Line Shape of the Mössbauer Line in the Presence of Ultrasonic Vibrations with Decaying Amplitudes

Abstract

A M\"ossbauer source that executes ultrasonic vibrations with decaying amplitudes has a center-line fraction that increases with time; the center line of the emitted radiation can be even narrower than half the natural width. The $n\mathrm{th}$ band fraction has its maximum when ${k}^{2}〈{x}^{2}〉\ensuremath{\approx}{n}^{2}$; sidebands can be either narrowed or widened; narrowing can take place with large initial amplitudes that decrease or small initial amplitudes that increase. Random fluctuations in ultrasonic amplitudes might explain the narrow side bands in Cranshaw and Reivari's ultrasonic experiment as a superposition of widened and narrowed lines.