Cross section for fission

This is illustrated in Fig. 11.1. Fission of may be taken as an example v is the average number of neutrons liberated in nuclear fission of by thermal neutrons and F[/Z a is the ratio of the macroscopic cross sections for fission and for absorption of neutrons. For pure nuclides (e.g. pure iTf/iTa = The fission factor... 

Pu and can be used as nuclear explosives, because they have sufficiently high cross sections for fission by fast neutons. By use of the equations in section 11.1, it can be assessed that, in the absence of a reflector, a sphere of about 50 kg uranium metal containing 94% or a sphere of about 16 kg plutonium metal ( Pu) is needed to reach criticality. If a reflector is provided, the critical masses are about 20 kg for and about 6 kg for Pu. The critical masses for are similar to those for Pu. 

The nuclear cross-section for fission of the two kinds of U and/or Pu are shown roughly in Fig. 8.1 where a,is plotted against the log o the incident neutron s energy. 

In order to maximize the cross section for fission, which is greatest for low energy neutrons, the neutrons are slowed down or "moderated by a material (the moderator) that elastically scatters neutrons but has a small neutron capture cross section. In LWRs ordinary (but very pure) water serves the purpose of both moderation and cooling (in other reactor types the moderator may be a liquid like D2O, a solid material like graphite or absent and the cooling medium may be a gas or a metal like lead, mercury or sodium). 

Fermi in any case was more interested in pursuing a chain reaction in natural uranium than in attempting to separate isotopes. He was not discouraged by the small cross-section for fission in the natural [element], comments Anderson. Stay with me, he advised, we ll work with natural uranium. You ll see. We ll be the first to make the chain reaction. I stuck with Fermi. ... 

The difference between thermal (e.g., light-water reactors) and fast reactors (fast breeder, nuclear weapons) is in the energy of the neutrons inducing the fission reaction. The reason for the distinction is the reaction cross sections for fission in ( Pu) and for competing (n,y)-reactions mainly in the main component of the fuel elements. 

Note SF, spontaneous fission o the cross section for fission—the cross section of natural luanium is 3.4 barn for capture of thermal neutrons and 4.2 for fission. 

The only large-scale use of deuterium in industry is as a moderator, in the form of D2O, for nuclear reactors. Because of its favorable slowing-down properties and its small capture cross section for neutrons, deuterium moderation permits the use of uranium containing the natural abundance of uranium-235, thus avoiding an isotope enrichment step in the preparation of reactor fuel. Heavy water-moderated thermal neutron reactors fueled with uranium-233 and surrounded with a natural thorium blanket offer the prospect of successful fuel breeding, ie, production of greater amounts of (by neutron capture in thorium) than are consumed by nuclear fission in the operation of the reactor. The advantages of heavy water-moderated reactors are difficult to assess. 

In nuclear reactors one has neutrons with energies ranging from thermal (0.025 eV) to several MeV. There are a series of sharp peaks in the total cross section for neutrons with energies between 0.2 and 3000 eV that are called resonances. These resonances correspond to exciting a specific isolated level in the compound nucleus that can decay by fission. The situation is particularly interesting for the neutron irradiation of even-even nuclei, such as 240Pu at subthreshold energies... 

Figure 14.1 Neutron-induced fission cross section for 235U and 238U as function of the neutron energy, En. (From D. T. Hughes and R. B. Schwartz, Neutron Cross Sections, 2nd ed., Brookhaven National Laboratory Report 325, 1958.)...

This isotope, 239Pu, was shown to have a cross section for thermal neutron-induced fission that exceeded that of 235U, a property that made it important for nuclear weapons, considering that it could be prepared by chemical separation as compared to isotopic separation that was necessary for 235U. 

The shape resonances have been described by Feshbach in elastic scattering cross-section for the processes of neutron capture and nuclear fission [7] in the cloudy crystal ball model of nuclear reactions. These scattering theory is dealing with configuration interaction in multi-channel processes involving states with different spatial locations. Therefore these resonances can be called also Feshbach shape resonances. These resonances are a clear well established manifestation of the non locality of quantum mechanics and appear in many fields of physics and chemistry [8,192] such as the molecular association and dissociation processes. 

Hopefully, our results (some of which have been presented previously [KUM83]) for the superheavy nuclei will also stimulate other theorists to recalculate fission lifetimes, and, especially, fusion cross-sections for the suggested target-projectile combinations. These cross-sections are expected to be small and the corresponding experiments are expected to be quite difficult. 

To define more accurately the boundaries of the mass regions that could be accessed with the proposed He-jet coupled mass separator system, production cross sections for both neutron-deficient and neutron-rich nuclei far from stability have been estimated for 800-MeV proton reactions. The spallation-product cross sections were estimated through use of the Rudstam systemstics [RUD66]. For estimation of the fission-product cross sections, however, there is no established, similar approach. Thus, an empirical approach was taken in... 

The cross sections for elements lighter than 113 decrease by factors of 4 and 10 per element in the case of cold and hot fusion, respectively. The decrease is explained as a combined effect of increasing probability for reseparation of projectile and target nucleus and fission of the compound nucleus. Theoretical consideration and empirical descriptions, see e.g. [61,62], suggest that the steep fall of cross sections for cold fusion reactions... 

Figure 8.19. Fission cross sections for the fission of by protons of various energies. (The Coulomb barrier for the fission by protons is 12.3 MeV, which explains the low values for 10 MeV protons.) (According to P. C. Stevenson, Physic. Rev. Ill (1958) 886 G. Friedlander BNL 8858 (1965)).

Table 11.1. Fission barriers, binding energies of an additional neutron and fission cross sections for some heavy nuclides.

Fig. 8.1. Fission cross section for U, U and Pu as a function of neutron energy.

There are three fast-flux reactors proposed for development the sodium cooled, the gas cooled, and the lead cooled. The fission cross sections for fast neutrons (high-energy spectrum neutrons) for all of the fissile actinides are nearly the same so the fast-flux reactors use all of the fissile actinides as fuel. The fast-flux isotopic fission cross sections are smaller than for thermal neutrons so the fraction of fissile isotopes (e.g., 235u 239pu, range of... 

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