Influence of the finite lifetime of hydrogen jump phase on the quasi-elastic neutron scattering by hydrogen in metals†

A complex jump diffusion model assuming a finite lifetime for hydrogen both in the jump and in the residence phases is developed as a straightforward extension of the known Rowe et al. theory 1], and also of the Multi-Sublattice Jump Diffusion Model 2]. The residence-residence, jump-jump, residence-jump and vice versa transitions of hydrogen are explicitly included in the model. This approach is a method for calculating the double differential, d²σ/dΩdω, and hence the differential, dσ/dΩ, cross section for quasi-elastic neutron scattering from metal hydrides, MeH_x. In terms of the model we have calculated the diffusion coefficient, which reveals explicitly the contributions of the residence and jump phases.