Neutron Reaction Cross Sections

Consider a monoenergetic parallel beam of neutrons hitting a thin target of thickness t (Fig. 4.26). The number of reactions per second, R, taking place in 

Since the nuclear radius is approximately 10 to 10 m, 1 b is approximately equal to the cross-sectional area of a nucleus. 

Neutron cross sections are defined separately for each type of reaction and isotope. For the reactions discussed in Sec. 4.9.1, one defines, for example, 

The total cross section—i.e., the total probability that a reaction of any type will take place—is equal to the sum of all the cr s  

Neutron cross sections depend strongly on the energy of the neutron as well as on the atomic weight and atomic number of the target nucleus. 

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We are limited in this modeling process by the accuracy with which measurements can be made and by the accuracy of the fission yields and neutron reaction cross sections which are used to interpret the results. As an example consider the Nd- Nd fission product pair, which has been used as an indicator of thermal neutron fluence because the capture cross section for the former is large and for the latter is small. The thermal cross section for l53Nd has recently been listed as 325 ( 10) barns (20), and more recently as 266 barns (11). Using the 325-barn value we deduce an age of about 2 to 27T billion years from neodymium to uranium ratios in the Oklo reactors, while an age of about 1.8 billion years is obtained using the 266-barn figure. 

Table 2.6 Examples of neutron reaction cross sections...

Takiue, M. and Ishikawa, H. 1978. Thermal neutron reaction cross section measurements for fourteen nuclides with a liquid scintillation spectrometer. Nucl Instrum Methods 148, 157-161. 

The energies of particles shown in parentheses correspond to the zero neutron energy. Standards of evaluation procedure for the neutron reactions cross sections have been done by Carlson (2004). By now there is suggested number of values of capture cross section of B-n reactions for neutrons of different energies and targets of different B isotopic compositions. 

For energies below the barrier, the reaction cross section falls very rapidly. For energies equal to the barrier height, the reaction cross section is remarkably independent of atomic weight in fact, the cross section for most elements lie between 0.3 and 0.5 barn, (see Fig. 3). This cross section is much smaller than the neutron reaction cross section, which for the heavier elements is about 2.5 bam. Above the barrier, the cross section may be calculated with surprising accuracy by elementary classical methods. The result is ... 

Thermal neutron absorption cross section. Simply designated cross section, it represents the ease with which a given nuclide can absorb a thermal neutron (energy less than or equal to 0.025 eV) and become a different nuclide. The cross section is given here in units of barns (1 barn = 10 cm ). If the mode of reaction is other than ( ,y), it is so indicated. 

The technologically most important isotope, Pu, has been produced in large quantities since 1944 from natural or partially enriched uranium in production reactors. This isotope is characterized by a high fission reaction cross section and is useful for fission weapons, as trigger for thermonuclear weapons, and as fuel for breeder reactors. A large future source of plutonium may be from fast-neutron breeder reactors. 

The amount of boron required for BNCT can be estimated using the neutron capture cross sections, which are atomic properties, and thus pertain to the number, and not the mass, of the atoms present. Conservative estimates for successful therapy result in boron concentrations of around 20 ppm in tumor tissue, to at least match the dose liberated by neutron capture reactions in the other elements of biological tissue. This would correspond to around 109 boron-10 atoms per cell, assuming that one cell corresponds to 10-9 g. 

The most sensitive method for determining trace amounts of technetium is the neutron activation . The Tc sample is irradiated by slow neutrons. The radioactive isotope Tc with a half-life of 15.8 s is formed by the reaction Tcfn, y) Tc, the neutron capture cross section of which is comparatively large (20 bams), so that it is possible to determine amounts < 2x 10 " g of Tc. However, the method is not widely used since the half-life of Tc is very short. Moreover, this method is only convenient when a reactor or a neutron source is available. 

Silvery-white lustrous metal face-centered cubic crystal structure ductile ferromagnetic density 8.908 g/cm at 20°C hardness 3.8 Mohs melts at 1,455°C vaporizes at 2,730°C electrical resistivity 6.97 microhm-cm at 20°C total emissivity 0.045, 0.060 and 0.190 erg/s.cm2 at 25, 100 and 1,000°C, respectively modulus of elasticity (tension) 206.0x10 MPa, modulus of elasticity (shear) 73.6x10 MPa Poisson s ratio 0.30 thermal neutron cross section (for neutron velocity of 2,200 m/s) absorption 4.5 barns, reaction cross section 17.5 barns insoluble in water dissolves in dilute nitric acid shghtly soluble in dilute HCl and H2SO4 insoluble in ammonia solution. Thermochemical Properties... 

A thin sample of gold was irradiated in a thermal neutrons flux of 10 neutrons cm sec- for 25.6 hrs. In the reaction the nuclide Au is produced with a half-life of 64 hours. If the thermal neutron absorption cross section is 98 barns, the specific activity of the sample is ... 

The total cross section is proportional to the size of the target nucleus and the size of the projectile nucleus. Since the wavelength of the projectile, X, goes to infinity as the projectile energy goes to zero, the cross sections for neutrons at low energies can be very large. The above discussion is based upon semiclassical mechanics. We need to indicate how the problem would look if we used quantum mechanics to treat it. In quantum mechanics, we can write a similar expression for the total reaction cross section ... 

Notice the de Broglie wavelength of thermal neutrons is much larger than the size of a typical nucleus (r 1-10 x 10-15 m) and similar to the size of a typical atom. Reaction cross sections for thermal neutrons exceed the geometrical area of the nucleus. 

The total neutron interaction cross section, atotal( ), is the sum of the various reaction cross sections ... 

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