Scattering length

Abstract: The primary interactions of low-energy x-rays within condensed matter, viz. photoabsorption and coherent scattering, have been described for photon energies outside the absorption threshold regions by using atomic scattering factors. The atomic scattering factors may be accurately determined from the atomic photoabsorption cross sections using modified Kramers-Kronig dispersion relations. From a synthesis of the currently available experimental data and recent theoretical calculations for photoabsorption, the angle-independent, forward-scattering components of the atomic scattering factors have been thus semiempirically determined and tabulated here for 92 elements and for the region 50-30,000 eV. Atomic scattering factors for all angles of coherent scattering and at the higher photon energies are obtained from these tabulated forward-scattering values by adding a simple angle-dependent form-factor correction. The incoherent scattering contributions that become significant for the light elements at the higher photon energies are similarly determined. The basic x-ray interaction relations that are used in applied x-ray physics are presented here in terms of the atomic scattering factors. The bulk optical constants are also related to the atomic scattering factors. These atomic and optical relations are applied to the detailed calculation of the reflectivity characteristics of a series of practical x-ray mirror, multilayer, and crystal monochromators. Comparisons of the results of this semiempirical, "atomic-like" description of x-ray interactions for the low-energy region with those of experiment and ab initio theory are presented.

Abstract: The application of thermal neutron scattering to the study of the structure and dynamics of condensed matter requires a knowledge of the scattering lengths and the corresponding scattering and absorption cross sections of the elements. Ln some cases, values for the individual isotopes are needed as well. This information is required to obtain an absolute normalization ofthe scatteredneutron distributions, tocalculate unit-cell structure factors in neutron crystallography, and to correct for effects such as absorption, self-shielding, extinction, multiple scattering, incoherent scattering, and detector efficiency.

Abstract: The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

Abstract: It has long been predicted that the scattering of ultracold atoms can be altered significantly through a so-called ‘Feshbach resonance’. Two such resonances have now been observed in optically trapped Bose–Einstein condensates of sodium atoms by varying an external magnetic field. They gave rise to enhanced inelastic processes and a dispersive variation of the scattering length by a factor of over ten. These resonances open new possibilities for the study and manipulation of Bose–Einstein condensates.