Fission products effective cross section

After Xe, the fission product with highest cross section and appreciable yield is Sm, whose cross section for 2200 m/s neutrons is 41,000 b and whose effective cross section in a typical water-cooled reactor is over 70,000 b. In addition, many of the fission-product nuclides that produce Sm by neutron capture or radioactive decay and several of the nuclides produced from Sm by successive neutron captures have high cross sections. Figure 2.17 illustrates the generic relationship between Sm and the principal nuclides that lead to it or are produced from it. 

The cross section of low-cross-section fission products, Op, has a single constant value independent of the fissile nuclide from which the fission products were produced and independent of the flux time to which the fission products were exposed. This assumption is an oversimplification, because the yield of individual fission products is different from each fissile nuclide, and individual fission products with hi er cross sections tend to be converted to those of lower cross section as irradiation progresses. Walker [Wl] has given tables from which may be determined the effective cross sections of fission products from U, U, Pu, and Pu as a function of the flux and flux time to which the fission products have been exposed. 

Thermal flux time, n/kb Effective cross section Op, in bams, of fission-product pairs from ... 

As inadiation progresses, the effective cross section of fission products from each fuel nuclide decreases. This decrease is partially offset by greater production of fission products from plutonium, which have a higher cross section than those from U. The constant value of Op = 80 given in Table 3.13 takes these two effects approximately into account. 

Also shown in Table 8.2 are the effective thermal cross sections for the individual nuclides, calculated for the neutron spectrum of a typical PWR and including the contributions from resonance absorption. The cross sections are multiplied by the atoms per fission-product pair to obtain the effective cross sections per fission-product pair listed in Table 8.2. Although the total effective cross section of 89.2 b/fission-product pair is calculated for the mixture of radionuclides existing 150 days after fuel discharge, it is a good approximation for the effective... 

Using effective cross-sections and yield values the amounts and radioactivities in Figure 21.7 and Table 21.2 were calculated. It is seen that Xe, Zr, Mo, Nd, Cs, and Ru, which are the elements formed in largest amounts in thermal fission (both by mole percent and by weight), constitute about 70% of the fission product weight after a cooling time of 10 y. 

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 cross-section curves excitation functions and the curves of the differential products response functions. In measuring R( and assuming relation (4.6), one can measure effective cross sections ([Pg.2625]

Fission product Half-life Decay constant (s ) Effective yield (atoms per fission) Thermal absorption cross section (b)... 

The value of 80 b given for fission-product pairs is an approximate, constant value to be used independent of the fuel from which the fission products are formed and independent of the flux time to vidiich the fission products are exposed after formation. For the present PWR, the effect of these variables on the cross sections of fission-product pairs, evaluated by extrapolation of Walker s [Wl] tables, is as follows ... 

NucUde Half-life (S = stable) Atoms per fission-product pair Effective thermal cross sections, b Neutron absorption, bams per fission-product pair... 

This increase can be determined by measuring either the cesium or xenon isotopic ratios. These results combined with the low flux fission yields can then be used to calculate the cross section of Xe135. The ideal experiment would be one in which the flux remains constant during the entire irradiation so that the amount of Xe136 present at any time is not dependent on flux variations. This approach has been used by Fickel and Tomlinson 28), who arrived at a value of 3.2 X 106 barns (1 barn = 10-24 cm2) for the neutron cross section of Xe136. Cross sections of other fission products have been measured 12, 63, 76) although the conditions in these experiments were such that the effect of flux variations could not be evaluated. 

A proper analysis of the tine dependent behavior of.a reactor operating on thermal neutrons must take into account the important effects on its criticality, reactivity, and stability which arise from such factors as fission i products of high thermal-neutron capture cross-section, depletion, temperature, average neutron lifetime in the reactor, flux level, and reactor period. As has been seen in the requirements placed on the.reactor, considerable excess reactivity must be built into the active core before start-up. The control rods must keep the reactivity below the critical value before and during start-up. 

Some 6% of all products from fission in uranium are in the form of the iodine-135 isotope. This is radioactive and decays with a characteristic half-life of 6.7 h into the xenon-135 isotope. Xenon-135 is remarkable for having the largest known absorption cross-section, a resonance effect close to thermal... 

The above applies to the stable fission products. There may be, however, numerous radioactive fission products (in addition to the Xe ) which have large cross sections. Their effect has been estimated by Miss Way on the basis of a statistics of the cross sections and she finds that those with an odd number of neutrons are most dangerous. All elements may give substantial contributions, the hfetime of which is an hour or more. Only those with a lifetime of more than a day have been surveyed to date and Miss Way estimates that they may cause a loss in efficiency of 3 % if the purification is carried out once a day. If this is done it is imlikely that the corrosion products will contribute much to the poisoning. 

VII.25-VII.27], and efforts have been made to validate computational methods using data selected from these compendiums [VII.27-VII.29]. The measured isotopic data that are available for validation are limited. Of farther concern is the fact that the database of fission product measurements is a small subset of the actinide measnrements. In addition, the cross-section data for fission product nuclides have had much less scrutiny over broad energy ranges than most actinides of importance in INF. Fission prodncts can provide 20-30% of the negative reactivity from bumup, yet the uncertainties in their cross-section data and isotopic predictions reduce their effectiveness in safety assessments with bnmnp credit. 

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. 

The first two-hour lecture session starts with a discussion of the fission process, toe production of neutrons during fission, the role of neutrons in inducing fission. Cross sections are introduced as measures of reaction probabilities, including capture-to-fission ratios. This leads into a discussion of fast fissioning systems, followed by neutron slowing down, moderator effects, and the criticality of solutions. Mixtures of finely divided fissile material, such as foil, wire, or powders, in moderating media are dtocussed as pseudo-solutions. 

Fission product nuclides may also be transformed by neutron capture the probability of an n,Y reaction increases with increasing halflife and with increasing neutron absorption cross section of the relevant nuclide. Therefore, in some cases the n,y reaction competes with the P decay and is the limiting parameter for the concentration of the relevant radionuclide in the fuel. The most important example of such a neutron capture conversion is Xe with a physical halflife of 9.17 hours and a reactor neutron absorption cross section a of 6.25 10 cm at a neutron flux, cp, of relevant energy distribution in the fuel at full-power operation of the plant of 5 10 cm s, its effective halflife is reduced according to... 

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