Mössbauer Absorption Spectra under Continuous Localized Diffusion

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Abstract
The problem of the Mössbauer lineshape broadening due to the diffusion of the Mössbauer atom in an arbitrary drift potential is reduced to a solution of the Schrödinger equation of the quantum mechanics. The spectral shape can be obtained in explicit form provided an exact solution of the quantum problem is known. By means of this method the diffusion analogues of the quantum oscillator and the Coulomb atom are considered and analytical expressions for the respective spectra are derived. The temperature dependence of the intensity of the unbroadened spectral component is shown to be related with the form of the arbitrary “diffusional” potential by a simple law. The temperature curves of the mean‐square Mössbauer atom displacement resulting from this relation show the nontrivial behaviour at each value of the wave vector of absorbed γ‐quanta even in the simplest case of anharmonical oscillator. Under certain choice of the parameters the temperature trend of these curves may simulate the phase transitions.