Resonance Absorption of Nuclear Gamma Rays and the Dynamics of Atomic Motions

Abstract

The theory of resonance absorption of nuclear $\gamma$ rays is generalized for an arbitrary system of interacting particles by expressing the relevant transition probability in terms of a space-time self-correlation function; and thus relating the resonance line shape to the incoherent differential scattering cross section for slow neutrons. Two limiting cases: (i) a gas and (ii) a solid have been considered. Discussion regarding the justification of the use of a classical self-diffusion function for a liquid is given and expressions for the broadening of the resonance line due to diffusive motions of the atoms of the interacting system are derived. It is suggested how Mössbauer-type experiment could be used to give information regarding the diffusive motions of atoms in a solid and also, under more favorable circumstances, in a liquid.