Isotope incoherence

Coherent and isotopic-incoherent scattering involve no spin-flip, whereas spin incoherent scattering (i.e., for hydrogenated molecules) inverts the neutron spin with a probability of 2/3. Since spin-polarized neutrons are used in the neutron spin-echo technique, the polarization of the neutron beam, after spin-incoherent scattering woifld be reversed and three times less intense. 

In most cases, samples are a mixture of isotopes j with different scattering length bj and it is assumed that they are randomly distributed over the sample. Such random distribution of different isotopes produces incoherent cross-section. In analogy with isotope incoherence, spin incoherence is also observed. For nuclei with spin I l, the interaction depends on the orientation between neutron and nuclear spins scattering lengths and b for parallel and untiparallel spin, respectively, are different and the orientations of spins are randomly distributed in the nuclei even if they are the same kinds of nuclei. Then, incoherent and coherent atomic cross-sections are given by... 

The scattering length for an individual nucleus (i.e. the amplitude of the neutron wave which it scatters) is not the same for all nuclei of a particular element due to two factors. These are spin incoherence and isotopic incoherence. 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

A primary hydration number of 6 for Fe + in aqueous (or D2O) solution has been indicated by neutron diffraction with isotopic substitution (NDIS), XRD, 16,1017 EXAFS, and for Fe " " by NDIS and EXAFS. Fe—O bond distances in aqueous solution have been determined, since 1984, for Fe(H20)/+ by EXAFS and neutron diffraction, for ternary Fe " "-aqua-anion species by XRD (in sulfate and in chloride media, and in bromide media ), for Fe(H20)g by neutron diffraction, and for ternary Fe -aqua-anion species. The NDIS studies hint at the second solvation shell in D2O solution high energy-resolution incoherent quasi-elastic neutron scattering (IQENS) can give some idea of the half-lives of water-protons in the secondary hydration shell of ions such as Fe aq. This is believed to be less than 5 X I0 s, whereas t>5x10 s for the binding time of protons in the primary hydration shell. X-Ray absorption spectroscopy (XAS—EXAFS and XANES) has been used... 

Another important observation is that, in addition to the isotope-induced change in the band width, there is a clear isotope-induced narrowing of the EDC s [16], as can be noticed by the broader black shadowed area for 160 sample (upper panels), with respect to the 180 sample (lower panels). The width changes become appreciable only in the incoherent part of the dispersion. Again the changes are maximum near the antinodal region. Panel c shows an explicit comparison of the EDC s where the EDC narrowing of the 180 sample can be clearly noted. 

D deuteron exchange NMR and 87Rb SLR time measurements in (DR ADA-32) PGs show that the 0-H---0 dipoles are not completely frozen out at low temperatures but show dynamic features characteristic of incoherent tunnelling. RADP and D-RADP are thus quantum glasses. A comparison of W 1 SLR rates show that minima occur at 90 K for D-RADP-42, whereas at 25 K for RADP-50, thus demonstrating the tremendous isotope effect in the intra-H-bond dynamics. 

Table 2 Bound scattering lengths, i>(fm) and cross section for selected isotopes and for selected naturally occurring isotopic mixtures of the elements u(hams, 1 bam = 100 fm ). Z, atomic number A, mass number I, spin of the nuclear groimd state i>coh> bine, coherent and incoherent scattering lengths ffa, ffeCh, coherent and incoherent cross sections ffa, absorption cross section for 2.2 km s neutrons ...

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). 

The amplitude of the neutron wave scattered by a nucleus of a given element varies from one isotope to another and also between the two spin states of the neutron-nucleus system. In addition to coherent scattering (leading to diffraction effects) this variation of scattered amplitude from atom to atom of the same species produces incoherent scattering in which there is no systematic interference between scattered... 

Both small angle X-ray (SAXS) cind neutron scattering (SANS) are established techniques and their experimental application is similar. However, limitations on sample size, thickness and containment are much more restricted with X-rays because of absorption of radiation. One problem which can arise with neutrons is the subtraction of the flat incoherent contribution which can be quite large in the case of hydrogenous materials. This disadvantage can be partially offset by the possibility of using isotopic substitution. SANS is particularly powerful because the penetrating power of neutrons makes it possible to study material microstructure in the wet state. Instrumentally, both SAXS and SANS require a source of radiation, collimation system, sample containment and a detection system. 

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