Size dependence of the Mِssbauer effect in one-dimension

Employing a model of coupled harmonic oscillators we analyze the nature of recoilless emission in the Mِssbauer effect for a finite sized 1D lattice. We demonstrate explicitly that under certain assumptions, recoilless probability first attains a maximum for a certain lattice size and then decreases with increasing lattice size. Further, we derive a scaling relation for this variation. Our treatment may have relevance to the recoilless probability in finite clusters such as nanocrystals and nanowires.