The line-shape of the gamma-emission spectrum for a harmonic crystal in the presence of sound wave



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It has been shown that a closed form for the scattering operator of a quantum oscillator subject to a transient classical force can be found.(1) This fact is exploited to calculate the gamma emission spectrum from a harmonic crystal for which the interval between consecutive emissions is on the average long compared to the emission time, a situation obtained in the Mossbauer effect. This approach is based upon the properties of the so-called coherent states of the harmonic oscillator. The fact that these states describe a coherent wave motion in space-time is used to calculate the line-shape of gamma emission by a harmonic crystal in presence of sound wave. The first chapter consists of a study of the coherent state of the quantum oscillator whose properties are used to establish the scattering operator. In the second chapter, the line-shape of gamma emission from a gas as well as from a crystal will be discussed in some detail. In the third chapter, previous results are applied to calculate the line-shape of gamma emission from a harmonic crystal in thermal equilibrium as well as in the presence of sound wave. Results of this calculation are discussed and compared with previous work published in the literature. In the fourth chapter, our results are discussed in same detail and suggestions are made of critical experiments to be performed. Finally, we suggest how the present theory can be extended to study other phenomena.