Debye Waller Factors and Lamb Factors in the Scattering of X-rays, -rays and Thermal Neutrons

The paper reviews the applicability of Debye-Waller factors and of Lamb factors to the non-resonant and resonant elastic scattering of X-rays, gamma-rays and thermal neutrons, emphasizing temporal aspects in the interactions. The influence of static disorder upon elastic scattering, in particular upon resonance scattering, is likewise treated. The scattering of X-rays, y-rays and thermal neutrons from atoms or nuclei bound in crystals can proceed via elastic and inelastic channels. Elastic scattering, in particular, diminishes in the presence of thermal inelastic scattering. By consequence, a reduction factor f appears in the amplitude for elastic scattering, which in limiting cases reduces to either the well-known Debye-Waller factor or to the Lamb factor. The presence of static disorder leads to an additional modification of the elastic scattered radiation, causing in particular a reduction of the scattering amplitudes in Bragg reflections. The various static and dynamic reduction factors will be discussed for non-resonant and for resonant scattering of X-rays, y-rays and thermal neutrons. cases of fast and of slow collisions, depending on whether the lifetime z of the intermediate (resonance) state is short or long compared to typical vibration times zTib of the scattering particle in the lattice. Following Trammel [I], we arrive at expressions applying to fast and slow collisions, by putting in equation (1) t 4 0 and t co, respectively : Fast Collisions, z 4 qib, Slow collisions, z b zvib,