Fission factor

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... 

While 8 is somewhat greater than 1, both p and / are somewhat smaller than 1. Therefore, for approximate calculations, epf can be set 1. The fission factor rj varies appreciably with the energy of the neutrons, as shown in Fig. 11.4 for The neutron losses in a reactor of finite dimensions can be taken into account approximately by the sum L +1 , where Ls is the mean slowing-down length of the fission neutrons in the moderator and L the mean diffusion length in the fuel-moderator mixture. For a spherical reactor of radius R the approximate relation is... 

Those fast neutrons that have energies greater than about 1 MeV may cause a limited amount of fission of fertile material. To account for this, the reactor designer usually specifies a quantity e, called the fast-fission factor, which is defined as the ratio of the net rate of production of fast neutrons to the rate of production of fast neutrons by thermal fission. The fraction e — 1 of the fast neutrons comes from fission of fertile material with fast neutrons e — 1 may be of the order of a few hundredths in a thermal power reactor. The net production rate of fast neutrons from fission is er N a 4>-... 

Because has a shorter half-life than " U, all uranium ores were richer in in the past. From Rb— Sr analysis the age of the Oklo dqxisit is known to be 1.74 X 10 y at that time the content of natural uranium was 3%. Although the fission factor i rapidly increases with content (about 1.8 for 3 % U), conditions in the natural Oklo deposit were such (e 1.0, p 0.4,/ 1.0) that < 1. The deposit is sedimentary and was formed in the presence of water, which greatly increases the resonance escape probability factor p for an atomic ratio H20 U of 3 1, p 0.8, and > 1. Thus conditions existed in the past for a spontaneous, continuing chain reaction to occur in the Oklo deposit. 

Abstract The chapter is devoted to the practical application of the fission process, mainly in nuclear reactors. After a historical discussion covering the natural reactors at Oklo and the first attempts to build artificial reactors, the fimdamental principles of chain reactions are discussed. In this context chain reactions with fast and thermal neutrons are covered as well as the process of neutron moderation. Criticality concepts (fission factor 77, criticality factor k) are discussed as well as reactor kinetics and the role of delayed neutrons. Examples of specific nuclear reactor types are presented briefly research reactors (TRIGA and ILL High Flux Reactor), and some reactor types used to drive nuclear power stations (pressurized water reactor [PWR], boiling water reactor [BWR], Reaktor Bolshoi Moshchnosti Kanalny [RBMK], fast breeder reactor [FBR]). The new concept of the accelerator-driven systems (ADS) is presented. The principle of fission weapons is outlined. Finally, the nuclear fuel cycle is briefly covered from mining, chemical isolation of the fuel and preparation of the fuel elements to reprocessing the spent fuel and conditioning for deposit in a final repository. 

However, in constructing a reactor, the primary question is at first whether a chain reaction (or a critical assembly) can be established. This question will be discussed in the following section. It can be described by the fission factor (77). 

Considering, e.g., natural uranium (a mixture of 0.71% of and 99.29% of U) and thermal neutrons, the fission factor obtained from Eq. (57.25) is 77 = 1.33. Here, a chain reaction is still possible but neutron losses in the moderator and in the construction materials must be kept very small. This requires the use of a very good moderator like D2O (see above). For a typical light-water reactor fuel (3% in U) a value of 77 = 1.83 is obtained. 

Cross sections for (n,7)-reactions a-c in barn] and neutron-induced fission reactions (o-f in barn) average total number of neutrons emitted after fission (v) (Choppin and Rydberg 1980) and fission factor (r ) for various fission reactions induced by thermal and fast neutrons (1 MeV)... 

Breeding more fissile material than is used up in the chain reaction requires a fission factor rj>2 (see Sect. 57.3.4). One neutron is needed for the chain reaction and the second neutron is required for the reaction (n,y) (decaying to Pu). 

Fission factor rj as a function of the neutron energy for the fission of and Pu (Zech 1988)... 

The subcadmium activation distributions were used in conjunction with cross sections computed by Westcott to calculate values of the thermal utilization f and the thermal migration area L in the usual way. A base value of V was calculated from Westcott values, assuming the neutron flux spectrum in the moderator to be Maxwellian at 2(PC. This value was then modified for flux hardening effects >y comparing the ratios of the 1/v activations (Cu and Mn) and the U-235 activations at various locations. Values of the fast fission factor < were obtained by comparing the fission product activities of natural and depleted uranium foils according to the technique described by Futch . The neutron age r was measured to indium resonance from isolated fuel assemblies in DjO. Corrections were calculated for the age to thermal energy and for lattice effects. 

A. Z. kranz, Measurements of Thermal Utilization, Resonance Escape Probability, and Fast Fission Factor of Water Moderated Slightly Enriched Uranium Lattices, WAPD-134 (Sept. 1955). 

The fast fission factor e, the material buckling B, the quantity Ap/AB were measured in critical assemblies of each fuel mixture. The thermal-neutron diffusion area L wa.8 calculated from thermal-neutron cross sections. The delayed-neutron fraction was determined from the delayed-neutron fractions for U and measured by Keepin and the "U-to- U fission ratio measured in the critical assemblies. 

Xhe constant ri In 2.2 1 Is the reproduction factor and is defined as the number of neutrons produced by Jbgrmal fission for each neutron absorbed In the fuel (exclusive of those captured in resonances) The constant is the fast fission factor and It accounts for fast fission In fast fission... 

A compilation of fast neutron cross sections from Reference 3 which are useful in calculating the fast fission factor is given in Table 2,3 2.2.1. 

Xhe fast fission factor following Spinrad s model is defined as the number of neutrons mskixig their first collision w 1th the moderators external to the fuel element per neutron arising from thermal fission. The... 

The calculation of the fast-fission factor e proceeds directly from results given in Table 10.5. In order to obtain we need simply sum the number of neutrons supplied to the slowing-down process from each fast-fission generation. These are the terms indicated in the last column. Thus we obtain... 

Answer Before the velocity of the newly-created fast neutrons is decreased to any great extent, they will cause a few fast fissions in the more abundant 1)238 nuclei, and also a negligible number in the relatively scarce 1) 35 nuclei. This effect is called the "fast fission" factor and it multiplies the number of neutrons created by thermal fissions each generation by a value slightly in excess of unity (about 1.03). 

Althou U-238 is not fissionable to slow neutrons, it will fission with a fast neutron, such as we get from fission. This is much like hitting the nucleus harder - so hard, in fact, that it splits. This is a fairly small effect, adding only about 3 to our neutrons, so now we have 1035 of 139> or about lii-35t of what we started with. This number, I.03 or 1035 is called the fast fission factor, and is denoted by the Greek letter epsilion, . So now we have fission neutrons from all fission. 

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