Quantum Mechanical Calculation of Mössbauer Transmission

Abstract

A quantum mechanical calculation of the time-dependent Mössbauer transmission has been performed neglecting solid-state effects. The source considered consists of nuclei which decay via a two-photon cascade, the second of which is emitted without recoil and is subject to resonant absorption by a foil whose resonance may be shifted due to a small relative velocity between source and absorber. The transmission is obtained when the transmitted recoiless photon is measured in coincidence with the first photon of the cascade. The result is in agreement with that obtained by considering the absorber as a classical dielectric slab capable of absorption and dispersion. The initial condition has been investigated in detail by considering the full cascade. In this manner, one sees that the usual simple assumption that the nucleus is in the first excited state immediately after the emission of the first photon, gives the correct boundary condition.