Characteristic energy, neutron interaction

Atoms in a crystal are not at rest. They execute small displacements about their equilibrium positions. The theory of crystal dynamics describes the crystal as a set of coupled harmonic oscillators. Atomic motions are considered a superposition of the normal modes of the crystal, each of which has a characteristic frequency a(q) related to the wave vector of the propagating mode, q, through dispersion relationships. Neutron interaction with crystals proceeds via two possible processes phonon creation or phonon annihilation with, respectively, a simultaneous loss or gain of neutron energy. The scattering function S Q,ai) involves the product of two delta functions. The first guarantees the energy conservation of the neutron phonon system and the other that of the wave vector. Because of the translational symmetry, these processes can occur only if the neutron momentum transfer, Q, is such that... 

The (n, y) interaction normally occurs in a thermal neutron flux, while the (n, p) and (n, a) reactions are induced with fast neutrons. Many of these products are radioactive and decay with the production of jS and y radiation. Figure 1 is the decay scheme for Au, showing the main y-ray energy at 0.4118 MeV. y-Rays are readily identified by their characteristic energies and so the activity of the product radionuclide is measured using y-ray spectrometry in multielement neutron activation analysis. Figure 2 shows schematically how the induced activity of the sample changes as it is irradiated for a time, and counted for a time, /measj after a decay period, /a-The y-ray intensity of the radionuclide, Ap, measured over time, /measj is quantified from the accumulated spectrum and expressed as counts per second (cps). 

A number of other spectroscopies provide information that is related to molecular structure, such as coordination symmetry, electronic splitting, and/or the nature and number of chemical functional groups in the species. This information can be used to develop models for the molecular structure of the system under study, and ultimately to determine the forces acting on the atoms in a molecule for any arbitrary displacement of the nuclei. According to the energy of the particles used for excitation (photons, electrons, neutrons, etc.), different parts of a molecule will interact, and different structural information will be obtained. Depending on the relaxation process, each method has a characteristic time scale over which the structural information is averaged. Especially for NMR, the relaxation rate may often be slower than the rate constant of a reaction under study. 

Atomic nuclei consist of nucleons (protons and neutrons). The total number of nucleons is denoted as A and is called the mass number. The nucleus charge, z, is equal to the number of protons. The nucleus bond energy comprises a combination of the nuclear interaction (attraction) energy of the nucleons and the Coulomb interaction (repulsion) energy of the protons. The characteristic feature of the nuclear forces appears to be short-range action nucleons interact only when they are in a very close contact at a distance of about 10 13 cm. Another important feature is the incompressibility of the nucleons and, due to this, the volume of the nucleus grows in proportion to the mass number and its radius, in proportion to Al,i. 

NAA is the most common form of activation analysis. The activation reaction is induced by the interaction of a neutron with the nucleus of an analyte element. Depending on the energy of the incident neutron and the reaction cross sections of the target elements, different types of reactions can take place, leading to activation products as described in O Sect. 30.2. This reaction is commonly followed by the measurement of a nuclide-characteristic de-excitation step (radioactive decay). It is this characteristic gamma-ray decay that is commonly used in the detection and determination of the element of interest. 

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