Neutron energy gain

Fig. 6.9 Temperature-dependent neutron energy gain spectrum of dihydrogen in Ceo (BT4, NIST). Reproduced from [23] with permission from the American Institute of Physics.

Fig. 11.13 INS spectra (IN6, ILL) obtained in neutron energy gain of the low energy region of (a) Qo at 300K, (b) Cao dimers in the quenched phase of RbCeo. (c) linear chains in pressure polymerized and (d) two-dimensional polymer sheets in pressure polymerized Cso (the material is a mixture of rhombohedral and tetragonal networks). Reproduced from [39] with permission from Gordon and Breach.

Fig. 26.13 shows the INS spectra (neutron-energy gain side) of a-MnDo 05 at a number of temperatures. The observed isotope effect on the splitting J of the vibrational ground states is consistent with the estimates (/h = 5 meV, = 1.5 meV) based on the theoretical model [127], if the actual parameters for a-MnHjc(D ) are used [124]. 

The temperature dependences of the integrated intensities of the 6.4 meV and 1.6 meV peaks are well described in terms of the Boltzmann thermal population factors of the split ground-state levels, both for the neutron-energy gain and neutron-energy loss. On the other hand, the observed temperature dependences of the peak intensities differ qualitatively from those expected for phonons or harmonic oscillators [124]. 

Figure 26.13 The difference between the INS spectra (neutron-energy gain side) of a-MnD 5 and a-Mn measured on the IN6 spectrometer (Institute Laue-Langevin). The spectra corresponding to different temperatures are shifted along the vertical axis. The a-MnDoos sample is contaminated with about 0.5 at.% H which manifests itself by the peak at 6.4 meV[126].

The third term is the probability for a neutron to gain energy such that... 

Fig. 10. The time-of-flight distributions of neutrons scattered from Nylon-6 at 65°. The abscissa corresponds to the number of 28 /4- ec, time-of-flight channels. A scale at the top of the figures shows the energy gain in mev while the arrows give the energies of the observed peaks in cm h The elastic peak occurs at Channel 165...

In INS a beam of monochromatic neutrons is fired at the sample under the study. The magnetic interaction between the neutrons (spin 1/2 particles) and the sample leads to scattering of the neutrons, with energy gain and loss, inducing transitions within the sample with the selection rules A5 = 0, 1 and AMs = 0, 1. Thus, INS can give direct information not only on ZES interactions (as in EPR) but also inter-multiplet splittings,... 

This cross section is for neutrons that are scattered into a solid angle of d/2 that lies in the direction given by the final wavevector, k. In the experiment the incident neutron energy is fixed and the initial and final states of the sample are also fixed, even if not known. The total energy of the system is conserved and that which is lost by the neutron is gained by the sample, so ... 

FIGURE 4 Tbne-of-flight neutron spectra in liquid and crystal phases of CH,CC1,. Energy-gain scales in millielectron volts and cmT1 are also shown. 

In addition to an energy weighting, each reaction type is assigned an importance Wj such that Wj is zero when neutrons are neither gained nor lost, unity when one neutron is either lost or gained, two if two neutrons are gained... 

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... 

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