Neutrons per fission

FIGURE 17.24 A self-sustaining chain reaction, in which neutrons are the chain carriers, takes place when induced fission produces more than one neutron per fission event. These newly produced neutrons can stimulate fission in increasingly greater numbers of other nuclei. 

Uranium-235 releases an average of 2.5 neutrons per fission, whereas plutonium-239 releases an average of 2.7 neutrons per fission. Which of these elements might you therefore expect to have the smaller critical mass ... 

Of the fast neutrons produced in fission, some of them will be moderated to thermal energies and will induce other fission reactions while others will be lost. The ratio of the number of neutrons in the next generation to that in the previous generation is called the multiplication factor k. If the value of k is less than 1, then the reactor is subcritical and the fission process is not self-sustaining. If the value of k is greater than 1, then the number of fissions will accelerate with time and the reactor is supercritical. The goal of reactor operation is to maintain the system in a critical state with k exactly equal to 1. The extreme upper limit for the multiplication factor would correspond to the mean number of neutrons per fission ( 2.5 for 235U(n,f)) if each neutron produces a secondary fission. 

Fig. 8. Spontaneous fission activity in hot spring water at the Cheleken peninsula after concentration by ion exchange and precipitation methods. Shown is the measured neutron multiplicity distribution (dots) compared with measured distributions for 238U, 246Cm and 252Cf spontaneous fission and calculated distributions for sets of v and a2, the average number of neutrons per fission and its variance. Reproduced from G.N. Flerov et al. [48], Fig. 1, copyright (2002), with permission from Springer-Verlag.

Since the neutron proton ratio for relatively stable nuclei having atomic numbers in the 90 s is greater than the ratio for those having atomic numbers in the 3G , 40 s, or 50 s, the fission of uranium yields products whicli would be too neutron rich for stability unless extra neutrons were emitted also. Some neutrons are indeed ejected (an average of about 2.5 neutrons per fission) thus, in a typical fission ... 

Mass, amu Effective MeV Fraction of decays Cross section, b Neutrons per fission... 

With very-low-energy neutrons, uranium of mass number 235 emits an average of two to three neutrons per fission event. Because more neutrons are released than absorbed, fission can result in a multiplication of successive fission events. This multipfication can reach very high numbers in about 10 to 10 seconds, resulting in the release of a great amount of energy in that time. This was the basis of the development of nuclear weapons. Soon after the discovery of fission it had been calculated that if a sufficient... 

Neutrons. The number of neutrons per fission caused by thermal neutrons is between two and three. This number increases linearly with the kinetic energy of the neutron inducing the fission. The average energy of a neutron emitted in fission is about 2 MeV. More than 99 percent of the neutrons are emitted at the time of fission and are called prompt neutrons. A very small fraction is emitted as delayed neutrons. Delayed neutrons are very important for the control of nuclear reactors. 

Some spontaneously fissioning radionuclides, such as produce 3-4 neutrons per fission with an energy spectrum of average energy of about 2-3 MeV. The neutron generation rate depends on the amount of which emits (2-3) X 10 neutrons s g ... 

The number of neutrons emerging from a collision is automatically determined when the collision is elastic scatter, absorption, (n, n ), ( , 2n), or an (n, 3n) reaction. At a fission, however, the number of secondaries is a function of the incident neutron energy. This function is described in the data library by the mean number of neutrons per fission, v, which is presented in the data library in a similar manner to cross section, except that, generally, fewer points are used and interpolation is linear for v against energy. The number of secondary neutrons released in a fission is an integral random variable whose expectation is equal to v. 

The number of neutrons per fission is calculated from vSf(/)/Zf(/) since T is not given explicitly for each group. 

The Stacey and Usachev-Gandini versions of GPT are only two of many other possible versions. A third version is illustrated in Section V,B,2. Actually, each mechanism used to restore criticality (physically or mathematically) has a corresponding version of GPT, The criticality reset mechanism of Stacey s version is the eigenvalue k-reset. It is equivalent 47) to an adjustment of the average number of neutrons per fission. The criticality reset mechanism of the a-reset. It is equivalent to an adjustment of the uniform concentration of a jv absorber throughout the system. 

IPPE and the Radiological Centre of the Medical Academy (Russian Federation). For such a reactor the problem was to provide maximum emission of neutrons from the reflector surface, because the fraction of emitted neutrons per fission is an important parameter for reactor type selection. 

The above experiments and calculations refer only to the resonance absorption of 28. There are, however, two other known effects on the resonance neutrons the resonance absorption of 25 and the fission of 25, induced by resonance neutrons. The first of these can easily be taken into account by adding the a and (3 of 25 to the corresponding quantities for 28. The 25 fission process, on the other hand, increases the number of neutrons by i/ — 1 instead of decreasing it by 1 as the resonance absorption does u 2.35 is the number of secondary neutrons per fission). Neglecting second order effects, one should add therefore to f a2sdE/E... 

In these and the above equations, the a are cross sections per imit volume, the a in (8) is scattering cross section, the average loss in r per collision. The are used because the material may contain different types of atoms. The (Ta is the thermal absorption cross section r(r) the resonance absorption cross section per unit volume. The = qef is the multiplication constant divided by the resonance escape probability. The product of thermal utilization / and (Ta is the effective cross section of uranium per unit volume, i.e., its cross section per unit volume multiplied by the thermal neutron density in it and divided by the average thermal neutron density. One can write, therefore, (Tu for f(Ta- If one multiplies this with rj the result is the same as crfU where fission cross section for thermal neutrons per unit volume, p the number of fast neutrons per fission. As a result, the third term in (7) can be written also as e is the multiplication by fast effect)... 

The chemical separation of U from thorium is readily accomplished with high purity. The fissionable iso-60 tope U will support a chain reaction, and has many desirable qualities. In particular, U gives a relatively high average neutron yield per fission, the value as presently known being about 2.37-2.4 neutrons per fission (average). 

It has been found in this connection that the 17 of or, in other words, the number of neutrons emitted per fission of a atom is about 2.37, thus providing a net 35 increase of 1.37 neutrons per fission. If all of these neutrons are absorbed in fertile material such as, fer example, thorium atoms, 1.37 atoms are produced for each atom consumed or destroyed by the chain reaction. However, it will be noted that the loss of as 0 much as 15 percent of the 2.37 neutrons by escape from the system or by parasitic absorption of other materials than the thorium results in a net increase of zero thus preventing the breeding of thermally fissionable material. An enumeration of the losses follows ... 

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