Cross section for capture

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. 

Production in Heavy Water Moderator. A small quantity of tritium is produced through neutron capture by deuterium in the heavy water used as moderator in the reactors. The thermal neutron capture cross section for deuterium is extremely small (about 6 x 10 consequendy the... 

Boric acid [B(OH)3] is employed in primary coolant systems as a soluble, core reactivity controlling agent (moderator). It has a high capture cross-section for neutrons and is typically present to the extent of perhaps 300 to 1,000 ppm (down from perhaps 500 to 2,500 ppm 25 years ago), depending on nuclear reactor plant design and the equilibrium concentration reached with lithium hydroxide. However, boric acid may be present to a maximum extent of 1,200 ppm product in hot power nuclear operations. 

Niobium (also known as columbium) is a soft, ductile, refractory metal with good strength retenti on at high temperature, and a low capture cross-section for thermal neutrons. Itis readily attacked by oxygen and other elements above 200°C. CVD is used to produce coatings or free standing shapes. The properties of niobium are summarized in Table 6.8. 

Table 5. Values of the single-electron capture cross-sections for the and states (in 10" cm ).

Boron nitride, in view of its unique properties, namely absence of electrical conductivity, oxidation resistance, optical transparency, and high neutron capture cross-section for special applications, offers advantages over other ceramics. Thus, for the... 

Fig. 6.3. Product aN of abundance and neutron capture cross-section for s-only nuclides in the Solar System. The main and weak s-process components are shown by the heavy and light curves respectively. Units are mb per 106 Si atoms. After Kappeler, Beer and Wisshak (1989). Copyright by IOP Publishing Ltd. Courtesy Franz Kappeler.

The emission intensity of the 4F3/2- 4/n/2 transition (laser transition) does not change appreciably for a range of x from 0.02 to 0.5. This is probably due to a balancing of the total capture cross section for the pump light with the reducing quantum efficiency of AFV1 state. Figure 32 shows the variation of threshold with concentration. Data were collected at room temperature. Curve A is for an FT-524 flash lamp with a half-width of approximately 100 /xsec, whereas curve B is for an FT-91 flash lamp with a half-width of approximately 10 psec in a small ellipse. 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

It appears that electron transfer to C5 l n=4 and 5 levels are dominant on the covered energy range. Total cross sections for both levels are of the same order around 10 15 cm2 below 10 keV/u, they decrease down to 10 19 cm2 at 500 keV/u. Capture cross sections for C5+n=3 and 6 levels present a typical bell-shape with a maximum of the order of 10-16 cm2 at about 50 keV/u. 

Figure 3 is an illustration of some calculated [H0M76] thermal correction factors for ground-state neutron-capture cross sections for a number of isotopes near the line of stability. From this figure it is clear that these correction factors can be significant. For the benefit of anyone who might like to attack this problem. Table I summarizes some of what we consider to be the most important quantities to better refine as input to the s-process. 

Figure 3 Correction factors, f, for the neutron-capture cross section for various Isotopes due to the thermal population of excited states at stellar temperatures (from [H0W76]). Isotopes with f > 10% are labeled.

On a personal note, the mathematical description of this series of neutron captures called the s process was solved by the writer in his Ph.D. thesis, and was published in 1961. This provided me the opportunity to assist in small ways with the development of programs of the measurement of neutron-capture cross sections for the s process, first at Oak Ridge and later at Karlsruhe. These were great privileges in a fortunate life. 

Fig. 8.6. The expected temperature dependence of the capture cross-section for multiphonon trapping at defects with different phonon coupling strength (Henry and Lang 1977).

Essentially, the absorption of neutrons occurs in two distinct stages. Fast neutrons are slowed down by elastic and inelastic scattering processes with nuclei, particularly light nuclei like carbon and hydrogen. The slowed-down neutrons are then captured, as the capture cross-section for low-energy neutrons is high for most elements. 

If the element being determined or a constituent of the sample matrix material has a high capture cross section for thermal or resonance neutrons, possible errors due to self-shielding cannot be ignored. 

Heavy-water reactors utilize heavy water (D2O) as a moderator. They can be operated with natural uranium, since the capture cross-section for the thermal neutrons, necessary for controlling nuclear chain reactions, is very low for D2O compared with H2O. Enrichment of U is therefore not necessary. The high price of heavy water (only present as 0.015% in natural water) is, however, a disadvantage. The resulting higher investment costs... 

---