Fission cross section

Figure 11.8 Neutron total and subbarrier fission cross sections of 240Pu as a function of neutron energy between 0.5 and 3 keV. (From H. Weigmann, Neutron-Induced Fission Cross Sections in C. Wagemans, The Nuclear Fission Process. Copyright 1991 CRC Press. Reprinted by permission of CRC Press.)...

Fig. 11.8). The resonances associated with fission appear to cluster in bunches. Not all resonances in the compound nucleus lead to fission. We can understand this situation with the help of Figure 11.9. The normal resonances correspond to excitation of levels in the compound nucleus, which are levels in the first minimum in Figure 11.9. When one of these metastable levels exactly corresponds to a level in the second minimum, then there will be an enhanced tunneling through the fission barrier and an enhanced fission cross section. 

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.)...

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)).

Figure 11.2. Fission cross section (Tn,f for and as a function of the neutron energy.

For the use of nuclides as nuclear fuel, their fissionability is the most important aspect. High fission yields by thermal neutrons are obtained if the binding energy of an additional neutron is higher than the fission barrier. Fission barriers, neutron binding energies and fission cross sections are listed for some nuclides in Table 11.1. The fission cross sections are high for and Pu, as already mentioned in... 

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

Nuclide Fission barrier [MeV] Binding energy of an additional neutron [MeV] Fission cross section Oa f [b]... 

The properties of some moderators and coolants are listed in Table 11.8. As already mentioned, the purpose of the moderator is to take away the energy of the fission neutrons by collisions, without absorbing appreciable amounts of the neutrons. The dependence of the fission cross section neutron energy is illustrated in Fig. 11.17. The absorption cross section is relatively low for graph-... 

Figure 11.17. Fission cross section <7f [b] for the fission of as a function of the neutron energy E [eV]. (According to D. J. ffughes, J. A. Harvey BNL, Neutron Cross Sections. United States Atomic Energy Commision. McGraw-Hill Book Comp. New York.)...

The discovery of Pu has been described in detail by Seaborg in his Plutonium Story (chapter 1 of the book The Transuranium Elements 1958). First, the separation of Pu from Th caused some difficulties, because both elements were in the oxidation state 4-4. After oxidation of Pu(IV) by persulfate to Pu(VI), separation became possible. Pu is produced in appreciable amounts in nuclear reactors (section 14.1), but it has not immediately been detected, due to its low specific activity caused by its long half-life. After the discovery of Pu, plutonium gained great practical importance, because of the high fission cross section of Pu by thermal neutrons. Very small amounts of Pu are present in uranium ores, due to (n, y) reaction of neutrons from cosmic radiation with The ratio Pu/ U is of the order of 10 In 1971, the longest-lived isotope of plutonium, Pu (ri/2 = 8.00 lO y) was found by Hoffman in the Ce-rich rare-earth mineral bastnaesite, in concentrations of the order of 10 gAg-... 

Nuclear fission is the phenomenon that occurs when a heavy nucleus splits into two or more intermediate heavy nuclei. In the field of radiochemistry, the fissions of U, Pu, induced by neutrons, are often treated, and especially that of by thermal neutrons is studied the most. The fission cross sections of several nuclides for thermal neutrons are shown in Table 4.1. 

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

Thermal neutron fission cross section, barns 0.102 (natural) 0.137 (natural) 0.112 (natural)... 

Thermal neutron fission cross section, barns — ... 

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... 

Bk-249 metal is a very soft beta-emitter with a half-life of only 320 days and a fairly high spontaneous fission cross-section, so that the target counting of effusion samples is quite difficult. 

Consider, for example, a PWR containing 80 te of uranium oxide enriched to 3%, with an average moderator temperature of 310 C. The effective specific volume of uranium oxide pellets will be 1.11 x 10 m /kg. The fission cross-section at a moderator temperature of 20°C/293 K, t/(293), is 582 x 10 m for U-235, while the corresponding figure for plutonium-239 is 743 x 10 m. Calculate NfOf at the start of life and at the end of life, and hence deduce the variation in the constant of proportionality, a. 

It is shown in Glasstone and Sesonske (1981) that, assuming complete thermalization, the fission cross-section at moderator temperature T K) is related to fission cross-section at To by the equation ... 

Table 2.8 lists capture and fission cross sections for the four nuclides fissile with thermal neutrons and gives the average number of neutrons produced per nuclide fissioned (v) and per... 

The principal nuclear reactions that take place when mixtures of U and U are used as fuel in a reactor are illustrated in Fig. 3.1. Fissile materials are double underlined, and their fission cross sections for 2200 m/s neutrons are given on upward-slanting arrows. Fertile materials are sin e underlined, and their capture cross sections for 2200 m/s neutrons are given on horizontal arrows. Beta-decay reactions with short enough half-lives to be important are shown by vertical arrows. 

Nuclide Subscript Absorption cross section, Ufl, b Neutrons produced Ratio of capture to fission cross section, a Poisoning ratio of high-cross section fission products, Q... 

In a PWR operating with plutonium recycle the thermal-neutron flux is lower than for uranium fueling because of the hi er fission cross section for plutonium. As a result, less C is produced by thermal-neutron activation within the fuel, as drown in Table 8.11. 

Am. The uotope Am is formed by the decay of Pu. It undergoes alpha decay, with a half-Ufe of 458 years, to form Np. Isotopically pure Am can be extracted from aged reactor-grade plutonium. Irradiation of separated Am is the basis of technology to produce gram quantities of Cm. This is also one route to the production of the transcurium elements. However, the first neutronheat evolution as contrasted to the production of transcurium isotopes from the irradiation of plutonium rich in the isotope Pu. 

Fission cross sections are denoted by For fissionable isotopes of thorium and elements of higher atomic number, the average number of neutrons produced per fission is listed in the same row as the fission cross section, in the same column as the mass, to conserve space in the table. The average number of prompt and delayed neutrons produced by fission with a thermal neutron is denoted by V. The average number of prompt neutrons produced by fission with a thermal neutron is denoted by Vp. The average number of neutrons emitted per spontaneous fission is denoted by t jp. ... 

In the determination of the number of fissions in an irradiated sample by the use of flux monitors, account must be taken of the flux depression in the sample due to self-shielding to obtain an effective flux. Also, the capture cross sections of the monitors and the fission cross sections of the sample are neutron energy dependent. It is, therefore, necessary to know the eneigy distribution of the neutrons or the neutron temperature and to determine effective cross sections (Section IV). This can be done by using two monitors such as cobalt and samarium, the one monitor being used to determine the neutron temperature corresponding to the neutron distribution as described by Fritze et al. (35). 

Example 4.22 What is the fission rate at a certain point inside a nuclear reactor where the neutron flux is known to be < = 2.5 X 10 " neutrons/(m s), if a thin foil of is placed there The fission cross section for is Of = 577 b. 

Measurement of the fission cross section for Pu, based on the known fission cross section for... 

Some partial cross-sections have their own names such as the scattering cross-section for elastic and inelastic scattering ), the activation cross-section (g ) for die formation of radioactive products, the fission cross-section (gf) for fission processes, and adsorption or capture cross-sections (g,, g or gj,pj) for the absorption or capture of particles. If all of these processes take place, one obtains (with caution to avoid overlapping reactions)... 

For fast neutrons ( 0.1 MeV) the cross sections are relatively small, 1 b. Fission dominates over radiative capture. Of particular importance is that becomes fissionable at a neutron energy of 0.6 MeV its fission cross section increases with neutron energy above the threshold to a constant value of 0.5 b at 2 MeV. 

A rough estimate of the critical radius of a homogeneous unreflected reactor may be obtained simply by estimating the neutron mean free path according to (14.6). Assuming metal with a density of 19 g cm and a fast fission cross section of 2 X crn, one obtains = 10 cm. A sphere with this radius weighs 80 ks. For an unreflected metal sphere containing 93.5% the correct value is 52 kg. Pu has the smallest unreflected critical size for Pu (5-phase, density 15.8 g cm ) it is 15.7 kg ( 6 kg reflected), and for 16.2 kg ( 6 kg reflected). 

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