Neutrons incoherent cross section

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 ...

For hydrocarbons in zeolites, only incoherent scattering has to be considered because of the large incoherent cross section of hydrogen. The neutron intensity scattered follows the incoherent scattering law 5i c(Q, (o), which is related to the self-motion of protons, where AQ and Aw denote the neutron momentum transfer and the neutron energy transfer, respectively. 

Despite the great incoherent cross-section of the H-atom, elastic coherent neutron scattering experiments may be used at a lower resolution to detect the presence of clusters of H2O molecules. The method used is that of small-angle neutron scattering, often labeled by its acronym SANS . In such an experiment, the scattered intensity of a sample is recorded as a fnnction of the angle 6 between the wave vectors of the scattered and initial waves or, equivalently, as a function of the amplitude Q of the wave vector difference Q = k -ic2 0f the scattered beam defined by and incident beam defined by ki (the wave vector defines the direction of propagation of a wave, as seen in eq. (3.6)). As can be seen in Figure 11.1, these quantities are related by the equation ... 

However, because of the nuclear spin incoherence of " Cl, the total incoherent cross section of chlorine is oinc (Cl) = 5.30 bam. Spin incoherence is particularly important for an understanding of the neutron scattering cross section of hydrogen nuclei. In = 1/2. 

In principle all the rotational transitions of dihydrogen are observable by INS spectroscopy but some transitions are rather weak since the incoherent neutron scattering cross section used generally in this book is inapplicable ( 2.1). This derives from the strict nuclear spin correlation found in dihydrogen, Transitions within the separate para- or orthohydrogen manifolds are controlled by the coherent cross section of hydrogen, 1.76 bam, and these transitions are too weak to be observed in its INS spectmm. 

Spin-flip transitions, between the manifolds, are controlled by the incoherent cross section of hydrogen, 80.3 bam, and are enabled by spin exchange with the neutron, / = 1/2. Thus, for the J(l -0) transition... 

To obtain further insight into the meaning of the inelastic neutron spectra, it is necessary to have specific theoretical models with which to compare the experimental results. In the harmonic approximation it is possible to calculate the incoherent inelastic neutron spectrum i.e., the neutron scattering cross section for the absorption or emission of a specific number of phonons can be obtained with the exact formulation of Zemach and Glauber.481 A full multiphonon inelastic spectrum can be evaluated by use of Fourier transform techniques.482 The availability of the normal-mode analysis for the BPTI136 has made possible detailed one-phonon calculations483 for this system the one-phonon spectrum arises from transitions between adjacent vibrational levels and is the dominant contribution to the scattering at low frequencies for typical experimental conditions.483 The calculated one-phonon neutron en-... 

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. 

We can use the result of such an experiment jointly with the result of another experiment performed with the same sample but without polarizing the neutrons. In fact, the contribution (6.4.41) is proportional to the incoherent cross-section given by (6.3.6). Thus, using two measurements it is possible by subtraction to obtain the coherent cross-section which is defined by (6.4.35) and which is the quantity of interest. 

Think of a possible reason why the incoherent neutron scattering cross sections of carbon and oxygen are both practically equal to zero, and confirm it by consulting a table of relevant nuclear data. 

Neutron wavelength Macroscopic number density Microscopic particle density operator Nucleus cross-section Nucleus coherent cross-section Nucleus incoherent cross-section... 

If the isotope has no spin, then < b > = < b as < b> = b and there is no incoherent scattering for neutrons. Only coherent scattering contains information on the stmcture of the sample. The incoherent cross section contains no information on interference effects and forms an isotropic (flat) background which must be subtracted off in SANS stmctural investigations. While most of the atoms encountered in neutron scattering from polymers are mainly coherent scatterers (e.g., carbon, oxygen, deuterium), there is one important exception [8,22,23]. In the case of hydrogen (H )... 

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