Scattering cross section isotopes

Beryllium has a high x-ray permeabiUty approximately seventeen times greater than that of aluminum. Natural beryUium contains 100% of the Be isotope. The principal isotopes and respective half-life are Be, 0.4 s Be, 53 d Be, 10 5 Be, stable Be, 2.5 x 10 yr. Beryllium can serve as a neutron source through either the (Oi,n) or (n,2n) reactions. Beryllium has alow (9 x 10 ° m°) absorption cross-section and a high (6 x 10 ° m°) scatter cross-section for thermal neutrons making it useful as a moderator and reflector in nuclear reactors (qv). Such appHcation has been limited, however, because of gas-producing reactions and the reactivity of beryUium toward high temperature water. 

RBS is capable of distinguishing the isotopes of heavier elements, however the more common use of RBS is for the determination of stoichiometric ratios and composition as a function of depth. RBS was used in another study of plasma grown oxide films on GaAs to determine the ratio of 0 to Ga and As (31). Based on the well known ion scattering cross-sections, a ratio approaching 1.5 was found for films greater than lOOoX thick. The composition of the oxide inferred from this result is a mixture of Ga 0. and As203<... 

Fig. 2. Scattering cross sections for pt with a hydrogen isotope nuclei from Refs. [12,18], showing the Ramsauer-Townsend minimum at around 10 eV for pt+p pt(F) +t cross sections plotted include both elastic and spin exchange reactions, where pt(0) is the singlet state and pt( 1) is the triplet state...

Equation (1) has several consequences. The intensity depends directly on the scattering cross section. The scattering cross sections are element- and isotope-dependent, as shown in Table I. The amplitude of motion is larger for light atoms, and so, because hydrogen has the largest cross section and the smallest mass of any element, it dominates the scattering. 

Total Scattering Cross Sections (5) of Elements (Isotopes) Relevant to Catalysis... 

Element (isotope) Total scattering cross section/barn (10... 

If b+ and b- are of different sign [e.g., H, V) there is a small coherent cross section and a large incoherent cross section. For this reason vanadium is used as a ccilibrant in incoherent scattering cross-section measurements (see below) and as a sample container (for polycrystaUine materials) for many of the experiments described below so that unwanted peaks are not introduced into the diffraction pattern. On the other hand, if an element has one isotope of zero nuclear spin in large abundance the scattering is almost entirely coherent [e.g., 0, Fe). 

X-rays are scattered by electron density - the more electrons an atom has, the more intensely it scatters. Neutrons, however, are scattered by a parameter of the atomic nucleus, which is different for different isotopes (but shows no general trend with nuclear mass). Hydrogen and deuterium have very different (but large) neutron scattering cross-sections and therefore neutron diffraction, which requires access to an atomic reactor, is used where location of hydrogen atoms is critical. 

Neutrons are sensitive not only to isotopic variation but to the breakdown of all spatial correlation. This includes the correlation of nuclear spins, through the neutron s own spin = 1/2. Without this extra incoherence, the scattering cross sections of chlorine would be... 

From these definitions, it is clear that bCO and blnC° can be changed merely by modifying the relative concentration of the various isotopes. This fact is of great practical importance in neutron experiments (isotopic substitution). The coherent and incoherent scattering cross-section are defined by... 

The position of the peak is found to depend strongly on the isotope (HoD) substitution. In fact, for a-MnDg Qj the low-energy peak appears at 1.6 meV. Because of a certain H contamination of the deuterated sample in experiments [124] and the large incoherent neutron scattering cross-section of H, the peaks at both 1.6 meV and 6.4 meV are present in the INS spectra of a-MnDo Q5. As an example of the data. 

Figure 11. Inelastic neutron scattering powder spectra of four isotopomers of BA at 5 K recorded with the TFXA spectrometer at ISIS (Rutherford Appleton Laboratories). The spectra are normalized for the mass of the samples and the total incident neutron flux. The differences in intensity are due to the differences in scattering cross section of the isotopes. (Adapted from Horsewill et al. [156].)...

For instance, neutron scattering experiments performed by Bates, Wignall, and Koehler22 with an isotopic mixture of polybutadiene at temperature T = 296 K showed the existence of this effect (Oak Ridge, USA, 1985). The mixture was made of equal volumes of deuterated and non-deuterated polybutadiene (Nw = 4600 and Nw/N = 1.10 for the deuterated sample, iVw = 4200 and Nw/N = 1.12 for the undeuterated one). From the intensity I(q) and the value KA of the instrument constant, they deduced the scattering cross-section per unit volume [see (7.2.54)]... 

Fig.l Neutron scattering cross-sections for some elements and isotopes. The larger the area of the circle, the larger the cross-section... 

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