Intricate partial waves in nuclear scattering

This article is meant as an encomium of the life-span endeavor of Jacques Raynal to relate nuclear scattering density matrices with numerical methods. The mathematical investigations he made involved intricate hypergeometric coupling algebras and transformations. He was among the first to appreciate the general importance of these studies. His efforts over 60 years are most praiseworthy and, for them, Jacques has gained much respect.

Nuclear Scattering

This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.