount of B delayed fission and neutron emission that occurs during the cascade back to the B stability line. 

A recent analysis by Thielemann et al. [THI83] of the effects of B" delayed processes on the progenitors of the Th-U-Pu chronometers showed that these processes (delayed fission in particular) did indeed significantly influence the final abundances of the chronometer progenitors. This leads to a long age for the Galaxy. In view of the importance of this result, it is useful to re-examine the calculation with a nuclear model that includes the effects of nuclear deformation on the B decay rates, fission barriers, and neutron separation energies self-consistently. 

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

If the nuclear flow towards increasing Z values reaches the actinide or transactinide region, it is stopped by neutron-induced or /3-delayed fissions which lead to a recycling of a portion of the material to lower Z values. At freezing of the neutron captures or inverse photodisintegrations, mainly /3-decays, but also spontaneous or /3-delayed fissions and single or multiple /3-delayed neutron emissions, drive the neutron-rich matter towards the valley of stability. These post-freezing transformations are shown schematically in Fig. 22. 

Of the neutrons formed, most are released virtually immediately, but a small proportion which depend on the fissionable isotopic composition of the fuel (U235 0-7%, Pu239 0-4%), are released at an appreciable time after fission—up to a minute or so. It is this special property of delayed fission neutron release that enables the plant to be controlled by manual or relatively straightforward automatic operating systems with control rods that move relatively slowly. 

Cylindrical reactor with source. An attempt is made here to describe the kinetics of a homogeneous cylindrical reactor with a point source of fast neutrons located at an arbitrary interior point on the axis of the reactor. The theory developed is quite general, at least to the extent that five delayed neutron groups are taken into consideration and appropriate ages are assigned to the source neutrons, the prompt fission neutrons, and each of five groups of delayed fission neutrons. Application of the theory is made to the problem of the determination of the power level in a so-called zero power critical assembly. 

In the following, exotic nuclear decay modes of heavy nuclei, cluster radioactivities, delayed fission, and spontaneous fission (SF) together with the recent progress on deformation paths toward fission are briefly introduced. 

Delayed fission is also an exotic nuclear decay process of heavy nuclei that is observed subsequent to P or EC decay. In the delayed fission process, P decays or electron captures (EC) of the parent nuclide populate excited states of the daughter nucleus, and if these states are of energies comparable to or greater than the fission barrier of the daughter nucleus, then fission may compete with other decay modes of the excited states. The process is schematically shown in O Fig. 18.12. Reviews give a detailed description of delayed fission (Oganessian and Lazarev 1985 Hall and Hoffinan 1992). 

Delayed fission permits studies of fission properties of nuclei far from stability and y deexcitation of nuclear levels in the second minimum of the potential energy surface (O Fig. 18.12). There has been also considerable theoretical interest in P-delayed fission process because it may significantly affect the final abundance of heavy elements produced in the astrophysical r-process and in other multiple neutron capture process taking place in very high neutron flux, such as thermonuclear explosions (Tielemann et al. 1983 Meyer et al. 1989 Cowan et al. 1991 Staut and Klapdor-Kleingrothaus 1992). The experimental data on the delayed fission are presented in Table 18.8. 

Schematic illustration of the delayed-fission process. The potential energy of the daughter nucleus as a function of deformation is shown, displaying the double-humped fission barrier prevalent in the actinides. Region I is the inner, or ground-state, well (first minimum) region II is the outer, or shape isomer, well (second minimum). The horizontal arrows indicate the various kinds of deformation toward fission...

Wene, C.-O., Johansson, S.A.E. The impmtance of delayed fission in the production of very heavy and superheavy elements. Phys. Scripta lOA, 156—161 (1974)... 

Since we are considering a critical reactor, we may assume that there is no primary source present. However, since we are interested in the effects of delayed neutrons, we must consider our source term to be composed of two parts the source of prompt fission neutrons and the source of delayed fission neutrons. If we let represent the fraction of the total number of fission neutrons that are delayed and the fraction that are associated with a single time of delay (a single precursor), then (1 - jS) is the fraction of fission neutrons that are emitted promptly. We can then write our prompt source term as before, except that it must be decreased by a factor (1 - jS). An additional source term must be included for the delay-neutron source. The rate of formation of delayed neutrons of the i h kind is equal to the rate of decay of its precursor, which is... 

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