Explicitly solvable model of Mössbauer scattering

An explicitly solvable model of Mössbauer scattering of $\gamma$ rays by a nucleus bound in a harmonic-oscillator potential is constructed. The probability of elastic scattering, which is proportional to the Debye–Waller factor, is calculated in the framework of the explicitly solvable scattering problem. It is assumed that the rms deviation $\Delta x$ of the nucleus and the photon wave numberk satisfy $k\Delta x\ll E_\gamma /E_\phi$, where $E_\gamma$ and $E_\phi$ are typical energy levels of the photon and the oscillator states.