Effect of Brownian Motion on the Mössbauer Line Shape

A general theoretical expression for the resonance-absorption cross section of $\gamma$ rays by particles in liquids is worked out. The treatment takes into account the general solution of the Langevin equation, thereby revealing the important role played by the characteristic time of the liquid. While the line shape predicted by Singwi and Sjölander takes care of atomic motion, it is inadequate for the motion of particles in liquids. When composite particles are used, the nuclear lifetimes of the Mössbauer isotopes may be compared with the characteristic time of the liquid. It is shown that, under certain conditions, narrowing of the Singwi-Sjölander line can be considerable.