Abstract
A multiple-scattering calculation of the neutron refractive index is performed by an extension of the Fermi-Huygens technique. The extension involves projecting the problem into a one-dimensional walk by integrating out the transverse coordinate in a semi-infinite medium and then partially summing parts of the walk to infinite order. The square of the refractive index is given by -1=-(4πρb/)/[1+ (4πρ/) da easin(a)h(a)], where is the incident wave propagation vector, b the nuclear scattering length, ρ the number density of nuclei (ρ≡1/, say), and h(a)=g(a)-1, where g(a) is the pair distribution function. The results parallel those obtained by constitutive equation methods, and offer a physical picture of local-field effects. When the mean scattering length vanishes (total incoherence), correlated multiple scattering yields -1∼(b/( ln[(]. Thus, the refractive index is exceedingly close to unity unless b is large (a resonance) or →0 (ultracold neutrons). The presence of the logarithmic term indicates that randomness in the scattering field apparently reduces the effective dimension.
- Received 1 March 1985
DOI:https://doi.org/10.1103/PhysRevB.32.6347
©1985 American Physical Society