An expression for the total, elastic and inelastic, differential cross section for scattering of thermal neutrons by a rigid polyatomic molecule is derived. In summing over the final rotational states of the molecule the change in energy of the neutron is assumed negligibly small compared to the neutron's initial energy. The validity of this approximation is discussed. The rigidity of the molecule is then relaxed and the expression obtained for the cross section amended to take account of the vibrational motion of the nuclei. It is shown that the elastic scattering from a vibrating molecule is equivalent to that from a set of uncoupled anisotropic oscillators placed at the mean nuclear sites. Detailed results are given for spherical top molecules of the type YX4. Good agreement is found with the experimental pattern of carbon tetrafluoride but not with that of methane.
The angular correlation of photons from the two-gamma decay of positrons in all sodium halides and all alkali chlorides has been measured. The data yields the momentum distribution of the two gamma rays which is also the momentum distribution of the annihilating electron-positron pairs. It is seen that the positive ion has very little influence on the momentum distribution in comparison with the negative ion. These distributions in momentum are compared with the distributions calculated from various models of electron and positron wave functions in the crystal. For fluorides and chlorides the electron-positron wavefunction products which yield fits to the experimental data resemble Hartree-Fock free-ion electron wave functions. Both the wave-function products and the free-ion wave functions yield density distributions which are similar to the electron densities obtained by x-ray measurements. This conclusion makes improbable a model of single-particle wave functions describing both the electrons and the positron tightly bound to the negative ion.
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