Neutron-Nucleus Interactions

Another crucial feature of the NCS method is the small value of the characteristic time Tgcatt of the neutron-nucleus interaction, the so-called "scattering time". It follows from the theory of NCS that each scattering angle 9 corresponds to a specific momentum transfer (from the neutron to the struck nucleus, e.g. a proton) and to an associated value of TSCatt- According to Sears [Sears 1984] and Watson [Watson 1996], the scattering time may be defined by... 

Neutron-nucleus interaction. A neutron interacts with a nucleus via nuclear and magnetic forces. For the nuclear part, since nuclear interactions are very short range compared to the(thermal) neutron wavelength, it can be shown that the interaction potential between a neutron located at r and a nucleus i located at r can be written as... 

Fundamentals. Neutrons can interact with matter in several ways. Depending on the neutron-nucleus interaction, they can be scattered coherently or incoherently and both processes can occur elastically or inelastically. For structural studies in electrochemical systems, diffraction, i.e. elastic coherent scattering, is of particular interest. Fundamentals of these modes of interaction, including spectroscopic aspects relevant for mobility studies, have been reviewed [989]. 

What then is the structural feature most characteristic of a proton conductor system It is generally believed that a proton is transferred through a solid in one of two distinct ways by a vehicular mechanism, whereby the proton rides on a carrier molecule of type NH4 or HjO ion, or by a Grotthuss mechanism, in which the proton jumps from a donor to a suitably placed acceptor molecule (typically, from H30 to H2O, or from H2O to OH ). How then is such a process sensed in a conventional diffraction experiment The nature of the diffraction method is such that we obtain a time- and space-average of the unit-cell content within the characteristic coherence length of the diffraction process (typically, hundreds of Angstroms), and over the duration of the experiment (days to weeks). This follows from the extremely short photon-electron and neutron-nucleus interaction times ( 10 s), which are significantly shorter than the characteristic time of the fastest of the dynamical processes in the structure ( 10 s for the vibration of a covalently bonded atom). It follows then that some type of structural... 

So far, the interaction of neutrons with (collections of) point-like scatterers, with 6 - functionlike neutron-nucleus interaction potential, has been considered. However, provided that the magnitude of the momentum transfer, Q = IQIdistance between nuclei), i.e., Q optical phenomena, like total reflection, diffraction by a slit, etc., can be explained for neutron beams. 

Where V(r) is the Fermi pseudo potential describing neutron-nucleus interaction during scattering, M the neutron mass and r the vector separation of neutron and nucleus. Considering one nucleus then the scattering amplitude from that nucleus is ... 

If this equation is compared to (2.2), we arrive at one of the basic probability functions for neutron-nucleus interactions ... 

The influence of these several factors on neutron-nucleus interactions is well displayed in the case of neutron scattering from hydrogen nuclei bound in molecules. This process has been studied in detail and experimental measurements of the scattering cross section of hydrogen in the water molecule show that there is a substantial change in the cross section... 

E represents the probability of neutron nucleus interaction per centimeter of neutron travel. Mean free path, mfp, is the inverse of E,... 

C. Nuclear Coefficient As the core temperature increases, the average neutron energy increases. With increasing neutron energy, the microscopic absorption cross section (excluding resonances) and the scattering cross section decrease. For most materials the absorption cross section varies as l/v for neutron-nucleus interaction energies below that of the first resonance. 

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